jainrahul1985 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.