PS: Number properties- factors

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GMAT Kolaveri: Master | Next Rank: 500 Posts; Posts: 287; Joined: Fri Mar 23, 2012 12:33 amFollowed by: 6 members; Location: Pune,India; Thanked: 60 times

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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Source: Beat The GMAT — Problem Solving | Fri Apr 20, 2012 8:57 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

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

Listing options: 1-15, 2-16, 3-17, 4-18 <-- success and pick a

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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