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 48,7,5,0,0.... MEAN is 4 again and NOT a part of set......

8 and 0 are equidistant from 4insuff

(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 47,6,5,2,0.... MEAN is 4 again and NOT a part of set...

2 and 6 are equidistant from 4insuff

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

_________________

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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