Problem:
The mean, median, and unique mode of the positive integers are all equal. What is the value of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because the mode is unique, it must be , so the mean must also be . The sum of the seven numbers is , which must be equal to . Therefore . The median of the numbers is also .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions