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Absolute Value Question

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Absolute Value Question

by la1214 » Thu Nov 22, 2012 1:32 pm
Hello,
Can someone please explain this question in detail?

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16
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Source: — Data Sufficiency |
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by jkaustubh » Thu Nov 22, 2012 9:01 pm
This question is solved here

https://www.beatthegmat.com/x-y-32-what- ... 63925.html
Replying a query takes patience and time. The least a person can do is to thank the reply.
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by la1214 » Fri Nov 23, 2012 8:54 am
unfortunately....i did not understand the explanation :(
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by GMATGuruNY » Fri Nov 23, 2012 12:38 pm
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0 (2) |x| - |y| = 16
Statement 1: -4x - 12y = 0.
-4x = 12y
x = -3y.

Substituting x= -3y into |x| + |y| = 32, we get:
|-3y| + |y| = 32
3|y| + |y| = 32
4|y| = 32
|y| = 8
y = 8 or y = -8.

If y=8, then x = -3*8 = -24, and xy = (-24)(8) = -192.
If y= -8, then x = -3*(-8) = 24, and xy = -8*24 = -192.
Since xy = -192 in each case, sufficient.

Statement 2: |x| - |y| = 16.
Adding this equation to |x| + |y| = 32, we get:
2|x| = 48.
|x| = 24
x=24 or x = -24.

This means:
24 + |y| = 32
|y| = 8.
y = 8 or y = -8.

If x=24 and y=8, then xy = 192.
If x= -24 and y=8, then xy = -192.
Since xy can be different values, insufficient.

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by la1214 » Fri Nov 23, 2012 4:42 pm
Thanks so much! Now, is there a way to generalize when |x|=|y|?
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