2016 AMC 12A Problem 4

Attempt Problem 4 of the 2016 AMC 12A 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 12A solutions, or check the answer key.

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

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

Set the mean equal to

x

\dfrac{540+x}{7}=x,

then confirm the median and mode

The mean condition gives

\begin{gathered} \small \dfrac{60+100+x+40+50+200+90}{7}\\ =\dfrac{540+x}{7}\\ =x, \end{gathered}

540+x=7x

and

x=90.

In nondecreasing order the data are

40, 50, 60, 90, 90, 100, 200,

so the median is

90

and the mode is

90,

as required.

Thus, the correct answer is D.

Problem 4 in other years