2016 AMC 12A Problem 4

The mean condition gives $$\begin{gathered} \small \dfrac{60+100+x+40+50+200+90}{7}\\ =\dfrac{540+x}{7}\\ =x, \end{gathered}$$ so $540+x=7x$ 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.