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# What is the value of x^2 – y^2 ? (1) x^2 + y^2 = 2xy (2) x = |y|

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
What is the value of x^2 – y^2 ? (1) x^2 + y^2 = 2xy (2) x = |y|  [#permalink]

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01 Oct 2017, 23:47
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:15) correct 46% (01:22) wrong based on 144 sessions

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What is the value of x^2 – y^2 ?

(1) x^2 + y^2 = 2xy

(2) x = |y|

_________________
Intern
Joined: 25 Jul 2017
Posts: 46
Re: What is the value of x^2 – y^2 ? (1) x^2 + y^2 = 2xy (2) x = |y|  [#permalink]

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02 Oct 2017, 00:14
1
1/ X^2 + Y^2 = 2XY => X^2-2XY +Y^2 = 0 => (X-Y)^2 = 0 => X=Y => X^2 - Y^2 = 0 => Suff

2/ X=|Y| => X^2 = Y^2 =>X^2 - Y^2 = 0 => Suff

SVP
Joined: 26 Mar 2013
Posts: 2002
What is the value of x^2 – y^2 ? (1) x^2 + y^2 = 2xy (2) x = |y|  [#permalink]

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10 Apr 2018, 19:26
Bunuel wrote:
What is the value of x^2 – y^2 ?

(1) x^2 + y^2 = 2xy

(2) x = |y|

(1) x^2 + y^2 = 2xy

Rearrange the equation: x^2 -2xy + y^2 = 0

(x - y)^2 =0.......x - y =0..then x = y

x^2 – y^2 = x^2 – x^2 = 0

Sufficient

(2) x = |y|

No matter the sign of x or y, it will be always positive as it is raised to power 2

x^2 – y^2 = |y|^2 – y^2 = 0

Sufficient

Manager
Joined: 16 Jan 2018
Posts: 62
Concentration: Finance, Technology
GMAT 1: 600 Q40 V33
Re: What is the value of x^2 – y^2 ? (1) x^2 + y^2 = 2xy (2) x = |y|  [#permalink]

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11 Apr 2018, 18:04
I doubt this is a 700 question specially going by bunuel's standard!

stem - (x+y)(x-y)

1) (x-y)^2 = 0; so (x-y) = 0. so sufficient

2) if y < 0 then stem is (y+(-y)) (y-(-y)) = 0
if y >0 then stem is (y+y)(y-y) = 0 sufficient
Re: What is the value of x^2 – y^2 ? (1) x^2 + y^2 = 2xy (2) x = |y| &nbs [#permalink] 11 Apr 2018, 18:04
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