Problem:
Suppose that
is an integer. Which of the following statements must be true about
Answer Choices:
A. It is negative.
B. It is even, but not necessarily a multiple of 3 .
C. It is a multiple of 3 , but not necessarily even.
D. It is a multiple of 6 , but not necessarily a multiple of 12 .
E. It is a multiple of 12 .
Solution:
Because
is an integer, must be even. The case shows that is not necessarily a multiple of 3 and that none of the other statements must be true.
The problems on this page are the property of the MAA's American Mathematics Competitions