For a set X containing n integers, is the mean even? (1) n : GMAT Data Sufficiency (DS)
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# For a set X containing n integers, is the mean even? (1) n

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For a set X containing n integers, is the mean even? (1) n [#permalink]

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09 Mar 2011, 09:15
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For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach
[Reveal] Spoiler: OA
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09 Mar 2011, 09:31
This one is tricky.

1. Insufficient
n = 2
X = {0,2} mean = 1. The answer is NO
X = {3,5} mean = 4. The answer is YES

2. Insufficient
X = {0,2} mean = 1. The answer is NO
X = {2,2} mean = 2. The answer is YES

1) + 2)
X = {0,2} mean = 1. The answer is NO
X = {2,2} mean = 2. The answer is YES

Hence E.

kannn wrote:
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach

Last edited by gmat1220 on 09 Mar 2011, 09:32, edited 1 time in total.
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For a set X containing n integers, is the mean even? (1) n [#permalink]

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09 Mar 2011, 09:32
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kannn wrote:
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach

For a set X containing n integers, is the mean even?

The mean of a set = The sum of the elements / number of elements, so the question is whether mean=sum/n=even.

(1) n is even --> mean=sum/even. Not sufficient.

(2) All of the integers in set X are even --> so the sum of the elements is even --> mean=even/n. Not sufficient.

(1)+(2) The question becomes whether mean=even/even=even, which can not be determined as even/even could be even (for example 4/2=2=even), could be odd (for example 6/2=3=odd) or could be non-integer (for example 6/4=3/2). Not sufficient.

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09 Mar 2011, 20:55
From (1), 1,2 mean = 1.5 or 4,8 mean = 6, so (1) is not enough

Again, 2,4 mean = 3 or 4,8 mean = 6, so (2) is not enough

From (1) and (2), there is no definitive conclusion, so answer is E.
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Re: For a set X containing n integers, is the mean even? [#permalink]

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10 Sep 2012, 05:05
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For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Doesn't both the statements combined give an odd answer? Thus Statement (C) is correct but the MGMAT says that (E) is correct. Can someone explain the answer.

take Set S as {2,4} then you will get the mean as 3 (odd)
take Set S as {4,4,4,4} then you will get the mean as 4 (even)

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Re: For a set X containing n integers, is the mean even? [#permalink]

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09 May 2014, 09:40
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Trick here is that integers in Set S is NOT UNIQUE EVEN INTEGER. Hence Ans. E. If integers were unique EVEN integers then Ans. would have been C.
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Re: For a set X containing n integers, is the mean even? (1) n [#permalink]

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24 Jun 2014, 10:33
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Re: For a set X containing n integers, is the mean even? (1) n [#permalink]

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28 Aug 2015, 22:18
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For a set X containing n integers, is the mean even? (1) n [#permalink]

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16 Sep 2015, 18:21
asif780 wrote:
Trick here is that integers in Set S is NOT UNIQUE EVEN INTEGER. Hence Ans. E. If integers were unique EVEN integers then Ans. would have been C.

Not true, for instance.

If set {2,4}, then Avg. = 3
If set {2,6}, then Avg. = 4

Since both sets are unique even integers, the average can still be odd of even, and therefore whatever is above is not valid.
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Re: For a set X containing n integers, is the mean even? (1) n [#permalink]

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03 Feb 2016, 01:34
Bunuel wrote:
kannn wrote:
For a set X containing n integers, is the mean even?

(1) n is even.

(2) All of the integers in set X are even.

Best approach

For a set X containing n integers, is the mean even?

The mean of a set = The sum of the elements / number of elements, so the question is whether mean=sum/n=even.

(1) n is even --> mean=sum/even. Not sufficient.

(2) All of the integers in set X are even --> so the sum of the elements is even --> mean=even/n. Not sufficient.

(1)+(2) The question becomes whether mean=even/even=even, which can not be determined as even/even could be even (for example 4/2=2=even), could be odd (for example 6/2=3=odd) or could be non-integer (for example 6/4=3/2). Not sufficient.

Hi Bunuel,

I still do not understand how to solve these kind of questions methodically because everytime we have to consider cases I forget one or other cases to consider. So instead of trying numbers can you please describe a methodical approach to test this.

For eg when we consider cases how many cases are possible and how to check against them. Such as we know that for the mean to be even the sum mandatorily has to be even however the base could be even or odd and can yield even or odd mean in both the cases i.e when N= even or when n=odd as non integers are also included.
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Re: For a set X containing n integers, is the mean even? (1) n [#permalink]

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08 Jul 2016, 21:40
One doubt - if the question had mentioned n positive integers, how does the answer varies ? My doubt is - whether the addition of "zero" to the set changes the even\odd nature of the mean ?
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Re: For a set X containing n integers, is the mean even? (1) n [#permalink]

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09 Jul 2016, 06:09
good question

take 2,4,6,8 and 4444 for both statements

and will come out to be E

hope it helps
Re: For a set X containing n integers, is the mean even? (1) n   [#permalink] 09 Jul 2016, 06:09
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