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Set S contains exactly four distinct positive integers. Is t

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Set S contains exactly four distinct positive integers. Is t [#permalink]

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New post 07 Jan 2013, 06:42
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Set S contains exactly four distinct positive integers. Is the mean of S equal to the median of S?

(1) The smallest term in S is equal to the sum of the two middle terms minus the largest term in S.
(2) When the range of S is added to the sum of all the terms in S, the resulting sum is equal to the smallest term in S plus three times the largest term in S.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Jan 2013, 10:30, edited 1 time in total.
Edited the OA.
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Re: Set S contains exactly four distinct positive integers. Is t [#permalink]

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New post 07 Jan 2013, 08:03
Expert's post
daviesj wrote:
Set S contains exactly four distinct positive integers. Is the mean of S equal to the median of S?

(1) The smallest term in S is equal to the sum of the two middle terms minus the largest term in S.
(2) When the range of S is added to the sum of all the terms in S, the resulting sum is equal to the
smallest term in S plus three times the largest term in S.


Let the 4 distinct integers be w,x,y and z, where these are arranged in ascending order.
Mean of S=(w+x+y+z)/4
Median of S= (x+y)/2
The question is asking whether (w+x+y+z)/4=(x+y)/2? or is (w+x+y+z)=2x +2y or Is \(w+z=x+y?\)

Statement 1)
\(w=x+y-z\) or \(w+z=x+y\).
Sufficient

Statement 2)
Range=z-w
When this range is added to sum of all the terms in S, then the resulting sum is equal to the smallest term in S plus three times the largest term in S.
(z-w)+(w+x+y+z)= w+3z
The above can be rewritten as (x+y+2z)=w+3z or \(x+y=w+z\).
This is what statement 1 is saying.
Sufficient.

IMO the answer has to be D and not C.
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Re: Set S contains exactly four distinct positive integers. Is t [#permalink]

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New post 07 Jan 2013, 10:16
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oh yes...D is the answer...:)...can't edit via mobile though..:(

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Re: Set S contains exactly four distinct positive integers. Is t [#permalink]

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New post 22 Jul 2014, 03:43
If mean = median then you have an evenly spaced set. So question is "is S an evenly spaced set?"

(1) This a property of an evenly spaced set. (you can test if you like). Suff.
(2) Also a property of an evenly spaced set. (Test once more..) Suff.

Ans. D.
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Re: Set S contains exactly four distinct positive integers. Is t [#permalink]

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New post 09 Feb 2016, 01:09
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Re: Set S contains exactly four distinct positive integers. Is t   [#permalink] 09 Feb 2016, 01:09
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