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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
If x-y=x+y , what is x in terms of y?  [#permalink]

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

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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
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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3565
If x-y=x+y , what is x in terms of y?  [#permalink]

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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
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Manager  B
Joined: 23 Oct 2017
Posts: 61
Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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

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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
$$(\sqrt{x}+\sqrt{y})((√x-√y-1)=0$$
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Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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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 V
Joined: 22 May 2016
Posts: 3565
If x-y=x+y , what is x in terms of y?  [#permalink]

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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.
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Math Revolution GMAT Instructor V
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]

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=>

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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Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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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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GMAT 1: 500 Q39 V21 Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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

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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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Manager  S
Joined: 11 Jun 2018
Posts: 98
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21 Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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

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

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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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Re: If x-y=x+y , what is x in terms of y?  [#permalink]

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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. $$1+y$$

$$x-y=\sqrt{x}+\sqrt{y}$$
$$x-y=\sqrt{x}^2-\sqrt{y}^2…x-y=(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})$$
$$[equate:1,2]\sqrt{x}+\sqrt{y}=(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})…\sqrt{x}-\sqrt{y}=1…\sqrt{x}=1+\sqrt{y}$$ Re: If x-y=x+y , what is x in terms of y?   [#permalink] 13 Sep 2019, 06:22
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