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Intern  Joined: 21 Nov 2013
Posts: 12
If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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21 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:46) correct 33% (03:01) wrong based on 310 sessions

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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

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Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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1
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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Karishma
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Intern  Joined: 21 Nov 2013
Posts: 12
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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@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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Director  G
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 564
Location: India
GMAT 1: 780 Q51 V46 Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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2
1
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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Intern  Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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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.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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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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Karishma
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Intern  Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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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.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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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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Karishma
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Manager  B
Joined: 11 Nov 2011
Posts: 60
Location: United States
Concentration: Finance, Human Resources
GPA: 3.33
WE: Consulting (Non-Profit and Government)
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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VeritasPrepKarishma your solution is excellence. I am wondering, how do we know that one form of fraction (you mentioned it as case) is easier to manipulate than another? I tried to solve this problem using the original form of fraction but I ended up nowhere. Do you have the solution using original form of the fraction?
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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evdo wrote:
VeritasPrepKarishma your solution is excellence. I am wondering, how do we know that one form of fraction (you mentioned it as case) is easier to manipulate than another? I tried to solve this problem using the original form of fraction but I ended up nowhere. Do you have the solution using original form of the fraction?

When you need to separate the variables, multiple terms in the numerator are easy to handle since you can split them:

(x+y)/ x = x/x + y/x = 1 + y/x

But if they are in the denominator, you cannot separate them.

You can start with the equations as they are but you will eventually cross multiply to simplify the denominator. If you do different things with the equations, you will get different but equivalent expressions. So a case can be made to do the question by number plugging instead.
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Intern  B
Joined: 07 Jan 2018
Posts: 5
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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Hello,

Could someone explain why is it not possible to assume that: x = n(x+y) and x = m(x-y); so n(x+y) = m(x-y) if we solve this we arrive to x/y = (n+m) / (m-n)

I know it is not the correct answer, but I would like to understand my mistake. Many thanks
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not  [#permalink]

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jmmanquez wrote:
Hello,

Could someone explain why is it not possible to assume that: x = n(x+y) and x = m(x-y); so n(x+y) = m(x-y) if we solve this we arrive to x/y = (n+m) / (m-n)

I know it is not the correct answer, but I would like to understand my mistake. Many thanks

It is not incorrect, it is just not what you need. Different manipulations can lead to different but equivalent expressions.
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Karishma
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Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not   [#permalink] 08 Oct 2018, 02:48
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