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If x

by gmat25 » Sat Jul 16, 2011 12:19 am
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 GMATGuruNY » Sat Jul 16, 2011 3:23 am
gmat25 wrote: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 Anurag@Gurome » Sat Jul 16, 2011 3:30 am
gmat25 wrote: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 ---> x = -3y
This means if x and y have different signs.

Now, two cases are possible,
  • 1. x > 0 and y < 0 ---> x - y = 32 ---> -3y - y = 32 ---> y = -8 and x = 24
    1. x < 0 and y > 0 ---> -x + y = 32 ---> 3y + y = 32 ---> y = 8 and x = -24
In both of the above cases, xy = -(8*24)

Sufficient

Statement 2: |x| - |y| = 16
Combining this with |x| + |y| = 32, we have 2|x| = 48 ---> x = ±24 ---> y = ±8

Hence, xy = ±(8*24)

Not sufficient

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