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Is |xy| + xy <= 0? 1/ |x| + xy <= 0 2/ |y| + xy <=

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Is |xy| + xy <= 0? 1/ |x| + xy <= 0 2/ |y| + xy <= [#permalink] New post 02 Oct 2009, 02:04
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Is |xy| + xy <= 0?

1/ |x| + xy <= 0
2/ |y| + xy <= 0
1 KUDOS received
Director
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Re: Absolute value [#permalink] New post 02 Oct 2009, 02:49
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andrewng wrote:
Is |xy| + xy <= 0?

1/ |x| + xy <= 0
2/ |y| + xy <= 0

IMO D.

This was a killer for me.

Basically the question is asking : Is |xy| + xy = 0, i.e. is xy < 0 ?
This is because, |xy| + xy can only be >=0, it cannot be < 0.

stmt 1.
If x is -ve, -x + xy <= 0 => -x <= -xy => x >= xy => 1 <= y , so y is +ve.
hence, xy < 0.

If x is +ve, x <= -xy => 1 <= -y => -1 >= y , so y is -ve.
hence, xy < 0.

Sufficient.

Similar reasoning for stmt2 by taking y<0 and y>0.

Last edited by Economist on 02 Oct 2009, 04:17, edited 1 time in total.
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Re: Absolute value [#permalink] New post 02 Oct 2009, 03:22
Agree.

Its D.
The question basically is whether XY=+ve?
Both are sufficient.
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Re: Absolute value [#permalink] New post 02 Oct 2009, 04:12
Economist wrote:
andrewng wrote:
Is |xy| + xy <= 0?

1/ |x| + xy <= 0
2/ |y| + xy <= 0

IMO D.

This was a killer for me.

Basically the question is asking : Is |xy| + xy = 0, i.e. is xy < 0 ?
This is because, |xy| + xy can only be >=0, it cannot be < 0.

stmt 1.
If x is -ve, -x + xy <= 0 => -x <= -xy => x >= xy => 1 <= y , so y is +ve.
hence, xy < 0.

If x is +ve, x <= -xy => 1 <= -y => -1 >= y , so y is -ve.
hence, xy < 0.

Sufficient.

Similar reasoning for stmt2 by taking y<0 and y>0.



Brilliant!!! You deserve 1 Kudo.

Thanks
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Re: Absolute value [#permalink] New post 02 Oct 2009, 04:18
Thanks andrewng:) btw what is the source?
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Re: Absolute value [#permalink] New post 02 Oct 2009, 05:24
Economist wrote:
Thanks andrewng:) btw what is the source?


It's from Manhattan archive!
Re: Absolute value   [#permalink] 02 Oct 2009, 05:24
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