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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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New post 08 Feb 2013, 13:32
4
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A
B
C
D
E

Difficulty:

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Question Stats:

78% (01:27) correct 22% (01:39) wrong based on 206 sessions

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

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New post 08 Feb 2013, 20:54
1
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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New post 09 Feb 2013, 12:03
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Re: If x/(x+y) = 6 then y/(y+x)  [#permalink]

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New post 09 Feb 2013, 21:25
1
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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New post 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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New post 19 Feb 2013, 00:53
2
2
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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New post 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..
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Re: If x/(x+y) = 6 then y/(y+x)  [#permalink]

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New post 10 Apr 2017, 19:02
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1
Hi All,

This question can be solved rather easily by TESTing VALUES.

We're told that (X)/(X+Y) = 6

IF....
X = 6
Y = -5
(6)/(6 - 5) = 6

The question asks for the value of (Y)/(Y+X).... (-5)/(-5 + 6) = -5/1 = -5

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

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New post 18 Apr 2017, 15:20
2
1
exploringm wrote:
If \(\frac{x}{x+y}\)=6 then \(\frac{y}{y+x}\) =

A -5
B 5/11
C 1
D 11/5
E 5


We can simplify the given equation:

x/(x+y) = 6

x = 6x + 6y

-5x = 6y

x = 6y/-5 = -6y/5

We can substitute -6y/5 for x in the expression y/(y+x) and we have:

y/(y + -6y/5)

y/(5y/5 - 6y/5)

y/(-y/5) = 5y/-y = -5

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

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New post 26 Nov 2018, 15:04
Manipulate equation 1, to get parts of 2 [y/(y+x)]

x/(x+y) = 6 this is equivalent to x+y = x/6 (A)
Now to get the numerator of equation 2, here "y" from the equation before
y= x/6 - x
simplified y = -5x/6 (B)

SUB (A) and (B) into original equation 2
(-5x/6)(6/x)
Therefore,
y/(x+y) = -5
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Re: If x/(x+y) = 6 then y/(y+x) &nbs [#permalink] 26 Nov 2018, 15:04
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