2019 AMC 12B Problem 7

The mean is $\dfrac{4+6+8+17+x}{5}=\dfrac{35+x}{5}.$ If $x\le6,$ the median is $6,$ so $\dfrac{35+x}{5}=6$ gives $x=-5,$ which is consistent. If $6\lt x\lt8,$ the median is $x,$ so $\dfrac{35+x}{5}=x$ gives $x=8.75,$ not in range. If $x\ge8,$ the median is $8,$ so $\dfrac{35+x}{5}=8$ gives $x=5,$ not in range. The only solution is $x=-5,$ so the sum is $-5.$ Thus, A is the correct answer.