If x/(x+y) = 6 then y/(y+x) : GMAT Problem Solving (PS)
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# If x/(x+y) = 6 then y/(y+x)

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If x/(x+y) = 6 then y/(y+x) [#permalink]

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08 Feb 2013, 13:32
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If $$\frac{x}{x+y}$$=6 then $$\frac{y}{y+x}$$ =

A -5
B 5/11
C 1
D 11/5
E 5
[Reveal] Spoiler: OA
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink]

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08 Feb 2013, 20:54
x/(x+y) = 6
=> (x+y-y)/(x+y) = 6
=> 1 - y/(x+y) = 6
=> y/(x+y) = -5

Option A
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink]

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09 Feb 2013, 12:03
GyanOne wrote:
x/(x+y) = 6
=> (x+y-y)/(x+y) = 6
=> 1 - y/(x+y) = 6
=> y/(x+y) = -5

Option A

I do not understand this passage
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink]

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09 Feb 2013, 21:25
1
KUDOS
Here is another method:
x/(x+y) = 6
=> x/(x+y) - 1 = 6 - 1
=> (x -x -y)/(x+y) = 5
=> -y/(x+y) = 5
or y/(x+y) -5

Option A
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink]

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16 Feb 2013, 13:48
carcass wrote:
GyanOne wrote:
x/(x+y) = 6
=> (x+y-y)/(x+y) = 6
=> 1 - y/(x+y) = 6
=> y/(x+y) = -5

Option A

I do not understand this passage

x/(x+y) = 6 //this statement is already given in the question
=> (x+y-y)/(x+y) = 6 // this statement adds and subtracts y from the numerator so that we get the form y/(x+y) on one side
=> 1 - y/(x+y) = 6 // this step groups ((x+y)/(x+y) -y/(x+y))
=> y/(x+y) = -5
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink]

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19 Feb 2013, 00:53
Method I:

$$\frac{x}{x+y} = 6$$

Reciprocal both sides

$$\frac{x+y}{x} = \frac{1}{6}$$

$$1 + \frac{y}{x} = \frac{1}{6}$$

$$\frac{y}{x} = \frac{-5}{6}$$

Apply componendo / dividendo

$$\frac{y}{x+y} = \frac{-5}{6-5}$$

$$\frac{y}{x+y} = -5$$

Method II

$$\frac{x}{x+y} = 6$$

$$x+y = \frac{x}{6}$$.............. (1)

$$y = \frac{x}{6} - x$$

$$y = \frac{-5x}{6}$$ ............ (2)

Dividing (2) by (1)

$$\frac{y}{x+y} = \frac{-5x}{6} * \frac{6}{x}$$

$$\frac{y}{x+y} = -5$$
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink]

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08 Jul 2014, 02:21
x/(x+y) = 6
=(x+y-y)/(x+y) = 6
=1 - y/(x+y) = 6
=y/(x+y) = -5 Ans
Option A (-5) is correct..
Re: If x/(x+y) = 6 then y/(y+x)   [#permalink] 08 Jul 2014, 02:21
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