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# The mean of set S does not exceed mean of any subset of set

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Joined: 11 May 2008
Posts: 551
The mean of set S does not exceed mean of any subset of set [#permalink]

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28 Aug 2008, 20:30
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

* none of the three qualities is necessary
* II only
* III only
* II and III only
* I, II, and III

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Joined: 14 Aug 2007
Posts: 697
Re: roman sets [#permalink]

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28 Aug 2008, 21:31
arjtryarjtry wrote:
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

* none of the three qualities is necessary
* II only
* III only
* II and III only
* I, II, and III

D.

Consider any set that has different elements => 1, 2, 3, 4, 5
mean of set = 3
consider a subset of this set {4,5} mean is higher
consider another subset of this set {1} or {1,2} mean is lower.

If all the elements are same, however, mean will be same for all subsets => does not exceed mean of original set.

for any such set (having all elements same) mean and median will always be same.

But it is not necessary to have only 1 element into it.

Thus D

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: roman sets   [#permalink] 28 Aug 2008, 21:31
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# The mean of set S does not exceed mean of any subset of set

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