Problem:
The mean of three numbers is more than the least of the numbers and less than the greatest. The median of the three numbers is . What is their sum?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since the median is , we can write the three numbers as , and , where
If we add these equations, we get
and solving for gives . Hence the sum of the numbers .
Let be the mean of the three numbers. Then the least of the numbers is and the greatest is . The middle of the three numbers is the median, . So
and . Hence, the sum of the three numbers is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions