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## list of numbers

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shrutib Rising GMAT Star
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list of numbers Wed May 30, 2012 9:19 pm
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Are all the numbers of a certain list of 15 numbers are equal?

1. The sum of all the numbers in the list is 60.

2.The sum of any three number in the list is 12.

P.S. I saw the OG explanation. Did not get it. Please explain

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Anurag@Gurome GMAT Instructor
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Wed May 30, 2012 9:22 pm
shrutib wrote:
Are all the numbers of a certain list of 15 numbers are equal?

1. The sum of all the numbers in the list is 60.

2.The sum of any three number in the list is 12.

P.S. I saw the OG explanation. Did not get it. Please explain
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.

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Thu May 31, 2012 3:54 am

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