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PS: Number properties- factors

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by GMAT Kolaveri » Fri Apr 20, 2012 8:57 pm
If x and y are integers such that x+y = 14, which of the following could be their product?

-72
-40
9
21
32

Need to know alternate methods of solving this problem
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by pemdas » Fri Apr 20, 2012 10:37 pm
P=answer choice, then xy=P and x+y=14 --> x=14-y
y(14-y)=P, y^2-14y+P=0. By FOIL-ing we get y_1+y_2=-14 and y_1*y_2 equivalent to P :)
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GMAT Kolaveri wrote:If x and y are integers such that x+y = 14, which of the following could be their product?

-72
-40
9
21
32

Need to know alternate methods of solving this problem
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by GMATGuruNY » Sat Apr 21, 2012 2:15 am
GMAT Kolaveri wrote:If x and y are integers such that x+y = 14, which of the following could be their product?

-72
-40
9
21
32

Need to know alternate methods of solving this problem
Use the answers.
Look for a factor pair with a sum of 14.

A: -72
Factors of 72: 8*9, 6*12, 4*18...
We can stop there.
If x=18 and y=-4, then xy=-72 and x+y=18+(-4) = 14.

The correct answer is A.
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