Problem:
For positive integers and such that , both the mean and the median of the set are equal to . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that the given conditions imply that the 6 values are listed in increasing order. Because the median of the these 6 values is , the mean of the middle two values must be , so
which implies . Because the mean of the set is also ,
so and . Then , and the requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions