2016 AMC 10A Problem 7 — Solution | LIVE by Po-Shen Loh

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2016 AMC 10A Problem 7

Attempt Problem 7 of the 2016 AMC 10A 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 2016 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

7.

The mean, median, and mode of the $7$ data values $60, 100, x, 40, 50, 200, 90$ are all equal to $x.$ What is the value of $x?$

$50$

$60$

$75$

$90$

$100$

Answer: D

Concepts:mean median (data)mode

Difficulty rating: 960

Solution:

The sum of the seven data values is $540+x$ . If the mean equals $x$ , then $\frac{540+x}{7}=x,$ so $540=6x$ and $x=90$ .

With $x=90$ , the ordered data set is $40,50,60,90,90,100,200$ . Its median is $90$ , and its mode is also $90$ , so the value works.

Thus, the correct answer is D.

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