Problem:
What is the smallest possible average of four distinct positive even integers?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The smallest average will occur when the numbers are as small as possible. The four smallest distinct positive even integers are , and and their average is .
Note: These numbers form an arithmetic sequence. The average of the numbers in any arithmetic sequence is the average of the first and last terms.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions