










  



















 





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THE OFFICIAL GUIDE FOR GMAT® REVIEW, 12TH EDITION










 


 
 


 







 













         







































































































































































































































































 





















 



 
 



 







 


 









 















 



























 

 

 




 







 
















 

















 










 

 

 

 



 
 
 



 
 




 
 






 
 
 

















 


 
 


 
 
 





 




 
 
 
 
 












 






 
 

 













 
 



 
 











 





 






 















 













  
  

  






 













 

 

 




 


  

  


 






 







 



































 












 


















 

















 




 







 

 
 

 

 
 
 
 
  

 









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 

 
 
 



































 
 





































 


































































 






































 


 

 








 


 





















         
 













 



 





  













 






































 












 

















 













 















 

 








 

 

 










 
















 










 







 
























 




 









 


 

 


 


 




 
 








  
 









 










 




 








 









 


 


 










 




 






 








 









 






 







 







 







 












 









 



















 





 


































 









































































































































































 














 





























































































 
















 



























































 
















 



















 




















 




































 



























 


 









 




















































 




























 










 






























































 































 


























 
















 


















































 























 


















































 









 
































 











 





















































 




























 
































 






 






























 

































 

























 































 














 























 









































 





 




















 































 












































 



















 



































 




















































 























 





 























  


 
  
 

  
 
 
  
 
 
  
 
 
  
 
 
  
 
 
  
 
 
  
 


  
 
 
  
 
 
  
 
 
 

 
 
 

 
 
  
 
 
  
 
 
  
 
 
  
 
 
 
 
 
 
 
 
 


 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 
 
 
 
 
 
 
 
 


 
 
 



 

















































































 






 






 

 





 





















 

  
















 



  






 


 











































 








 

  

  



 






 
 
 

























































 




 

 

 







 

 



 



 


 

 




 
 



 



 


 







 
 







 
 

  
   
  



 


 
 





 

 































 




 

 



 














 


 

 










  





 

 
 



















 




 





 












 



 











 
  













 


 





 

 





 
 
   








 





















 


 
















 


















 








 








 












 
 


 

 

 
 


 



















  



 















 

 
  
  

 






 






































 
 
   
 
 
 
 
 
 


 








 










 

 






















 
 

















 
 


 

 
 




 



 









 

 
 



 






 

 

 














 

 
 


 


 




 








 













 

 



 





 



 






 










 




 

 




 

 











 





 



 






 

 











 





 

 





 





 

 




 

 

 









 




 













 

 















  




 





 
 

 

  



 







 

 


 

 











 


 







 



 

 






 

 

 







 
 


 





 



 


 









 


 

If 5x < 1, then
=
< 1 since
x
= 5 ; SUFFICIENT.
 

x+2<2
add 2 to both sides
5x + 2 < 52
<1


because a < b implies 5a < 5b
divide both sides by 52 = 25;
 

 










 





 





 


 

 






 









 



 





 







 





















 




 If D is the distance Paula drove then
 

 
 





 


 








 


 



D > 200 and
>
=
so t >
and
t may or may not be less than 3; NOT sufficient.
<
<

 <
<

 

 








 


 






 





  






 

 











  

 


 

 














 





 


 




 
 
 
 

 


 



 
 






 




 







 


 

 










 





 







 

 






 





 







 



 



 









 








 







 





 


 






 

 


 

 











 































 




 




 




 

 

 





 



  
 
   
  

  
 


 

  






 

 




 














 




 





 



























 


  



 



 



 


 



























 
 

 


 



 







  



 


 

 





























 
 



 







 








 

 



 
















 

 


































 






 

 










































 









 













 



  









 


 


 





  




 


 


 

  


 











































 





 

 


 






  









 






  


 

 


 


 




 



 




 



 






  




















 

 



















 




 


 


 



































 

 



  



















 




 







 

 

 
 


 







 





























 


 




 




 






 
 






















  





 



  




  



 



 



 








 


 


 
 


 


 
 







































  







 






























 
























 




 


 



  



 








 





















 

 





















  


 



 




 
























  





 

  
 



 

 


 






















  






 
 




  


 


 






















  






 




 
 

 


 
































  

 
 

 

 
 


 































 


  










 


 




























  







 


 


 















 



  



 








  










 


 































 


  





 


 


 



































 

  


 

 


 

















 


  
 




 

 
 


  


 

 


 


























 

 

 




  

 


 






















 



 

  





 

 


 


















 





 




 



  

 

 


 























 









  



 
 



 


 





















  





 


  

 



 

 


 



























 

 
 

  
 
 

 


 




























 




 
 


  

 



 




 




 




















 















 






  






 





 


 
 



































 




 










  









 







 
 


























 


 








  





















  



















  



 
 































 
 

















 



  



 































 
 























 























 



 



 

 






















 





 
 


























  



  

 















 








 






















 













 




















  





 
























 







 
 
































 




 









  






  






 




 





 
 

























 
  


 





























 
 
































 




  



 


 













 




 





 



 



























 


 



 












 


 









 
 



















 






 













 


 





































 
 
































 

 










  






 






 






  



































 


















 











 
 













 


 




















 


 

 

  














 



  


 




 








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






















 
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








  
  










 

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





















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

















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 























 

 





 


   







 


 

   



 



 



 


  
  

 


    
   
 

 




  





  
 
   


  

 
  
 
       
       
       


    
  
 
     

     
     
     




      









 



  




       
  
 




 



















     





 




       



   


  
 


 
 

 

 

























  

      



 
 


 
  





 

 



 



 



    
 
              
             




          




 
 
 
     
 
    
 







  


     

       












 



 
 






 



  




  
 

 
  
 


 







        



 
      







       
 


  






 

 







  






 





  

  
   
  


 


 

 









 





 

 


 




 























    





    


 



 



 


         
         





























 

 


 



   







 





 




      
 

   
   
  
 
 










  
      
      
         

 



 



 







   

 







 




  






 





 



 


 

 ({  }) =
{  }
= 




   
  


   



 

   
            
   
{   } 
          (    ) =
= 


 


 
 
 


  

     
   
  




=
{} 
= 
{ } 
  
    
   

 




=
{}
= 
{   } 

 
 




             


 




 





 

 
  









   
 

 

 



 


















 




  
  
 
   
   
   

  
 












 







 

 








  
  







  



  


 


 







 
 





 




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
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
  

         
        
     
  
 

 
 



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




 



  



 


 

 


 

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










 


 









 
 
 

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 
 







 

 


 


 


 




 





  



 







 

 






     
 

    
   








 


    

 



 
  




 
  

 
  
   
 
  
 










 

 



 

 

  



 



 

 
 

 


 


   




 


     


 

    


 

 

 

 
  

 
   
 
      




 




 
 


 
 






























   











 



 

  
 
  
 

 











     

  










 

 




 
  
  




 

  







  
 
 

 








 
          









  




  




 




 

 

  
 


  







  
 
 



 







 







   























 

 





 

 














 
 


   

 


  












  










 









   
  
  













     


 
   







 












 




 








 
 













 






    

 


 
 



  



   


    

  
 
    
 
   

 

  










 
 






 





 

   


     
  
 

 

















 


 















 





 




       




















 


























  












 








 



 
 






 















 
 











 




 






 


  
    
  


 



   








  
 
  

 


  
 

 
  







 





  
 
  
  



     
   
  




 





 







 


 
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
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




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 






 






  
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
  



 
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 





 
  
 

 
  

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 





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 
 

 




 










 


















 


















 

 
 


 















 











  

















 


























































 



 
 

 
 
 


 






 













 
 

























  








 






 









 
 
 
 





















 



 

 




 




























































































 














 







 













 
 







 
















 
















 




























 







 




 

 

 

 

































 

 



 



 
 




 


 


 

 

 








 



 


 

 

 

 




 


  























+ 





 

 






+ 









 





 




















 



 


 






















 












 













 




















 




 

 

 




 






  























 









    






 



 


 


 














 


 


 


 





 
 
  
   





 


 

 

 
 























 




 


 























 










 




 








 

 
 
 









 








 










 



 

 

 

 





























 









 




 


















 








 


 

 

 















 












 

 











   

 



 



 












 


























 








 




 







 






 

 

 

 


 




 
























 


 







 



 

 

 


 






















 



 




 






 







 


  

 


  



 

 






  

  






 























 




 





















 







 

 

 

 


 

















 












   =  





















  

  
  



 



  











 




 


 






 






 








 

 

 


  















 














 


































  

  

  

  
(  )( )
(  )( )(  ) 



 









 








 





 









 











 


















 



















 


















 


















 





 













 
 








 













 















 







 



 
 



















 




 

 

 

 

 

 

 












 



 

 

 

 


 

















        


     
 





 












 







 





 

 
 












  













 
















 


 

 

 




 















  










 















 


 

 








 

   












 



 











 







 








 












 





  



  



  


 


 

   


  






 




























 





 

























 



+







 + 

 +


 +

 + + 
 










 




 






 




 











 



 

 


 








 

 
















 

































 













 














  





  

 


   














 
















 














 





























    



 


 






















 


 







 





 

















 

 




















     
  











 

 
 



 


 











 

 

 















 


 







 






















 













 



 





















 














 








 

 

 



 








 

















 














 


 















 







 


 + 


 




 


 + 





 






 

 



 







 







 




 























 





 

 

 

 




 









 



  

  

 

 


 



 








 

 

























 





 

 

 

 


 
 (  + )
















 

























 









 






 



 



 








 









 +


 + 


 + 


 



 

 

 

 

 
   


 




+


 + 


  

 

















 
















 


 










 



















 

 

 

















 





 

 






 


 




   
 














 


   


 

 






 
 

 

 

  

  

  


  














 










 

 
















 



   





 






 


















 

  
  




 





































 














  




















 

















 

 











 












 











 










  


 
























 



 















  

    


 

 








  
  





 







  
















 











 





 








 

















  
  


  
 
 


 




 





 


















 


 














  
  

  

 
  

 

 










 












 


 











 





 


























 






  

  




 









 


  
  
  












 

  

 








 

















 





 
 



 
 
 
  
  
 
 
 



 




 
 

 
 











 



 
 
  

  
 
  
 
 
 


 
 
 








 










 










 
 








 




































 

 

   
 

















 


 


 




  


  



















 






 





 

 

  

 







 

 




 

  
  




 








 

















 

 















 






 

 

 















 









   


 




 





 
 




 
 




 
 





 
 





















 






 
 





























 




  
  
 










 


  
  




  
  








 

 

 

  
 

 

 

  
 

 

 

  
 

 

 

  
 

 

 

  
 

 

 

  
 

 

 

  
 

 

 

  
 

 

 

  
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 
 

 

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 









 

 

 


















 
 


 

 
























   

  









   

  





   

   



   

  




   

  














  +    +  =  +  




 








 



 
















 







 


(   ) +  (   ) + (   ) + (   )

  +   +   +  





 


 





()() = ()(  )( )










 


























 

 










 











 


 



















 




 




 













 





 



 







 





 
 





 

 










   
 
 


 



 












 

 












 


 
 








 

























 
 
 







 







 



 


 

 















    



  

 


   



  



 
 
 






























 





 




 
 





 

 

 






 

 

 

 
 

  





  

 





 

 
 
 
 

 



 

 

 

 

 






 













 

 


()()

 ( )()






 



 
 

  

 























 







    






 
 






 

 




 
 













 














 


 


 



 


 





















 




 


  


+
+ 
 
 























 











 

 

 

 












 +  
  
 


 




 

 

 



 

 















 










 




 
 














 



  +  




 

  














 












 


 











 







 






 

 











 




 

 

 



















  

 







 





    





 
 

 
 
 

 



()( ) + ()( )  ()( ) + ()()
 




()(  + )



   + 

  




 
















 















 


 

 






   











 

















 

 


 
 
 
  
   



 

 

 

 


 



  

 

 
















 


 
 








 




 


 


 

 

 



 















 



 






 


 



 









 
 



 















 



 
 



 

 








 



 






 
 






 
 




 




 

 

 


 

 


 



 
 


 


 

 


 









  


 









 




 



















            
  
 



  
 
     

  
 
 

    



 
 








 
























      


 






 

 












 



















 

 




 








 


 
 



















 


 

 

 




 





 

 



  





  

 
  
 
 














 

 


  

 






















 














 


 
 
  
 
 



  
 
 



 


 



 
























 


 


 

 











 


 




   

 

 

 








 






  


   (  )  (  )
 

    
(
)( ) (

   

 




 






)(  )

 
 
 



 
























 
 

 
 
 


































 

 




 















 
 
 

























 
 
 
 




 

 

 

 





 




 



 

 
















 




 
 


 





 

 

 



 










 



 



 





 


 

 

 

 










 



 

 




 

 


















 






 
 






















 









 

 

 

 



 
 
 =  = 
 
 



 =
  
 


   





 
 





       
  


 




 





  






   




 







 
















 




 
 
 




 

 































 

 

 

 






 









 


 
 
 






























fi




















 


















 

 

 



 


 

















 
 
 
 






 



 
   =  













 

  
 

  


 




      













 

 



  










 



 


 


 




 




 
 
   






   



 

 
 

 
 

  





 


 




  




 
 


















 









 

 



 












 
        









     


   





 



 

 












 






(  )( )

(  )( )( )



 

 

 

 

 

 

 
 







  

  

  

  



( )( )
( )( )( )

 















 






 
 






























 

 







  


 
 

 



 

 

 

 





 
 












 































 





























 
 

















 
 

 

 


  
 
 

























 



 
 























 







 




 



 


 
 










 


 


 
 



 
 













 




 




 


 



















 

 
 


 




 


 
 






 












 














 



 

 










 

 












 


 
      



 







 








  



 



 







 
 
















 






 



 

 

 

 














 


 























 









 


















 
 


 
 




 

 

















 
     
  +  

    










 






 






















 








 





 + ( + ) + ( +  ) + ( +  ) + ( + )





  


 
 













 

 

 + 

 




 
 



















 




















 

















 
 















 





  



 


 





 



 

 


 
 






 































   
 







   

 

 





 
  














  


 






 
  

 
 


 

 









 


   







  



  



  

 

 
 


 

   














 


 

 


 
 










 
 


















 

 



 
 







 
















 









 
 








 




 



 









  



  



  


 


 

 
 














 






 
 




      


 























fi

 
   


   






 










  

  
 


 













 













 







 













 

 


 






 


 
 

 

    
 
 










 
 

 


























 


 






 













 





 
 



 

 
 



 




 






















 




 








 


 




                 



 







  

 

  
 
 

 



























 


 























 
  

 


   




 


 







 










 
 






















      

 

  


  

 
 

















 
 

  

 

  


















  




 


 





     




























 





    

 
  
  
   



 
  
 

 

   
   


   


 




 
 













 
 

























 














  




  

    


    










  



 

 

 


 


 



  



















 
  = 


  

 
= 
   
 

  =  



 

 
 



































 





    



 


 













   








  
 
 
 







 








   

       
 
    




  







 



 
  
 

    
  


 
 




 




 









 


 























 
 






 
 
































 





   

     
 

 
     
  







 

 



  

( )( ) 
( )( )() 




 
 






 


















 
 








()( )
()()(  )


 



 

 




 



 
 


 

 












 
 

 


 
























 

 

























 
   
      
   
 




 











 



 




 









 









 
 


















 
 

 
 




 
 

()()( ) 
   =



 






























 

 
 












 

 

 
 



 

 
 








 

 

 
 


 











 



  







 



 




   



 


 



 














 


  















  



 


  


 



 


 
 

 
 
 
 
 





















 






 

 




 








   
 
      
 
      


 
 



 
 




    
 




   +   
   

   

 


 

 



     



 

     

 


 


 


 




 
 + 
 + 

 
 




 













 



 + 


 


 






 




 + 










 

 
       

  



 

 






 




 





 


 
   
  (  )


         

 
 + (




  + 



  + 
 
)



 



 



  

  

 





               
 



 



  

  

 

 

















 








 


 


 










 


 








 

 
 

 
















 




 




 



 


  



  

 

 
 














 
 





 

 

 


 


















 



















 
 
 (  + )



























 
  









 

 



 


 

 


 
























 
 

















 


 






 





 



 

 

 

 

 





 

 

 




 

 



 


 
 
 


     
 
 
 









  



























 




 



 


 


 


 


  

 


  


 

 
 



 







   
  

 (  +  )  + 

 

 


 



 



 
  




 
 







 











 


 

  

 
 



















 




 


  


  



 
 


 









 

 

 






 











 











 

 



 



 
 








 


 











 



 
 











 

 





 


 


 




 


 

 



 



 




























 
 
 
 
 
 

 











 





 





  










 
 
  


 
 
 
  
 

  









 




  

 




















 







 



 

 


 
 
 



   






 








 













 















 






  


   








  

 

   


 

  
  







 
 =   =


 ()( ) ()( )



 


 










 
 






















 

















 



















 










 
 


 








 


 





 



 









  




















 

 















 
 















 

 
  



  




 





 




 







 


 











 

 




 
  




 
 
























 

 





    
 

      
 

 
 

  
  

  












 
 













 

 

    
 
















 


















 









  


 


















 

  


    

  










 






















 


 


 
 










 







 

 


    

   

 
 
 








 

















 

 
 

















 





  











 


 

 








 






 
  
  



















 
















 


 
 















 






 








































 















 





 



















 


















 
 





 

 

 

 





 

  

  






  


 
 









 



















 
 




 




 















 

  
  
  
 

 











   
 


 


 



 

  
 








 
 
 
 















 




 



 
 
 
 
















 













 









 
 + (  ) +  
=
=  


 
 


 


 
 

 








 
 














 


  
    
                  



 











 

 




 
 











 

 

 









 





 
 







 

 

 

 

 
 

  
 










  






 






 









 







 




 


  
  
  
















 
































 
 



 

 

 

 

 




 
 
  
  











 

  
 




 




 


  
 


 
 

  





  

  

 
 

 
 






 




 




 
 

 
 


 
 
 
 
 
 













 



 

 



  

 


 

 
 








 
 
    




   

    










   
  

 

 






 












  
 


 



 
 
 

 
 






 
 
 
 










 
 
 













 

 

 
 


 










 
 

































 








 

 






 

 












 










 
 

     
 


  
   
  


 


 





   

  
  
 
  
 

 
  
  







 














 
 

 

   
 








  


 






 




 






 










 



 

 
 
 


 



 
 
 




=  
 (  + )  + 


 
 
 















  
















 
 










































 




















  

 







 

 













    





 







   



 
















 




 
 

  
  















  














 




              




  
   




 














 
 






 











 

 

 






 











 










 
















 




 










 






 

 


 


 

  


 








 







 




 


 





 











 











 




    
       


 












 
 



 














 



 





 
 




 
 




 
 




















 


 








 

 



 















 


 























 
 


 

 


 

  










 


 




 


  
  


  


  
  
  
 

































 

  



 

 


  
  













 




 

 

  
 


 


































 





 






 
 
 
 





















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 


 





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 



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 




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 














































 
































































 




 








 

 
 

 










































 



 






















 











 


 


















 




 












 














 




 





















  
 





















 




 




 
 




 







 


 







 
















 


  







 





 









 










 









 
 






 




 










 
  

 







 
 







 





 




 







 








 

































 














 








 


  
 
  

 









 






 


 

















 


 









 






 









 




 









  

 


 








 




 





 














 










 






 








 

 

 
 


















 









 











  

 







 
















 






 













 











 





 










 





 















 


 





 







 



 





 
 






 



 
 















 







 









 




 












 






 

       



 




 








 






 




 









 




 















 







 























 














 






 






 



 


 







 








 








 


 











 







 







 









 






 






 






 


 




 












 











 











  



 










 


 




 





 



 




 







 




 













 








 

 











 






 







 






 



















 









 







 









 
   

 













 







 







 














 




 





 















 






 
   






  
 





 





 
 











 














 







 



 


 


 










 





 










 



 








 

 


 









 










 











 








 

 
 







   




 

 






 







  







 


 


 











  

 

  
 






 







 


     

 
 














       




 
  



 




 





 




 
   

     


 









  




 




 


    

 


 

 



 









 







 




 


 



 

 

 





 

 

 





 

 

 






 

 

 




 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 

 





 

 







 

 







 

 







 

 







 

 







 

 





















  




  







 


 


 

 























  





 


 


 

 










 















 




















 









 







 










 

 







 








 


 
 

 




 

















  





 





 

 



 


















 







 





  


 







  




   



 


  
 


   



 


 

 












 









 

 


 








 


 
 








 

 



 

 










 





 


 




 

 



 


 


 


 



 







 



 














 



 




 

 







 


 

 



 




   




 














  





  



 








 


  




 

 



 



 



 

 

 


  






 

 


















 







 


    







 

    





  




   

 










    
 



 









 



 

  
 












 
 
 




 



 

 










 




 
















 










 







 










 

 











 




 







 
 





 

 




 

 


 

 



















 

 

 



















 

 









 

 


 







 

 





 


 


 








 









   
 



    


 


    





 




     


 

 

 










 


 



 



 






 

 
 







 




 

 



 


 






 


 

 


 
 

 


 









 




 



 
 
















 






 














 

 



 













 




 






 




 

 
 





 

  
 
 






 


 

 





















 

  




