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If x/(x+y) = 6 then y/(y+x)

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exploringm
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If x/(x+y) = 6 then y/(y+x) [#permalink] New post   08 Feb 2013, 14:32
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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
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A
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PareshGmat
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink] New post   19 Feb 2013, 01:53
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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] New post   08 Feb 2013, 21:54
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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] New post   09 Feb 2013, 13:03
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] New post   09 Feb 2013, 22:25
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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] New post   16 Feb 2013, 14:48
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] New post   08 Jul 2014, 03:21
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] New post   10 Apr 2017, 20:02
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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

Final Answer:
Show Spoiler
A


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Re: If x/(x+y) = 6 then y/(y+x) [#permalink] New post   18 Apr 2017, 16:20
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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] New post   26 Nov 2018, 16:04
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) [#permalink] New post   15 Apr 2020, 20:56
x/(x+y) = 6
or, (x+y-y)/(x+y) = 6
or, 1 - y/(x+y) = 6
or, y/(x+y) = -5

correct answer A
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink] New post   04 Aug 2020, 23:14
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


Asked: If \(\frac{x}{x+y}\)=6 then \(\frac{y}{y+x}\) =

\(\frac{x}{x+y}\)=6
\(1 - \frac{x}{x+y} = \frac{y}{y+x} = 1- 6 = - 5\)

IMO A
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink] New post   18 Dec 2020, 08:09
Dear BrentGMATPrepNow, could you please help me with my questions below and tell me the related concepts? Thanks for any answers in advance!

In @PareshGmat's solution, how y/x+y becomes -5/6-5?

In the previous line, he rephrases the main equation, such as y/x = -5/6
so, can we say y = -5 and x= 6?
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink] New post   19 Dec 2020, 07:08
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sjuniv32 wrote:
Dear BrentGMATPrepNow, could you please help me with my questions below and tell me the related concepts? Thanks for any answers in advance!

In @PareshGmat's solution, how y/x+y becomes -5/6-5?

In the previous line, he rephrases the main equation, such as y/x = -5/6
so, can we say y = -5 and x= 6?


Once we know that y/x = -5/6, there are infinitely many possible pairs of values for x and y. Fortunately, every pair of values yields the same value of y/(x+y)
For example, if y/x = -5/6, then it COULD be the case that y = -5 and x = 6, in which case y/(x+y) = -5/(6 + -5) = -5.
It could also be the case that y = -10 and x = 12, in which case y/(x+y) = -10/(12 + -10) = -10/2 = -5.
Or it could be the case that y = -15 and x = 18, in which case y/(x+y) = -15/(18 + -15) = -15/3 = -5.
And so on
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink] New post   11 Sep 2023, 09:21
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

Plug in....

Let , x = 6 and y = -5

Thus, \(\frac{x}{x+y}=\frac{6}{(6-5)}\)

Now, \(\frac{y}{y+x}\) = \(\frac{-5}{(-5+6)}=-5\), Answer must be (A)
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Re: If x/(x+y) = 6 then y/(y+x) [#permalink] New post   11 Sep 2023, 12:03
=>x/(x+y) = 6
multiplying -1 on both sides
=>-x/(x+y) = -6
adding 1 on both sides
=> 1-[x/(x+y)] = 1-6 => (x+y-x)/[x+y]=-5
=> y/x+y = -5

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