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Value of xy

by apex231 » Sun Dec 11, 2011 5:08 pm
If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x - 12y = 0
(2) |x| - |y| = 16

OA A
Last edited by apex231 on Sun Dec 11, 2011 6:46 pm, edited 1 time in total.
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by chieftang » Sun Dec 11, 2011 5:32 pm
apex231 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x - 12y = 0
(2) |x| - |y| = 16
(1)
-4x - 12y = 0
x = -3y
|-3y| + |y| = 32
y=8,-8 so x = 24,-24
But x = -3y means x and y are opposite signs. So the product xy is always negative.
SUFFICIENT

(2)
|x| - |y| = 16
|x| = |y| + 16
|y| + |16| + |y| = 32
2|y| = 16
|y| = 8
y=8,-8, so x=24,-24
x and y can be any sign. So xy can be positive or negative.
INSUFFICENT

Answer: A
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by Anurag@Gurome » Sun Dec 11, 2011 8:21 pm
apex231 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x - 12y = 0
(2) |x| - |y| = 16

OA A

(1) -4x - 12y = 0 implies -4x = 12y or x = -3y
So, |x| + |y| = 32 implies |-3y| + |y| = 32

Case I: If y > 0, then 3y + y = 32 or y = 8, x = -24

Case II: If y < 0, then -3y - y = 32 or y = -8, x = 24
In both the cases, xy = -(24) * 8 = -192; SUFFICIENT.

(2) |x| - |y| = 16

Case I: Both x and y > 0
x - y = 16
x + y = 32
Adding the equations, we get, 2x = 48 or x = 24, y = 8

Case II: x > 0 and y < 0
x + y = 16
x - y = 32
Adding the equations we get, 2x = 48 or x = 24, y = -8

In both the above cases, the value of xy is different. We don't get a definite answer; NOT sufficient.

The correct answer is A.
Anurag Mairal, Ph.D., MBA
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