Problem:
If and are integers and is even, which of the following is impossible?
Answer Choices:
A. and are even
B. and are odd
C. is even
D. is odd
E. none of these is impossible
Solution:
If is even, then and are either both even or both odd, which means and are either both even or both odd. If and are both even, their sum is even. If and are both odd, their sum is even. Because is never odd, is the impossible choice.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions