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, 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) $25$

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