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Set and subset

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Set and subset

by Mormuse » Fri Mar 29, 2013 4:36 am
If the mean of set S does not exceed mean of any subset of S, which of the following must be true about S?...
1) S contains only one element
2) all elements of set S are equal
3) median of set S equals the mean of set S

Answer choice: Classic roman numeral choices.
I don't get why 1 is not possible? I answered 1,2 and 3 but the answer is 2 and 3. Help anyone?
Thanks!!!
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by GMATGuruNY » Fri Mar 29, 2013 7:32 am
claudayst wrote:If the mean of set S does not exceed mean of any subset of S, which of the following must be true about S?...

I: S contains only one element

I don't get why 1 is not possible?
The question stems asks not whether statement I is POSSIBLE but whether statement 1 MUST BE TRUE.
The constraint in the question stem -- that the mean of set S does not exceed the mean of any subset of S -- is satisfied by the following case:
S = {1,1}.
Thus, it does not have to true that S contains only one element.
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by Mormuse » Fri Mar 29, 2013 7:49 am
Seems like i fell upright in the trap!! Thx!
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by Jim@StratusPrep » Fri Mar 29, 2013 7:52 am
One element would mean only one 2 ------ {2}

However, you can have more than one ------- {2, 2, 2, 2}
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