2002 AMC 12A Problem 15
Below is the professionally curated solution for Problem 15 of the 2002 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12A solutions, or check the answer key.
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Difficulty rating: 1660
15.
The mean, median, unique mode, and range of a collection of eight integers are all equal to The largest integer that can be an element of this collection is
Solution:
The collection has mean, median, unique mode, and range all equal to so is attainable.
Suppose the largest were The range forces the smallest to be and the median fixes the two middle values as Then so the remaining four values sum to averaging At least one would be below contradicting the minimum. So is impossible.
Thus, the correct answer is D.
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