Data Sufficiency

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

(1) -4x - 12y = 0

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

[spoiler]OA : A[/spoiler]

buoyant 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.

The correct answer is A.

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.

Hi Mitch,

After the above step, i put the values of y back into the absolute value equation |x| + |y| = 32
instead of into the equation x=-3y
This gave me values of x = 24 or -24

So, i chose this statement as insufficient.

What was wrong with my approach?

buoyant wrote: i put the values of y back into the absolute value equation |x| + |y| = 32
instead of into the equation x=-3y
This gave me values of x = 24 or -24

So, i chose this statement as insufficient.

What was wrong with my approach?

Your approach is perfect, but you neglected to answer the question stem, which asks not for the value of x but for the value of xy.
You correctly determined that x=±24.
Statement 1 requires that x=-3y.
Thus:
If x=24, then y=-8, in which case xy = (24)(-8) = -192.
If x=-24, then y=8, in which case xy = (-24)(8) = -192.
Since the value of xy is THE SAME in each case, statement 1 is SUFFICIENT.

You are right..
Thank You.