2001 AMC 8 Problem 21
Attempt Problem 21 of the 2001 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
The mean of a set of five different positive integers is The median is The maximum possible value of the largest of these five integers is
Answer: D
Small hint:
The five numbers sum to
Big hint:
Make the other four numbers as small as possible
Solution:
The median of the set of numbers is the third largest number, which is There are two numbers less than and two numbers greater than it.
The mean of the set is so the sum of all the numbers is In order to maximize the largest number with this sum, the other numbers must be as small as possible.
The two numbers less than must be positive and distinct, so they must be and
The number immediately after must also be as small as possible, so it must be
Therefore, the remaining number, the maximum possible value in the set, is
Thus, D is the correct answer.
Problem 21 in other years
- 1985 AMC 8
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