Problem:
Which of the following integers cannot be written as the sum of four consecutive odd integers?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The sum of consecutive odd integers is always a multiple of . Among the given choices, only is not a multiple of . The other four numbers can each be written as the sum of four consecutive odd numbers:
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions