CEMC Cayley, 2009

Combinatorics Difficulty 2.0 Junior Find the answer Canada

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.)

(A) $15$ (B) $16$ (C) $17$ (D) $24$ (E) $25$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.