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If x-y=x+y , what is x in terms of y?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4705
GPA: 3.82
If x-y=x+y , what is x in terms of y? [#permalink]

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12 Dec 2017, 23:41
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[GMAT math practice question]

If $$x-y=\sqrt{x}+\sqrt{y}$$ , what is $$\sqrt{x}$$ in terms of $$y$$?

A. $$1+\sqrt{y}$$
B. $$1-\sqrt{y}$$
C. $$\sqrt{y}-1$$
D. $$1-y$$
E. $$1+y$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5537
Re: If x-y=x+y , what is x in terms of y? [#permalink]

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13 Dec 2017, 03:13
1
KUDOS
Expert's post
MathRevolution wrote:
[GMAT math practice question]

If $$x-y=\sqrt{x}+\sqrt{y}$$ , what is $$\sqrt{x}$$ in terms of $$y$$?

A. $$1+\sqrt{y}$$
B. $$1-\sqrt{y}$$
C. $$\sqrt{y}-1$$
D. $$1-y$$
E. $$1+y$$

Hi..
Since √x and √y are there, we can convert x and y too in those terms..

x-y=√x+√y...$$√x^2-√y^2=√x+√y$$...
(√x-√y)(√x+√y)=√x+√y...
(√x-√y)(√x+√y)-(√x+√y)=0..
(√x-√y-1)(√x+√y)=0
So either √x=1+√y or √x=-√y
A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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VP
Joined: 22 May 2016
Posts: 1259
If x-y=x+y , what is x in terms of y? [#permalink]

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13 Dec 2017, 08:56
chetan2u wrote:
MathRevolution wrote:
[GMAT math practice question]

If $$x-y=\sqrt{x}+\sqrt{y}$$ , what is $$\sqrt{x}$$ in terms of $$y$$?

A. $$1+\sqrt{y}$$
B. $$1-\sqrt{y}$$
C. $$\sqrt{y}-1$$
D. $$1-y$$
E. $$1+y$$

Hi..
Since √x and √y are there, we can convert x and y too in those terms..

x-y=√x+√y...$$√x^2-√y^2=√x+√y$$...
(√x-√y)(√x+√y)=√x+√y...
(√x-√y)(√x+√y)-(√x+√y)=0..
(√x-√y-1)(√x+√y)=0
So either √x=1+√y or √x=-√y
A

chetan2u , how did you get from here
(√x-√y)(√x+√y)-(√x+√y)=0
To here?
(√x-√y-1)(√x+√y)=0
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Manager
Joined: 23 Oct 2017
Posts: 63
Re: If x-y=x+y , what is x in terms of y? [#permalink]

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13 Dec 2017, 16:21
x-y= √x+√y
Look at equation x-y from the perspective as a^2-b^2=(a+b)(a-b)
Here a= √x and b= √y
Thus x-y=(√x- √y)(√x+ √y)
√x- √y=1=> √x= 1+√y
Math Expert
Joined: 02 Aug 2009
Posts: 5537
Re: If x-y=x+y , what is x in terms of y? [#permalink]

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13 Dec 2017, 16:36
1
KUDOS
Expert's post
genxer123 wrote:
chetan2u wrote:
MathRevolution wrote:
[GMAT math practice question]

If $$x-y=\sqrt{x}+\sqrt{y}$$ , what is $$\sqrt{x}$$ in terms of $$y$$?

A. $$1+\sqrt{y}$$
B. $$1-\sqrt{y}$$
C. $$\sqrt{y}-1$$
D. $$1-y$$
E. $$1+y$$

Hi..
Since √x and √y are there, we can convert x and y too in those terms..

x-y=√x+√y...$$√x^2-√y^2=√x+√y$$...
(√x-√y)(√x+√y)=√x+√y...
(√x-√y)(√x+√y)-(√x+√y)=0..
(√x-√y-1)(√x+√y)=0
So either √x=1+√y or √x=-√y
A

chetan2u , how did you get from here
(√x-√y)(√x+√y)-(√x+√y)=0
To here?
(√x-√y-1)(√x+√y)=0

hi..
(√x-√y)(√x+√y)-(√x+√y)=0
take out (√x+√y) as it is common
$$(\sqrt{x}+\sqrt{y})((√x-√y-1)=0$$
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Manager
Joined: 13 Jun 2012
Posts: 185
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: If x-y=x+y , what is x in terms of y? [#permalink]

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13 Dec 2017, 17:45
1
KUDOS
This is true x−y=√x+√y when x=25; y=16

25-16=√25+√16
9=9
So, √X or √25= 5
only A gives 5 as a answer √y+1= √16+1=4+1=5
VP
Joined: 22 May 2016
Posts: 1259
If x-y=x+y , what is x in terms of y? [#permalink]

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13 Dec 2017, 17:48
chetan2u wrote:

hi..
(√x-√y)(√x+√y)-(√x+√y)=0
take out (√x+√y) as it is common
$$(\sqrt{x}+\sqrt{y})((√x-√y-1)=0$$

chetan2u , thanks. And now I shall see if I can get my brain to unfreeze.
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4705
GPA: 3.82
Re: If x-y=x+y , what is x in terms of y? [#permalink]

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15 Dec 2017, 07:27
=>

Since $$x-y=(\sqrt{x}+ \sqrt{y})(\sqrt{x}-\sqrt{y}) and x-y=\sqrt{x}+\sqrt{y}, we have \sqrt{x} -\sqrt{y} = 1. Thus \sqrt{x} = 1+\sqrt{y}.$$

Therefore, the answer is A.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
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Re: If x-y=x+y , what is x in terms of y?   [#permalink] 15 Dec 2017, 07:27
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