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2021 AMC 10B Problem 19

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2021 AMC 10B Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Statistics & Data · difficulty 3 of 5 · about 5 min · position P16-20

Suppose that $S$ is a finite set of positive integers. If the greatest integer in $S$ is removed from $S$ , then the average value (arithmetic mean) of the integers remaining is $32$ . If the least integer in $S$ is also removed, then the average value of the integers remaining is $35$ . If the greatest integer is then returned to the set, the average value of the integers rises to $40$ . The greatest integer in the original set $S$ is $72$ greater than the least integer in $S$ . What is the average value of all the integers in the set $S$ ?

A)
$36.2$
B)
$36.4$
C)
$36.6$
D)
$36.8$
E)
$37$

2021 AMC 10B Problem 19

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