Problem:
The set is augmented by a fifth element , not equal to any of the other four. The median of the resulting set is equal to its mean. What is the sum of all possible values of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The mean of the augmented set is . If , the median of that set is 6 , so , and . If , the median is , so , and . If , the median is 9 , so , and . Thus the sum of all possible values of is .
The problems on this page are the property of the MAA's American Mathematics Competitions