gmatnmein2010 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

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

Please search
https://www.beatthegmat.com/x-and-y-t21771.html

gmatnmein2010 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

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

IMO A

(1) -4x-12y=0 --> x+3y=0 --> x=-3y --> x and y have opposite signs --> either |x|+|y|=-x+y=3y+y=4y=32: y=8 x=-3, xy=-24 OR |x|+|y|=x+(-y)=-3y-y=-4y=32: y=-8, x=3, xy=-24. The same answer. Sufficient.

(2) Multiple choices. Not sufficient.

gmatnmein2010 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

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

|x| + |y| = 32 represnts area bounded by four lines x+y=32, x-y=32, -x+y =32, -x-y=32.
St.1 : -4x-12y = 0 --> x=-3y
so |-3y | + |y| = 32 --> |4y| = 32 --> y = =+/-8
if y = 8 , x = -24 xy = -192
if y =-8, x=24 xy =-192
so we get xy =-192 hence suff.
St.2 |x| - |y| = 16 is the area bounded by lines x+y =16, x-y =16 , -x+y =16, -x-y =16 ....so it s a rectangle which conatins many points...
hence not sufficient to calculate xy

Ans A