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

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

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New post 13 Dec 2017, 00:41
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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. \(1+y\)

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

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New post 13 Dec 2017, 04:13
1
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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 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
_________________

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that within me there lay an invincible summer.

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

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New post 13 Dec 2017, 17:21
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
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Re: If x-y=x+y , what is x in terms of y? [#permalink]

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New post 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
\((\sqrt{x}+\sqrt{y})((√x-√y-1)=0\)
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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

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New post 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.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

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

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

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New post 06 Apr 2018, 08:00
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] 06 Apr 2018, 08:00
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