1. How many positive integers less than 200 are divisible by 2, 3 and 5?
2. The digits of a four-digit positive integer add up to 14. The sum of the two middle
digits is nine, and the thousands digit minus the units digit is one. If the integer is
divisible by 11, what is the integer?
3. How many positive three-digit integers are divisible by neither 2 nor 3?
4. Kaleb defined a "clever integer" as an even integer that is greater than 20, less
than 120, and such that the sum of its digits is 9. What fraction of all clever
integers is divisible by 27? Express your answer as a common fraction.
5. What is the smallest positive five-digit integer, with all different digits, that is
divisible by each of its non-zero digits?
1. Answer: 6 2. Answer: 3542 3, Answer: 300 4. Answer: 2/5 5. Answer: 10236