Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?

(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three

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Hope it helps.
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Actually that (such numbers) could be a trap in this question.

You might remember -
If set is evenly spaced then for sure mean=median
But, if mean=median, it doesnt mean that set is evenly spaced. It may or may not be.

So, if we make x=0 and x=20, and find mean and median =10. We are pratically limiting our scope only to evenly spaced sets. And thus we get a few solutions-but not all.

We still need to look for solution for the other case where set is not evenly spaced. (Also x=10 doesnt give u an evenly spaced set.. so concept cant be applied directly, it would be more evident if the number of elements in set is even).

One easy concept that u can use though is, if median =mean then numbers in the set will be symmetrical around median. Why it helps is that finding median is usually very simple,without calculation.
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The mean is always equal to median when numbers in a set have equal deviation. For instance, in our case if deviation is 4, the x should 0 or 20.
Another case when a set is ascending from the mean out both sides. x should be 10. Please, look the atachments. Hope, it helps.

The answer is D

First rearrange the given set in ascending order = {4,8, 12,16} {x}
average = (40 + x) / 5

now depending on value of x, the median will change, also
median can be one of 8, 12, x

(1) suppose median = x, then average = median
(40 + x)/5 = x => 4x = 40 => x = 10

(2) suppose median = 12, then average = 12
(40 + x)/5 = 12 => x = 20

(3) suppose median = 8, then average = 8
(40 + x)/5 = 8 => x = 0

so there are three possible values of x {0, 10, 20} for which median = mean => (D)