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Data Sufficiency questions 700 level - problem

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by ashwinhirawat » Sun Apr 22, 2012 1:15 pm
|x| + |y| = 32 ; what is the value of xy ?

1. -4x - 12y = 0

2. |x| -|y| = 16

I solved it as follows -

Statement 1:
x = -3y
Original Statement :
x + y = 32 Using statement 1. y = -16
-x +y = 32 Using Statement 1. y = 8
x - y = 32 Using Statement 2. y = -8

And so 1 is not sufficient . However the Original Answer is A

They do not consider all 3 cases that I did. Is it wrong to consider all the cases as I did ?
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Source: — Data Sufficiency |
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by seal4913 » Sun Apr 22, 2012 3:12 pm
If x = -3y.

Then you have |x| or |-x|. So |-3y| = 3y and |-(-3y)| = 3y
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by hackscript » Mon Apr 23, 2012 4:24 am
Considering (1)
x=-3y, so if x is positive y is negative

Considering x positive: x-y=32 and x=-3y solving, y=-8 and x=24
Considering x negative: -x+y=32 and x=-3y solving, y=8 and x=-24

The product is the same so (1) is suf

Considering (2)

Adding both equations, x=24 or x=-24 and so y=8 or y=-8
Can't no if product is 8*24 or -8*24

so (2) is insuf

Answer: A
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by GMATGuruNY » Mon Apr 23, 2012 4:40 am
I posted an explanation here:

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