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# x2 > y2 and x > –|y|

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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x2 > y2 and x > –|y| [#permalink]  02 Sep 2018, 07:32
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Question Stats:

61% (00:42) correct 38% (00:12) wrong based on 18 sessions
$$x^2 > y^2$$ and $$x > -|y|$$

 Quantity A Quantity B x y

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Re: x2 > y2 and x > –|y| [#permalink]  03 Sep 2018, 10:26
1
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sandy wrote:
$$x^2 > y^2$$ and $$x > -|y|$$

 Quantity A Quantity B x y

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Given $$x^2 > y^2$$ and $$x > -|y|$$

From $$x^2 > y^2$$ => $$x^2$$ - $$y^2$$ > 0 => ( x + y ) ( x - y ) > 0.

Here ( x + y ) ( x - y ) > 0 either both should be +ve or both -ve to be greater than 0.

But from $$x > -|y|$$ we get ( x + y ) > 0 ( Note here |y| is converted to y )

Since we came to know that ( x + y ) > 0 then must be ( x - y ) > 0

So ( x - y ) > 0 => x > y.

A.
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Joined: 28 Aug 2018
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Re: x2 > y2 and x > –|y| [#permalink]  03 Sep 2018, 15:40
1
KUDOS
if $$x^2>y^2$$, then $$|x|>|y|$$

if x>0 y>0, then x>y since $$|x|>|y|$$;

if x>0 y<0, then x>y. Because $$x>-|y|$$ and $$-|y|=-(-y)=y$$;

x<0 y>0 is not possible. Because $$x>-|y|$$ and $$-|y|=-y$$, so $$x>-y$$, which means $$|x|<|y|$$, but we already know $$|x|>|y|$$, so this is a contradiction;

x<0 y<0 is also not possbile, Because $$x>-|y|$$ and $$-|y|=-(-y)=y$$ therefore x>y but then $$|x|<|y|$$, and we already know $$|x|>|y|$$, so this is a contradiction;
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Re: x2 > y2 and x > –|y|   [#permalink] 03 Sep 2018, 15:40
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