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# what is the value of xy?

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what is the value of xy? [#permalink]  16 Jan 2009, 04:37
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16
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kris

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Re: what is the value of xy? [#permalink]  16 Jan 2009, 07:08
krishan wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

take the absolute value out for a second and just solve for X and Y, through algebra manipulation you should arrive at a set of answer such X = 24 and Y = 8. But since we're only interested in the magnitude, X can be +24 or -24 and Y can be +8 or -8.

Plug numbers back to equation 1 you will find that only 1 of X or Y must be negative and the other must be positive in order for it to hold, which means you have (positive number )*(negative number ) = (negative number)

24*8 = 192, but value must be negative, thus -192 is the answer
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Re: what is the value of xy? [#permalink]  16 Jan 2009, 09:56
krishan wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

the 1st is clearly sufficient.
x=-3y; if x<0 y>0 and if x>0, y<0. Either case xy<0. Solving euqation we get xy.
(2)=> let x and y>0.
x+y=32
x-y=16 i.e. x=24 and y=8. So xy is found for x and y >0.
Now, x and y<0
-x-y=32
-x+y=16 i.e. x=-24 and y=-8 again xy is found for x and y both less than 0.
if x> and y<0,
x-y=32
x+y=16 so, x=24 and y=-8.
But thee is no way to say whether xy is greater or less than zero.
Hence, A.
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tusharvk

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Re: what is the value of xy? [#permalink]  16 Jan 2009, 10:20
krishan 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

1: -4x – 12y = 0
x + 3y = 0
x = -3y
y = -x/3
suff cuz either one is -ve and x = l24l and y = l8l.
so xy = -(24x8) = -192

(2) |x| – |y| = 16
|x| = 24 and |y| = 8

Not suff cuz but x and y could have same or different signs.

So A is it.
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Re: what is the value of xy? [#permalink]  16 Jan 2009, 16:56
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

This is a value question.
x and y could be of any sign ( positive or negative)

statement 1. -4 ( x + 3y) = 0
so x + 3y = 0
x = - 3y
which means x and y are different signs

we can find that x = absolute value of 24 and y = absolute value of 8

so xy is - 192.

statement1 is sufficient

statement2.
we can find that x = absolute value of 24 and y = absolute value of 8
but we have no information about the signs of x and y. so xy could be 192 or -192
statement2 is insufficient.

Re: what is the value of xy?   [#permalink] 16 Jan 2009, 16:56
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