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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 $x$? (2016 AMC 10A Problems, Question \#7) 
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Since $x$ is the mean, $$ \begin{aligned} x \& =\frac{60+100+x+40+50+200+90}{7} \textbackslash\textbackslash{} \& =\frac{540+x}{7} . \end{aligned} $$  Therefore, $7 x=540+x$, so $x=$ (D) $90$. 