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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 Updated on: 07 Jan 2013, 09:30
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A
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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.

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Originally posted by daviesj on 07 Jan 2013, 05:42.
Last edited by Bunuel on 07 Jan 2013, 09:30, 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, 07:03
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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, 09:16
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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, 02:43
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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Set S contains exactly four distinct positive integers.  [#permalink]

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New post 22 May 2018, 00:51
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.
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Re: Set S contains exactly four distinct positive integers.  [#permalink]

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New post 22 May 2018, 00:58
MANHATTAN GMAT OFFICIAL SOLUTION:

Since the four integers in the set are distinct positive integers, give them distinct ordered
variables to represent their relative sizes: a, b, c, and d are the terms of set S, such that a < b < c < d.
The mean of S is \(\frac{(a+b+c+d)}{4}\). The median of S is the average of the two middle terms, \(\frac{(b+c)}{2}\) .
Express the question algebraically:
\(\frac{(a+b+c+d)}{4}\) = \(\frac{(b+c)}{2}\)
2(a + b + c + d) = 4(b + c)
(a + b + c + d) = 2(b + c)
a + b + c + d = 2b + 2
Is a + d = b + c?
In words, this question has been rephrased as, “Is the sum of the largest and smallest terms in S equal
to the sum of the two middle terms?”
(1) SUFFICIENT: If the smallest term is equal to the sum of the two middle terms minus the largest
term, then the question is satisfied:
a = b + c − d
a + d = b + c
The answer to the rephrased question is a definite “Yes.”
(2) SUFFICIENT: If the sum of the range of S and all the terms in S is equal to the smallest term in S
plus three times the largest term in S, then:
(d − a) + (a + b + c + d) = a + 3d
b + c + 2d = a + 3d
b + c = a + d
The answer to the rephrased question is a definite “Yes.”
The correct answer is (D).
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Re: Set S contains exactly four distinct positive integers. Is t  [#permalink]

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New post 22 May 2018, 03:40
CAMANISHPARMAR 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.

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Re: Set S contains exactly four distinct positive integers. Is t &nbs [#permalink] 22 May 2018, 03:40
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