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# If x / (x+y) = n, and x / (x-y) = m, then x/y=?

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If x / (x+y) = n, and x / (x-y) = m, then x/y=? [#permalink]  19 Feb 2014, 21:05
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68% (04:39) correct 31% (02:39) wrong based on 29 sessions
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)

A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm
[Reveal] Spoiler: OA

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Re: If x / (x+y) = n, and x / (x-y) = m, then x/y=? [#permalink]  19 Feb 2014, 21:36
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Expert's post
MrWallSt wrote:
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)

A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm

You can do it either algebraically or by assuming numbers:

Algebra:
Note that we are happier with (x+y)/x rather than x/(x+y) since in the former case we can make manipulations easily. So let's take the inverse of both n and m

\frac{1}{n} = \frac{(x+y)}{x} = 1 + \frac{y}{x} ....(I)
\frac{1}{m} = \frac{(x-y)}{x} = 1 - \frac{y}{x} .....(II)

Since we have both m and n in our answer, lets subtract II from I to get

\frac{1}{n} - \frac{1}{m} = \frac{2y}{x}

\frac{(m-n)}{2mn} = \frac{y}{x}

\frac{x}{y} = \frac{2mn}{(m-n)}

Or Plug in numbers: x = 2, y = 1
n = x/(x+y) = 2/3
m = x/(x-y) = 2

x/y = 2

Now put n = 2/3 and m = 2 in the options. Only option (D) gives you x/y = 2.

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Re: If x / (x+y) = n, and x / (x-y) = m, then x/y=? [#permalink]  19 Feb 2014, 21:59
@Karishma thanks for the post. Your blogs are extremely helpful btw. I am not sure if you ever followed up about your CFA, but I hope that went well for you.
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Re: If x / (x+y) = n, and x / (x-y) = m, then x/y=? [#permalink]  19 Feb 2014, 22:32
1
KUDOS
MrWallSt wrote:
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)

A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm

Let us say x = 3, y = 1, n = 0.75, m = 1.5

x/y = 3

(A) 3(3/2)(3/4) = 9/8 (Eliminated)
(B) 3(3/2) 2(3/4) = (Eliminated)
(C) (3/4) (3/2 + 2)/2 = (Eliminated)
(D) 2(3/4)(3/2)/(.75) = 3 (BINGO!)
(E) Eliminated

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Re: If x / (x+y) = n, and x / (x-y) = m, then x/y=?   [#permalink] 19 Feb 2014, 22:32
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# If x / (x+y) = n, and x / (x-y) = m, then x/y=?

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