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If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not

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If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post 19 Feb 2014, 21:05
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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 = ? (|x| does not [#permalink] New post 19 Feb 2014, 21:36
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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

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

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

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

Answer (D)

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.

Hence answer (D)
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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post 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 = ? (|x| does not [#permalink] New post 19 Feb 2014, 22:32
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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

Hence answer is D
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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post 24 May 2015, 21:24
CrackVerbalGMAT wrote:
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

Hence answer is D


Sorry for opening a long answered question.

with algebric solution, i am getting many answers in terms of m & n. so the problem needed to be solved by picking numbers.
when we pick x = 3 & y = 1. I am getting B & D both as answer and but with x = 2 & y= 3. I am getting D as an answer. shouldnt it be unique for all numbers, since there is no restriction (like x, y = consequetive or x>y or viceversa) on picking numbers.
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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post 24 May 2015, 21:53
Expert's post
Alaukik wrote:
CrackVerbalGMAT wrote:
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

Hence answer is D


Sorry for opening a long answered question.

with algebric solution, i am getting many answers in terms of m & n. so the problem needed to be solved by picking numbers.
when we pick x = 3 & y = 1. I am getting B & D both as answer and but with x = 2 & y= 3. I am getting D as an answer. shouldnt it be unique for all numbers, since there is no restriction (like x, y = consequetive or x>y or viceversa) on picking numbers.


When you take one of the numbers as 1 or 0, or when you take numbers to be equal, you could get multiple options satisfying your conditions.

For example, if n = 1
3n/(m+n) will give the same result as 3/(m+n).

Sometimes, you will get the same answer from multiple options if the options are written intelligently. So you could need to try out 2 or even 3 sets of values.
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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post 25 May 2015, 03:57
VeritasPrepKarishma wrote:
When you take one of the numbers as 1 or 0, or when you take numbers to be equal, you could get multiple options satisfying your conditions.

For example, if n = 1
3n/(m+n) will give the same result as 3/(m+n).

Sometimes, you will get the same answer from multiple options if the options are written intelligently. So you could need to try out 2 or even 3 sets of values.


well the question states xy != 0, so x or y cant be 0. also |x| != |y| so they cant be equal either.

I was hoping for a more bullet proof solution for this question. as 2 sets will take more time. we will get answer but at a huge expense of time.
Expert Post
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Joined: 16 Oct 2010
Posts: 5739
Location: Pune, India
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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post 25 May 2015, 19:25
Expert's post
Alaukik wrote:
VeritasPrepKarishma wrote:
When you take one of the numbers as 1 or 0, or when you take numbers to be equal, you could get multiple options satisfying your conditions.

For example, if n = 1
3n/(m+n) will give the same result as 3/(m+n).

Sometimes, you will get the same answer from multiple options if the options are written intelligently. So you could need to try out 2 or even 3 sets of values.


well the question states xy != 0, so x or y cant be 0. also |x| != |y| so they cant be equal either.

I was hoping for a more bullet proof solution for this question. as 2 sets will take more time. we will get answer but at a huge expense of time.


Note that it is a generic comment about number plugging - not just specific to this question.

Also, I have given the algebra solution above - as "bulletproof" as you can get.
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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not   [#permalink] 25 May 2015, 19:25
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