2001 AMC 10 Problem 16

Below is the professionally curated solution for Problem 16 of the 2001 AMC 10, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 10 solutions, or check the answer key.

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Concepts:mean median (data)linear equation

Difficulty rating: 1280

16.

The mean of three numbers is $10$ more than the least of the numbers and $15$ less than the greatest. The median of the three numbers is $5.$ What is their sum?

$5$

$20$

$25$

$30$

$36$

Solution:

Let $m$ be the mean. The least number is $m-10$ and the greatest is $m+15,$ with median $5.$

Since the mean of the three is $m,$ $\tfrac13\big((m-10)+5+(m+15)\big)=m,$ which gives $m=10.$

The sum is $3m=30.$ Thus, the correct answer is D.

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