Problem:
If and are positive integers and and are odd, then is
Answer Choices:
A. odd for all choices of
B. even for all choices of
C. odd, if is even; even, if is odd
D. odd, if is odd; even, if is even
E. odd, if is not a multiple of ; even, if is a multiple of
Solution:
The number is odd, and is even. Therefore is even and so is . Hence the sum is odd for all choices of . Note that is odd whether is even or odd.