Problem:
The mean of a set of five different positive integers is . The median is . The maximum possible value of the largest of these five integers is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The sum of all five numbers is . Let the numbers be and in increasing order. For to be as large as possible, make and as small as possible. The smallest possible values are and . Then the sum of and is , and the difference, , is the largest possible value of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions