Bunuel wrote:

If set \(S\) consists of positive integers, is the median of set \(S\) larger than its range?

(1) All elements of set \(S\) are smaller than 40.

(2) All elements of set \(S\) are larger than 20.

I did it this way:

Let's say Median = M, Smallest element = S, and Largest element = L

Q: is M > L - S? or M + S > L?

(1) L <= 39, S & M unknown. Not Sufficient

(2) All elements > 20, so L, M & S unknown. Not sufficient

Together (1) & (2)

From (1) we know that L>=39, so let's say L is the maximum possible integer, so L = 39

From (2), we know that S could be any positive integer from 21 to 39, so let's say S is the smallest possible integer in the range, S = 21. We are left with M. Let's keep M as low as S, so M= S = 21

Q: Q: is M > L - S? or M + S > L? 21 > 39 -21? or 21 + 21 > 39? Yes. SUFFICIENT.

Hope this way of getting to the answer is ok.

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