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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: 8017
GMAT 1: 760 Q51 V42
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If x-y=x+y , what is x in terms of y?  [#permalink]

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13 Dec 2017, 00:41
13
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:56) correct 43% (02:31) wrong based on 128 sessions

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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. $$1+y$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7991 If x-y=x+y , what is x in terms of y? [#permalink] ### Show Tags 13 Dec 2017, 04:13 3 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 $$\sqrt{x}$$ and $$\sqrt{y}$$ are there, we can convert x and y too in those terms.. $$x-y=\sqrt{x}+\sqrt{y}$$... $$\sqrt{x^2}-\sqrt{y^2}=\sqrt{x}+\sqrt{y}$$... $$(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})=\sqrt{x}+\sqrt{y}$$... $$(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})-(\sqrt{x}+\sqrt{y})=0$$... $$(\sqrt{x}-\sqrt{y}-1)(\sqrt{x}+\sqrt{y})=0$$... .. So either $$\sqrt{x}=\sqrt{y}+1$$ or $$\sqrt{x}=-\sqrt{y}$$ A _________________ Senior SC Moderator Joined: 22 May 2016 Posts: 3565 If x-y=x+y , what is x in terms of y? [#permalink] ### Show Tags 13 Dec 2017, 09:56 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 _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver Manager Joined: 23 Oct 2017 Posts: 61 Re: If x-y=x+y , what is x in terms of y? [#permalink] ### Show Tags 13 Dec 2017, 17:21 2 1 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: 7991 Re: If x-y=x+y , what is x in terms of y? [#permalink] ### Show Tags 13 Dec 2017, 17:36 1 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 $$(\sqrt{x}+\sqrt{y})((√x-√y-1)=0$$ _________________ Manager Joined: 13 Jun 2012 Posts: 199 Location: United States WE: Supply Chain Management (Computer Hardware) Re: If x-y=x+y , what is x in terms of y? [#permalink] ### Show Tags 13 Dec 2017, 18:45 1 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 Senior SC Moderator Joined: 22 May 2016 Posts: 3565 If x-y=x+y , what is x in terms of y? [#permalink] ### Show Tags 13 Dec 2017, 18:48 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. _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x-y=x+y , what is x in terms of y? [#permalink] ### Show Tags 15 Dec 2017, 08:27 => 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. Answer: A _________________ 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. "Only$79 for 1 month Online Course"
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Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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06 Apr 2018, 08:00
1
Turkish wrote:
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

How the hell did you think of these numbers.. amazing.. any advise?
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Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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14 Jan 2019, 08:11
chetan2u Please confirm if my approach is correct

x-y= √x+√y

Squaring both sides

X^2-y^2= x + y
(X+Y)(X-Y)=X+Y
X+Y=(X+Y)/(X+Y)
X+Y=1
X=1+Y

Square root both sides

√x=1 +√y
Math Expert
Joined: 02 Aug 2009
Posts: 7991
Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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14 Jan 2019, 10:01
Manat wrote:
chetan2u Please confirm if my approach is correct

x-y= √x+√y

Squaring both sides

X^2-y^2= x + y
(X+Y)(X-Y)=X+Y
X+Y=(X+Y)/(X+Y)
X+Y=1
X=1+Y

Square root both sides

√x=1 +√y

No..
When you square two sides..
x-y= √x+√y. => $$(x-y)^2=(√x+√y)^2.....x^2+y^2-2xy=x+y+2√(xy)$$
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Posts: 98
Schools: DeGroote "22 (S)
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Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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14 Jan 2019, 10:14
chetan2u wrote:
Manat wrote:
chetan2u Please confirm if my approach is correct

x-y= √x+√y

Squaring both sides

X^2-y^2= x + y
(X+Y)(X-Y)=X+Y
X+Y=(X+Y)/(X+Y)
X+Y=1
X=1+Y

Square root both sides

√x=1 +√y

No..
When you square two sides..
x-y= √x+√y. => $$(x-y)^2=(√x+√y)^2.....x^2+y^2-2xy=x+y+2√(xy)$$

Right! i understood your solution,

Is the below solution correct

x-y=√x+√y

√x^2−√y^2=√x+√y

(√x-√y)(√x+√y)=√x+√y

(√x-√y)=(√x+√y)/(√x+√y)

√x-√y=1

√x=1+√y
Director
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Location: India
Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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14 Jan 2019, 10:45
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. $$1+y$$

Took values and solved
$$x-y=\sqrt{x}+\sqrt{y}$$
$$16-9=\sqrt{16}+\sqrt{9}$$

$$\sqrt{x}$$ = $$1+\sqrt{y}$$
$$\sqrt{16}$$ = $$1+\sqrt{9}$$

4 = 1+3

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Math Expert
Joined: 02 Aug 2009
Posts: 7991
Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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14 Jan 2019, 10:48
1
Manat wrote:
chetan2u wrote:
Manat wrote:
chetan2u Please confirm if my approach is correct

x-y= √x+√y

Squaring both sides

X^2-y^2= x + y
(X+Y)(X-Y)=X+Y
X+Y=(X+Y)/(X+Y)
X+Y=1
X=1+Y

Square root both sides

√x=1 +√y

No..
When you square two sides..
x-y= √x+√y. => $$(x-y)^2=(√x+√y)^2.....x^2+y^2-2xy=x+y+2√(xy)$$

Right! i understood your solution,

Is the below solution correct

x-y=√x+√y

√x^2−√y^2=√x+√y

(√x-√y)(√x+√y)=√x+√y

(√x-√y)=(√x+√y)/(√x+√y)

√x-√y=1

√x=1+√y

Yes that is correct...
However a point ..
(√x-√y)(√x+√y)=√x+√y..
Do not cross multiply as you do not know whether √x=√y=0..
So you have two answers..one as you have found and other could be √x=√y=0...
But only one option is given so it is ok
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Location: United States
Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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13 Sep 2019, 06:22
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. $$1+y$$

$$[1]x-y=\sqrt{x}+\sqrt{y}$$
$$[2]x-y=\sqrt{x}^2-\sqrt{y}^2…x-y=(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})$$
$$[equate:1,2]\sqrt{x}+\sqrt{y}=(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})…\sqrt{x}-\sqrt{y}=1…\sqrt{x}=1+\sqrt{y}$$

Re: If x-y=x+y , what is x in terms of y?   [#permalink] 13 Sep 2019, 06:22
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