Problem:
How many subsets of two elements can be removed from the set
so that the mean (average) of the nine remaining numbers is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the average of the remaining numbers is , then their sum is . Because the sum of the numbers in the original set is , the sum of the two numbers removed must be . There are five such subsets: , , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions