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by leumas » Thu Mar 01, 2012 7:26 am
How much greater is the square of the sum of three different positive integers than the sum of their squares?

(1) The sum of the products of all possible pairs of two different integers out of the original set of three is 61.

(2) The largest of the three integers, 7, is equal to the sum of the two smaller integers.

OA is A. i thought it is C.

Regards
Samuel
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Source: — Data Sufficiency |
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by leumas » Thu Mar 01, 2012 7:41 am
leumas wrote:How much greater is the square of the sum of three different positive integers than the sum of their squares?

(1) The sum of the products of all possible pairs of two different integers out of the original set of three is 61.

(2) The largest of the three integers, 7, is equal to the sum of the two smaller integers.

OA is A. i thought it is C.

Regards
Samuel

Ah, just got it.

Formula for (a+b+c)^2 = a^2+b^2+c^2+ 2(ab+bc+ca)

Question: How much is 2(ab+bc+ca)??

1. Gives us ab+bc+ca = 61---> Sufficient
2. Can be multiple combinaiton

So A is sufficient!!

Regards
Samuel
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by Jim@StratusPrep » Thu Mar 01, 2012 7:58 am
Let's call them a, b, and c.

1) ab + ac + bc = 61 Since these are positive integers, let's try to find out what might work:

3(4) + 3(7) + 4(7) = 12 + 21 + 28 = 61

There is no other set of numbers that work. SUFFICIENT

2) 1,6, 7 or 2, 5, 7 or 3, 4, 7 INSUFFICIENT
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by Eshika » Mon Apr 02, 2012 10:15 am
How much greater is the square of the sum of three different positive integers than the sum of their squares?

(1) The sum of the products of all possible pairs of two different integers out of the original set of three is 61.

(2) The largest of the three integers, 7, is equal to the sum of the two smaller integers.

OA is A. But how as there are 2 options for this:-
3,4,7 & 2,3,11 both add to 61.

Kindly clarofy
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by leumas » Mon Apr 02, 2012 10:53 am
Eshika wrote:How much greater is the square of the sum of three different positive integers than the sum of their squares?

(1) The sum of the products of all possible pairs of two different integers out of the original set of three is 61.

(2) The largest of the three integers, 7, is equal to the sum of the two smaller integers.

OA is A. But how as there are 2 options for this:-
3,4,7 & 2,3,11 both add to 61.

Kindly clarofy
The question is not asking for the pairs. But the difference between (a+b+c)^3 and a^2+b^2+c^2. Now you can see my previous post.

Regards
Samuel
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