Problem:
When is appended to a list of integers, the mean is increased by . When is appended to the enlarged list, the mean of the enlarged list is decreased by . How many integers were in the original list?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let denote the number of integers in the original list, and the original mean. Then the sum of the original numbers is . After is appended to the list, we have the sum
After is appended to the enlarged list, we have the sum
Solving and gives and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions