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# Is |x^2| - |y^2| = |x^2–y^2| ?

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Intern
Joined: 24 Jul 2012
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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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Question Stats:

49% (02:08) correct 51% (00:55) wrong based on 95 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] 12 Sep 2013, 09:54
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