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# For S, a set of five integers, is the mean of the set an integer in S?

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Manager
Joined: 07 Jun 2017
Posts: 177
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
For S, a set of five integers, is the mean of the set an integer in S? [#permalink]

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01 Nov 2017, 22:52
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65% (hard)

Question Stats:

59% (00:59) correct 41% (01:35) wrong based on 34 sessions

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For S, a set of five integers, is the mean of the set an integer in S?

(1) The difference between the smallest integer in S and the median of S is the same as the difference between the median and the highest integer in S.

(2) The difference between the second smallest integer in S and the median of S is the same as the difference between the median and the second highest integer in S.

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Naveen
email: nkmungila@gmail.com
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Joined: 02 Aug 2009
Posts: 6199
Re: For S, a set of five integers, is the mean of the set an integer in S? [#permalink]

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02 Nov 2017, 05:42
nkmungila wrote:
For S, a set of five integers, is the mean of the set an integer in S?

(1) The difference between the smallest integer in S and the median of S is the same as the difference between the median and the highest integer in S.

(2) The difference between the second smallest integer in S and the median of S is the same as the difference between the median and the second highest integer in S.

hi..

(1) The difference between the smallest integer in S and the median of S is the same as the difference between the median and the highest integer in S.
WE do not know anything about the other THREE numbers.
for example...
8,4,4,4,0... MEAN is 4 and a part of set.....8 and 0 are equidistant from 4
8,7,5,0,0.... MEAN is 4 again and NOT a part of set......8 and 0 are equidistant from 4
insuff

(2) The difference between the second smallest integer in S and the median of S is the same as the difference between the median and the second highest integer in S.
WE do not know anything about the other THREE numbers.
for example...
8,6,4,2,0... MEAN is 4 and a part of set.. 2 and 6 are equidistant from 4
7,6,5,2,0.... MEAN is 4 again and NOT a part of set...2 and 6 are equidistant from 4
insuff

Combined..
statement I means the SUM of the highest and smallest number is equal to MEAN
statement II means the SUM of the second highest and second smallest number is equal to MEAN
so the FOUR numbers are equal to mean, 5TH has to be MEAN itself
so suff

algebraically ..
highest $$M+a$$, so smallest = $$M-a$$
second highest = $$M+b$$, so second smallest = $$M-b$$...
let FIFTH be x..
so SUM = $$M+a+M-a+M+b+M-b+x = 4M+x$$..
but the SUM as per MEAN is 5*mean = 5M
so $$5M = 4M+x......x=M$$
so mean is in set
suff

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: For S, a set of five integers, is the mean of the set an integer in S?   [#permalink] 02 Nov 2017, 05:42
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