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The sum of two positive numbers

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by chieftang » Mon Dec 26, 2011 10:55 pm
The product of two positive numbers is 9 and the sum of their squares is 31. What is their sum?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

OA: [spoiler]C, Anurag's explanation hits the spot![/spoiler]
Last edited by chieftang on Tue Dec 27, 2011 8:13 am, edited 1 time in total.
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by Anurag@Gurome » Mon Dec 26, 2011 11:25 pm
chieftang wrote:The product of two positive numbers is 9 and the sum of their squares is 31. What is their sum?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

OA: To be given after discussion.
Let the two numbers are x and y.
Then xy = 9 and x² + y² = 31, so we have to find x + y.
Now we know that, (x + y)² = x² + y² + 2xy
So, (x + y)² = 31 + 2(9)
(x + y)² = 49
x + y = 7

The correct answer is C.
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