Question

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 $X?$

$10$

$26$

$32$

$36$

$40$

Answer: D

Concepts:mean casework

Difficulty rating: 1270

Solution:

The known numbers sum to $20,$ so the mean is $\dfrac{20+X}{6},$ which must equal an element of the set.

Setting it to $5$ gives $X=10;$ to $7$ gives $X=22;$ and to $X$ itself gives $20+X=6X,$ so $X=4.$ Values $1$ and $2$ give negative $X.$

The positive values are $10,22,4,$ summing to $36.$

Thus, the correct answer is D.

2022 AMC 12A Problem 6

Answer: D

Difficulty rating: 1270

Solution:

Problem 6 in Other Years