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number properties

by GMAT Kolaveri » Sun May 06, 2012 6:46 pm
Are all of the numbers in a certain list of 15 numbers equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.

[spoiler]OA:B[/spoiler]
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by Anurag@Gurome » Sun May 06, 2012 7:07 pm
GMAT Kolaveri wrote:Are all of the numbers in a certain list of 15 numbers equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.

[spoiler]OA:B[/spoiler]
Statement 1: The sum of all the numbers in the list is 60.
We can have different set of 15 numbers such that their sum is 60.

Not sufficient

Statement 2: The sum of any 3 numbers in the list is 12.
This is only possible when all the numbers in the set are equal. Consider the case when we have a single different number, say a and other are equal, say b. Now the selection of any three numbers may result (a, b, b) and (b, b, b). Now according to the question, (a + b + b) and (b + b + b) both must be equal to 12. Which is only possible when a = b = 4.

This can shown for other combinations too. (Like 2 different, others equal etc)

Sufficient

The correct answer is B.
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by GMATGuruNY » Mon May 07, 2012 3:27 am
I posted an explanation here:

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by GmatKiss » Mon May 07, 2012 4:19 am
IMO: B
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