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Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0

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S
Joined: 22 Apr 2017
Posts: 115
Location: India
GMAT 1: 620 Q46 V30
GMAT 2: 620 Q47 V29
GMAT 3: 630 Q49 V26
GMAT 4: 690 Q48 V35
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink]

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New post 20 Jan 2018, 20:31
Can anyone tell me the flaw in my logic

|x - y| > |x| - |y|
Squaring both sides
x^2 +y^2-2xy> x^2 +y^2-2|x||y|
simplifying, xy<|x||y|,

It will only be possible when product of xy is -ve. or xy<0, Hence B.
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink]

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New post 22 Jan 2018, 02:27
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ManishKM1 wrote:
Can anyone tell me the flaw in my logic

|x - y| > |x| - |y|
Squaring both sides
x^2 +y^2-2xy> x^2 +y^2-2|x||y|
simplifying, xy<|x||y|,

It will only be possible when product of xy is -ve. or xy<0, Hence B.


Given:
|x - y| > |x| - |y|, you cannot square it. You can square only when you know that both sides are positive. Here, the right hand side may not be positive. For example, if x is 2 and y is 5.
3 > -3
Squaring does not work here since you get 9 > 9 which doesn't hold.
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Re: Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0   [#permalink] 22 Jan 2018, 02:27

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