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x2 > y2 and x > –|y|

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GMAT Club Legend
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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] New post 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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Re: x2 > y2 and x > –|y| [#permalink] New post 03 Sep 2018, 10:26
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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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Re: x2 > y2 and x > –|y| [#permalink] New post 03 Sep 2018, 15:40
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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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