Problem:
The average (arithmetic mean) of different positive whole numbers is . The largest possible value of any of these numbers is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since the mean is , it follows that the sum of the numbers is . Taking the smallest possible values for the smaller numbers would give the largest possible value of the tenth number. Thus, the largest possible number is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions