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What is the value of x - y?

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What is the value of x - y?  [#permalink]

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New post 18 Nov 2013, 07:25
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What is the value of x - y?

(1) (x + y)^2 = 4xy

(2) x^2 - y^2 = 0
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Re: What is the value of x - y?  [#permalink]

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New post 18 Nov 2013, 07:30
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Re: What is the value of x - y?  [#permalink]

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New post 07 Sep 2016, 23:29
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A) (x+y)^2 = 4xy => x^2+y^2+2xy = 4xy
=> x^2+y^2 -2xy = 0 => (x-y)^2 =0 i.e. x-y = 0, sufficient

B) x^2-y^2 = 0
(x+y)(x-y)=0
now either of them can be 0 or both of them can be 0, not sufficient

answer is A
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Re: What is the value of x - y?  [#permalink]

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New post 03 Oct 2017, 11:06
Bunuel wrote:
What is the value of x - y?

(1) (x + y)^2 = 4xy --> \(x^2+2xy+y^2=4xy\) --> \(x^2-2xy+y^2=0\) --> \((x-y)^2=0\) --> \(x-y=0\). Sufficient.

(2) x^2 - y^2 = 0 --> \((x-y)(x+y)=0\) --> \(x-y=0\) or \(x+y=0\). Not sufficient.

Answer: A.

Hope it's clear.

Hi,
I am just curious as to why statement 2 isnt sufficient: bcos from statement 2: x-y=0 (i know x+y=0 too but question didn't ask about x+y so I am thinking its answer is irrelevant and that the important question of x-y has been answered). Besides its not like x-y is giving us two answers.
What am I missing here?
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Re: What is the value of x - y?  [#permalink]

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New post 03 Oct 2017, 11:09
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rmamissah wrote:
Bunuel wrote:
What is the value of x - y?

(1) (x + y)^2 = 4xy --> \(x^2+2xy+y^2=4xy\) --> \(x^2-2xy+y^2=0\) --> \((x-y)^2=0\) --> \(x-y=0\). Sufficient.

(2) x^2 - y^2 = 0 --> \((x-y)(x+y)=0\) --> \(x-y=0\) or \(x+y=0\). Not sufficient.

Answer: A.

Hope it's clear.

Hi,
I am just curious as to why statement 2 isnt sufficient: bcos from statement 2: x-y=0 (i know x+y=0 too but question didn't ask about x+y so I am thinking its answer is irrelevant and that the important question of x-y has been answered). Besides its not like x-y is giving us two answers.
What am I missing here?


The point is that from \((x-y)(x+y)=0\) it follows that \(x-y=0\) OR \(x+y=0\) (not and). For example, if x = 1 and y = -1, then x + y = 0 but x - y = 2.

Hope it's clear.
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Re: What is the value of x - y?   [#permalink] 05 Mar 2019, 07:40
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