Problem:
Let be an odd whole number and let be any whole number. Which of the following statements about the whole number Is always true?
Answer Choices:
A. it is always odd
B. it is always even
C. it is even onIy if is even
D. it is odd only if is odd
E. it is odd only if is even
Solution:
The number is always odd. Now is odd if is odd and even if is even. Thus the sum is even if is odd, since the sum of two odd numbers is even; the sum is odd if is even, since the sum of an odd number and an even number is odd.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions