Data Sufficiency

Can someone please provide a solution

750+ wrote:Can someone please provide a solution

(1) Sufficient. Since 7<x<11, x must be the median. So we have {2 7 x 11 16} in our set. The mean of the four digits is (11 + 16 + 2 + 7)/4 = 36/4 = 9. We want a number x such that the median equals the new mean - only one value works, namely 9. If x is 9, then the median is 9 and the mean remains 9. Any other value of x will result in an arithmetic mean that differs from the median. You can see this by looking at the numbers in the set - 2 is 7 less than 9, 7 is 2 less than 9, 11 is 2 more than 9, 16 is 7 more than 9. Note the figures are symmetrical on both sides of the median. Any other value, besides nine, will upset this symmetry.

(2) Sufficient. We are told that x is the median. By the same logic set forth above, x must be 9.

Answer is D.

This is a great problem involving a lot of the higher order thinking the GMAT likes to test: so great, in fact, that we have a dedicated blog post detailing how to approach it. (Check it out!)