NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 13:10 It is currently 26 Apr 2024, 13:10
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
MrWallSt
Intern
Intern
Joined: 21 Nov 2013
Posts: 11
Own Kudos [?]: 71 [61]
Given Kudos: 9
Send PM
If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   19 Feb 2014, 22:05
1
Kudos
60
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

63% (02:43) correct 37% (03:11) wrong based on 619 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [17]
Given Kudos: 427
Location: Pune, India
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   19 Feb 2014, 22:36
13
Kudos
4
Bookmarks
Expert Reply
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)
General Discussion
avatar
MrWallSt
Intern
Intern
Joined: 21 Nov 2013
Posts: 11
Own Kudos [?]: 71 [0]
Given Kudos: 9
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   19 Feb 2014, 22:59
@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.
User avatar
L
CrackverbalGMAT
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4946
Own Kudos [?]: 7629 [4]
Given Kudos: 215
Location: India
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   19 Feb 2014, 23:32
3
Kudos
1
Bookmarks
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
avatar
Alaukik
Intern
Intern
Joined: 01 Aug 2014
Posts: 36
Own Kudos [?]: 16 [0]
Given Kudos: 46
Location: India
Schools: McDonough '18 (M)
GPA: 3.65
Send PM
GMAT ToolKit User
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   24 May 2015, 22:24
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.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [1]
Given Kudos: 427
Location: Pune, India
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   24 May 2015, 22:53
1
Bookmarks
Expert Reply
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.
avatar
Alaukik
Intern
Intern
Joined: 01 Aug 2014
Posts: 36
Own Kudos [?]: 16 [0]
Given Kudos: 46
Location: India
Schools: McDonough '18 (M)
GPA: 3.65
Send PM
GMAT ToolKit User
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   25 May 2015, 04:57
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.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [0]
Given Kudos: 427
Location: Pune, India
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   25 May 2015, 20:25
Expert Reply
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.
User avatar
B
evdo
Intern
Intern
Joined: 11 Nov 2011
Posts: 45
Own Kudos [?]: 19 [0]
Given Kudos: 101
Location: United States
Concentration: Finance, Human Resources
Schools: Urbana-Champaign '19
GPA: 3.33
WE:Consulting (Non-Profit and Government)
Send PM
GMAT ToolKit User
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   02 Aug 2015, 06:55
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?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [3]
Given Kudos: 427
Location: Pune, India
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   02 Aug 2015, 23:30
3
Kudos
Expert Reply
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.
avatar
B
jmmanquez
Intern
Intern
Joined: 07 Jan 2018
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 7
Schools: Kellogg '21 (WL) LBS '21 (WL) Duke '21 (WL)
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   07 Oct 2018, 11:40
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
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [1]
Given Kudos: 427
Location: Pune, India
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   08 Oct 2018, 02:48
1
Kudos
Expert Reply
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.
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3968 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   05 Aug 2020, 00:14
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


Asked: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not equal |y|, xy does not equal 0)

Let us take x = 3; y = 2
x/y = 3/2 = 1.5
3/5 = n = .6
2/1 = m = 2

A. 3mn/2
3*2*.6/2 = 1.8; NO
B. (3m)/(2n)
6*1.2 = 7.2; NO
C. (n * (m+2))/2
.6*4/2 = 1.2; NO
D. 2nm / (m-n)
2*.6*2/(2-.6) = 2.4/1.4 = 12/7; NO
E. (n^2 - m^2) / nm
(.36 - 4 )1.2 ; NO

MrWallSt
All answers seem incorrect.
Please check.
User avatar
G
sambitspm
Senior Manager
Senior Manager
Joined: 05 Aug 2019
Posts: 317
Own Kudos [?]: 279 [0]
Given Kudos: 130
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   05 Aug 2020, 00:37
Kindly see the attachment.
It took me around 2:45 min to solve this.

At first, my answer didn't match any of the options. I tried checking my calculation but didn't get to the right choice. Lastly, I went to replacing m and n in options and landed in D. Option D was my first guess, but since it was not exam mode, I was inclined on solving this.

VeritasKarishma, your both approaches help to get a new perspective on this question.
Attachments

1.jpeg
1.jpeg [ 100.83 KiB | Viewed 6908 times ]

User avatar
P
rxb266
Manager
Manager
Joined: 30 Nov 2018
Posts: 202
Own Kudos [?]: 149 [1]
Given Kudos: 79
Location: India
Concentration: Strategy, Marketing
Schools: HEC MiM '21 HEC Sept'22 Intake ISB '24 Rotman '24
GPA: 4
Send PM
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   05 Aug 2020, 09:27
1
Kudos
This is the simplest question

substitute values to each variable and check with the option provided

assuming x=5 and y = 1
m =5/4 and n=5/6

and my x/y should be = 5 (ie,5/1)

only in option D when i substitute the variables I get the value as 5.. Hence my answer is D

(In Gmat the time is a luxury.. try to avoid algebra whenever possible)
User avatar
S
Poojita
Manager
Manager
Joined: 30 Dec 2019
Posts: 73
Own Kudos [?]: 43 [1]
Given Kudos: 659
Location: India
Schools: LBS MFA "23
Send PM
Reviews Badge
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   23 Aug 2021, 14:18
1
Kudos
sambitspm wrote:
Kindly see the attachment.
It took me around 2:45 min to solve this.

At first, my answer didn't match any of the options. I tried checking my calculation but didn't get to the right choice. Lastly, I went to replacing m and n in options and landed in D. Option D was my first guess, but since it was not exam mode, I was inclined on solving this.

VeritasKarishma, your both approaches help to get a new perspective on this question.


Hi
I dont quite seem to understand how did you checked each answer? could you please elaborate more on that?
Also , after getting x/y as m+n/m-n , i assumed m=5 and n=4 but still none of the answer matches. could you help on that please?
User avatar
B
Prince1890Sharma
Intern
Intern
Joined: 19 Mar 2023
Posts: 19
Own Kudos [?]: 8 [0]
Given Kudos: 33
Send PM
CAT Tests
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] New post   29 Mar 2024, 23:12
Hello

Can someone please tell what is wrong with this way of solving....none of the answer choice is matching

Posted from my mobile device
Attachments

17117791278328023142324845499614.jpg
17117791278328023142324845499614.jpg [ 377.44 KiB | Viewed 528 times ]

GMAT Club Bot
gmatclubot
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
29 Mar 2024, 23:12
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions