CAYLEY 2009 Problem 15

A list of 5 positive integers has all of the following properties:

  • the only integer in the list that occurs more than once is $8,
  • its median is 9, and
  • its average (mean) is 10.

What is the largest possible integer that could appear in the list?
(Note: The median of a set of five positive integers is the middle integer when the set is arranged in increasing order.)

Answer Choices
A. 15
B. 16
C. 17
D. 24
E. 25