2022 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 8 Easy

A data set consists of 6 (not distinct) positive integers: 1, 7, 5, 2, 5, and X. The average (arithmetic mean) of the 6 numbers equals a value in the data set. What is the sum of all positive values of X?

  • A.

    10

  • B.

    26

  • C.

    32

  • D.

    36

  • E.

    40

Answer:D

The possible values for the mean: 5, 7, x.

If mean =5, x=5\times6-(1+2+5+5+7)=10;

If mean =7, x=7\times6-(1+2+5+5+7)=22;

If mean =x, x=6x-20, then x=4.

Sum =10+22+4=36.

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