Bunuel wrote:
If the mean of set \(S\) does not exceed mean of any subset of set \(S\), which of the following must be true about set \(S\)?
I. Set \(S\) contains only one element
II. All elements in set \(S\) are equal
III. The median of set \(S\) equals the mean of set \(S\)
A. none of the three qualities is necessary
B. II only
C. III only
D. II and III only
E. I, II, and III
What 'mean of set S does not exceed mean of any subset of set S' also means is that range of set S is equals that of any subset of set S OR 'zero'. But since mean can also be anything or 'zero', range has to be 'zero'. Now, for the set S to have range 'zero', the elements in the set have to be equal OR there has to be only one element. The latter case is not always true since if all element in set S are equal it nullifies 'I'.
Hence 'II' is always true. Get rid of answer choices A,C and E.
For 'III', again it will be always true that median of set S equals the mean of set S.
Hence
Answer D.
_________________