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

[Harish Dorai]

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

(1) -4x - 12y = 0

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

Can some one help in solving this?

[ap]

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

(1) -4x - 12y = 0

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

Sholdn't the answer be "D"

You have two unknowns and two equations with each option.

[Guest]

Is the answer (E)?

[a7lee]

For A)

x = -3y

Plug this into the original equation |-3y| + |y| = 32 ---> 3y + y = 32 ----> 4y = 32 ---> y = 8 so x = -3(8) = -24 Thus xy = -24(8).

Sufficient.

For B)

You can add the original and B's equation.

|x| + |y| = 32
+|x| - |y| = 16
--------------------
2|x| = 48
|x| = 24 ---> |y| = 8. However |x| means +/- (x) and |y| means +/- (y). So xy could be.....24(8) or -24(8) or -24(-8) or 24(-8).

Insufficient.

Answer is A.

[Guest]

a7lee,

|-3y| + |y| = 32 There are two possible values of 8 or -8. I believe (A) is not sufficient.

[Guest]

Oops, in the last post I meant, there are two possible values of y 8 or -8. So (A) cannot be sufficient.

[a7lee]

Right..y could be 8 or -8. But the A's equation states that x= -3y. So if y is 8 then x would -24. If y is -8 then x would be 24. In either case xy would end up being less than 0. (-24*8) or (24*-8).

B's equation you don't know whether the xy > 0 or xy < 0.

[Guest]

Good point - product would always be -24X8. I didn't notice that. Thanks