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DS: For a set X containing n integers ("Even Mean")

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aaliquo
 Post subject: DS: For a set X containing n integers ("Even Mean")
 Post Posted: Thu Oct 08, 2009 12:39 pm 
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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.

For this question, I understand why the first and second statements are insufficient on their own, but I don't understand why they're not sufficient together.

When I put the statements together I know that the Sum (numerator) is even, and n (the denominator) is also even. If an even number is divided by another even number wouldn't the result also be even?

Thanks!
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snhassan1970
 Post subject: Re: DS: For a set X containing n integers ("Even Mean")
 Post Posted: Thu Oct 08, 2009 9:07 pm 
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Not really, lets take a simple example fo 4 even integers which satisfies both (1) and (2).

(2,4,6,8)--> Sum=20; --> Average(=20/4) = 5.--> An odd integer.

Thus, even we devide an even number by another even number, the result is not necessarily an even number. It could be odd and even it could be a fraction.

Hope this helps!
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aaliquo
 Post subject: Re: DS: For a set X containing n integers ("Even Mean")
 Post Posted: Fri Oct 09, 2009 12:21 pm 
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Posts: 2
Thanks for the response, now I see. Next time I'll try using real numbers to verify the answer.
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RonPurewal
 Post subject: Re: DS: For a set X containing n integers ("Even Mean")
 Post Posted: Mon Nov 02, 2009 10:06 pm 
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ManhattanGMAT Staff


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aaliquo wrote:
If an even number is divided by another even number wouldn't the result also be even?

Thanks!


nope.

(even) / (even) can be ANYTHING:
it can be even (24/6 = 4)
it can be odd (24/8 = 3)
it can be a fraction with two odds (10/6 = 5/3)
it can be a fraction that is odd/even (6/8 = 3/4)
it can be a fraction that is even/odd (8/6 = 4/3)

the only thing it can't be is even/even, because that fraction could be reduced.
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yousuf_azim
 Post subject: Re: DS: For a set X containing n integers ("Even Mean")
 Post Posted: Mon Sep 05, 2011 12:10 am 
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Students


Posts: 45
What is the ans?

BR
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shrive_
 Post subject: Re: DS: For a set X containing n integers ("Even Mean")
 Post Posted: Sat Sep 17, 2011 9:53 pm 
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Students


Posts: 1
E is answer
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StaceyKoprince
 Post subject: Re: DS: For a set X containing n integers ("Even Mean")
 Post Posted: Fri Nov 11, 2011 9:53 pm 
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Posts: 6064
Location: San Francisco
thanks!

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