If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not : GMAT Problem Solving (PS)
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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]

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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]

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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 21 Nov 2013 Posts: 13 Followers: 0 Kudos [?]: 19 [0], given: 9 Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] ### Show Tags 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. _________________ Any and all kudos are greatly appreciated. Thank you. Senior Manager Affiliations: CrackVerbal Joined: 03 Oct 2013 Posts: 356 Location: India GMAT 1: 780 Q51 V46 Followers: 69 Kudos [?]: 308 [1] , given: 5 Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] ### Show Tags 19 Feb 2014, 22:32 1 This post received 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 Hence answer is D _________________ For 5 common traps on CR check here : http://gmatonline.crackverbal.com/p/gmat-critical-reasoning For sentence correction videos check here - http://gmatonline.crackverbal.com/p/gmat-sentence-correction Learn all PS and DS strategies here- http://gmatonline.crackverbal.com/p/mastering-quant-on-gmat For more info on GMAT and MBA, follow us on @AskCrackVerbal Current Student Joined: 01 Aug 2014 Posts: 41 Location: India GPA: 3.65 Followers: 0 Kudos [?]: 13 [0], given: 46 Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] ### Show Tags 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7125 Location: Pune, India Followers: 2137 Kudos [?]: 13667 [0], given: 222 Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] ### Show Tags 24 May 2015, 21:53 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]

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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.
Veritas Prep GMAT Instructor
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Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]

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25 May 2015, 19:25
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 11 Nov 2011 Posts: 76 Location: United States Concentration: Finance, Human Resources GPA: 3.33 WE: Consulting (Non-Profit and Government) Followers: 1 Kudos [?]: 9 [1] , given: 86 Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] ### Show Tags 02 Aug 2015, 05:55 1 This post received KUDOS 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 Joined: 16 Oct 2010 Posts: 7125 Location: Pune, India Followers: 2137 Kudos [?]: 13667 [2] , given: 222 Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] ### Show Tags 02 Aug 2015, 22:30 2 This post received KUDOS Expert's post 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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