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# Is |x^2| - |y^2| = |x^2–y^2| ?

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Is |x^2| - |y^2| = |x^2–y^2| ? [#permalink]

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26 Jul 2012, 05:42
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52% (02:07) correct 48% (00:56) wrong based on 156 sessions

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Is |x^2| - |y^2| = |x^2–y^2| ?

(1) x > 0
(2) y < 0
[Reveal] Spoiler: OA
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Re: Is |X^2| - |Y^2| = |X^2–Y^2| ? [#permalink]

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26 Jul 2012, 06:27
Ans is E
Statement 1: x>0; if x = 1 & y =5, both sides are not same. if x = 10 & y =5, both sides are same. Not sufficient
Statement 2: y<0; if x = 1 & y = -5, both sides are not same. if x = 10 & y = -5, both sides are same. Not sufficient

Together x>0 & y<0 again not Sufficient as seen from above examples
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Re: Is |x^2| - |y^2| = |x^2–y^2| ? [#permalink]

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26 Jul 2012, 10:35
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The given equality can be rewritten as $$x^2-y^2=|x^2-y^2|$$.
As $$|a|=a$$ if and only if $$a\geq0$$, the question can be rephrased as "Is $$x^2-y^2\geq0$$ or $$x^2\geq{y^2}$$ ?".

Then, we can easily see that the given pieces of information don't help at all, neither each one alone, nor both together.

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Re: Is |x^2| - |y^2| = |x^2–y^2| ? [#permalink]

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12 Sep 2013, 09:54
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Re: Is |x^2| - |y^2| = |x^2–y^2| ? [#permalink]

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13 Jan 2017, 22:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is |x^2| - |y^2| = |x^2–y^2| ? [#permalink]

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13 Jan 2017, 22:25
The signs of x and y have no bearing on x^2 and y^2 (the only terms in the stem), so the information in the statements is not helpful at all. The answer must be E.
Re: Is |x^2| - |y^2| = |x^2–y^2| ?   [#permalink] 13 Jan 2017, 22:25
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