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# What is the value of x - y?

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Intern
Joined: 16 Nov 2013
Posts: 29
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
What is the value of x - y? [#permalink]

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18 Nov 2013, 07:25
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45% (medium)

Question Stats:

53% (00:50) correct 47% (01:06) wrong based on 239 sessions

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What is the value of x - y?

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

(2) x^2 - y^2 = 0
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 44401
Re: What is the value of x - y? [#permalink]

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18 Nov 2013, 07:30
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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.

Hope it's clear.
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Current Student
Joined: 08 Jun 2013
Posts: 34
Re: What is the value of x - y? [#permalink]

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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

Intern
Joined: 05 Sep 2017
Posts: 1
Re: What is the value of x - y? [#permalink]

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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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 44401
Re: What is the value of x - y? [#permalink]

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03 Oct 2017, 11:09
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Expert's post
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.

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.
_________________
Re: What is the value of x - y?   [#permalink] 03 Oct 2017, 11:09
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