2007 Math Kangaroo in USA
9th – 10th Grades
Sample Problems
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Question for 3 points:
Anh, Ben and Chen have 30 balls together. If Ben gives 5 balls to Chen,
Chen gives 4 balls to Anh and Anh gives 2 balls to Ben, then the boys will
have the same number of balls. How many balls did Anh have at the
beginning?
A) 8
B) 9
C) 11
D) 13
E) 15
Question for 4 points:
The students were solving an interesting problem from the ”Kangaroo”. As a
result the number of the boys who had solved the problem turned out to be
the same as the number of the girls who hadn’t solved the problem. Which
number is larger: students who had solved the problem, or all of the girls?
A) girls
C) equal
B) those who have solved the problem
D) impossible to find
E) the situation is not possible
Question for 5 points:
An island is inhabited by liars and truth-tellers (the liars always tell lies and
the truth-tellers always tell the truth). One day 12 islanders, both liars and
truth-tellers, gathered together and issued a few statements. Two people
said: ”Exactly two people among us twelve are liars”. The other four people
said: ”Exactly four people among us twelve are liars”. The other six people
said: ”Exactly six people among us twelve are liars”. How many liars were
there?
A) 2
B) 4
C) 6
D) 8
E) 10
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