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
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1) -4x=12y--->x=-3y. Make a substitution into |x|+|y|=32----> |-3y|+|y|=32---->3|y|+|y|=32---->4|y|=32----->|y|=8 so y=8 or -8. From x=-3y, (x,y)=(-24,8) or (24,-8). In both cases xy=-(24)(8). SUFFICIENT.
2) Add |x|+|y|=32 and |x|-|y|=16 to get 2|x|=48---->x=-24 or 24. From original equation (x,y)=(-24,-8) or (-24,8) or (24,-8) or (24, 8). Two possible values of xy: 8*24 and -8*24. INSUFFICIENT.
Ans: A
2) Add |x|+|y|=32 and |x|-|y|=16 to get 2|x|=48---->x=-24 or 24. From original equation (x,y)=(-24,-8) or (-24,8) or (24,-8) or (24, 8). Two possible values of xy: 8*24 and -8*24. INSUFFICIENT.
Ans: A
