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

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Intern
Joined: 29 Sep 2009
Posts: 16
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Kudos [?]: 27 [0], given: 3

Is |xy| + xy <= 0? 1/ |x| + xy <= 0 2/ |y| + xy <= [#permalink]

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02 Oct 2009, 01:04
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Is |xy| + xy <= 0?

1/ |x| + xy <= 0
2/ |y| + xy <= 0
Director
Joined: 01 Apr 2008
Posts: 897
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 28

Kudos [?]: 645 [1] , given: 18

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02 Oct 2009, 01:49
1
KUDOS
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, 03:17, edited 1 time in total.
Intern
Joined: 30 Aug 2009
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Kudos [?]: 0 [0], given: 0

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02 Oct 2009, 02:22
Agree.

Its D.
The question basically is whether XY=+ve?
Both are sufficient.
Intern
Joined: 29 Sep 2009
Posts: 16
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Kudos [?]: 27 [0], given: 3

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02 Oct 2009, 03:12
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
Director
Joined: 01 Apr 2008
Posts: 897
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 28

Kudos [?]: 645 [0], given: 18

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02 Oct 2009, 03:18
Thanks andrewng:) btw what is the source?
Intern
Joined: 29 Sep 2009
Posts: 16
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Kudos [?]: 27 [0], given: 3

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02 Oct 2009, 04:24
Economist wrote:
Thanks andrewng:) btw what is the source?

It's from Manhattan archive!
Re: Absolute value   [#permalink] 02 Oct 2009, 04:24
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# Is |xy| + xy <= 0? 1/ |x| + xy <= 0 2/ |y| + xy <=

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