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# Is |x-y| > |x| - |y|? 1) y<x 2) xy<0 I know the

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Director
Joined: 08 Feb 2007
Posts: 610
Location: New Haven, CT
Followers: 5

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

Is |x-y| > |x| - |y|? 1) y<x 2) xy<0 I know the [#permalink]

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29 Jul 2007, 09:31
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Is |x-y| > |x| - |y|?

1) y<x

2) xy<0

I know the mistake I made but thought this was a good question to post. Also, I want to see if some has a quicker approach than picking #s. I am sure someone does.
Senior Manager
Joined: 28 Feb 2007
Posts: 304
Followers: 1

Kudos [?]: 40 [0], given: 0

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29 Jul 2007, 10:19
B.

st1) x-y>0 : INSUFFbecause for any positive numbers- NO
but if Y is negative then YES

st2) Either X or Y negative so SUFF.
Manager
Joined: 08 Jul 2007
Posts: 173
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Kudos [?]: 8 [0], given: 0

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29 Jul 2007, 11:55
B.

Square both sides of the equation and you get (x^2)-2xy+(y^2)>(x^2)-2|x||y|+(y^2). Simplifying yields -2xy>-2|x||y|. Divide by -2 and you get xy<|x||y|. So for this to hold, x has to be negative or y has to be negative. So the question is, is xy negative? Only B answers this.
Director
Joined: 08 Feb 2007
Posts: 610
Location: New Haven, CT
Followers: 5

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

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29 Jul 2007, 12:30
Thank you Briks and UMB. Briks I love your method.
29 Jul 2007, 12:30
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