Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Jun 2016, 23:10
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 24 Jul 2010
Posts: 90
Followers: 3

Kudos [?]: 140 [1] , given: 12

If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 14 Apr 2011, 03:14
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:54) correct 31% (01:13) wrong based on 75 sessions

HideShow timer Statistics

If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?

(1) m < n
(2) x > 0

Topic locked. Open discussions at if-m-0-and-n-0-is-m-x-n-x-m-n-93967.html
[Reveal] Spoiler: OA
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2021
Followers: 155

Kudos [?]: 1482 [0], given: 376

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 14 Apr 2011, 03:50
whichscore wrote:
If m>0 and n>0, is (m+x)/(n+x) greater than m/n ?
1. m < n
2. x > 0


\(\frac{m+x}{n+x} > \frac{m}{n}\)

\(\frac{m+x}{n+x} - \frac{m}{n} > 0\)

\(\frac{mn+nx-mn-mx}{n(n+x)} > 0\)

A: Does \(\frac{x(n-m)}{n(n+x)} > 0\)?

1. \(m<n\)

\(m-n<0\)
\(n-m>0\)

But, what if \(x<0 \hspace{2} & \hspace{2} |x|<n\)
Then the answer to the question would be No.

If \(x>0\)
Then the answer to the question would be Yes.
Not Sufficient.

2. \(x>0\)

Denominator is +ve.
Numerator must be +ve to make the expression true.

\(n-m>0\)
\(n>m\) should be true to make the expression true. But, it is not given which of the two is greater.

If n>m, the answer would be Yes.
If n<m, the answer would be No.

Combining both statements:
Denominator becomes +ve.
Numerator also becomes +ve as m<n
Answer to the question is Yes.
Sufficient.

Ans: "C"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 299 [0], given: 123

Reviews Badge
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 14 Apr 2011, 04:26
1) Insufficient.
Lets consider m = 1 n = 2
If x = 0 The answer is NO
If x = 1 The answer is YES

2) Insufficient
consider m = n = 1 x = 1 The answer is NO
Consider m = 1 n = 2 x = 1 The answer is YES

1) + 2) Consider m = 1 n = 2 x = 1 The answer is YES. Sufficient

whichscore wrote:
If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?
1. m < n
2. x > 0
SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1673
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 34

Kudos [?]: 454 [0], given: 36

Premium Member Reviews Badge
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 14 Apr 2011, 05:24
As per (1)

m = 2, n = 3

m/n = 2/3

if x = -2, then 0/1 < 2/3

if x = 0 then (m+0)/(n +0) = m/n

if x = 2 then (2 + 2)/(3+2) = 4/5 > 2/3

(1) is insufficient

As per (2)

x > 0, but it's possible that m = n , and hence (m+x)/(n+x) = m/n

(2) is insufficient


(1) and (2) together

if x = 1, m = 2, n = 3

(2 + 1)/(3 + 1) = 3/4 hence m/n < (m+x)/(n+x)

if x = 2, m = 2, n = 3 then (2 + 2)/(3+2) = 4/5 > 2/3 hence m/n < (m+x)/(n+x)

So Answer - C
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 95 [0], given: 42

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 14 Apr 2011, 06:12
Rephrasing given expression we have ((n-m)x)/(n(n+x)) >0?

1. Not sufficient as we don't know anything about x.

2. Not sufficient as we don't know anything about m,n

Together we have n>m & x>0 . sufficient to answer.

Answer is C.

Posted from my mobile device Image
Expert Post
5 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6677
Location: Pune, India
Followers: 1829

Kudos [?]: 11136 [5] , given: 219

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 14 Apr 2011, 14:31
5
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
whichscore wrote:
If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?
1. m < n
2. x > 0


It is useful to understand that when you add the same positive number to the numerator and denominator of a positive fraction, it moves towards 1.

Say 1/2 = 0.5
I add 1 to both numerator and denominator, it becomes 2/3 = 0.67 i.e. closer to 1 than 1/2
Say 3/2 = 1.5
I add 1 to both numerator and denominator, it becomes 4/3 = 1.33 i.e. closer to 1

When you add the same negative number (or in other words, subtract the same positive number) to the numerator and denominator of a positive fraction, it moves away from 1.

Say 1/2 = 0.5
I add -1 to both numerator and denominator, it becomes 0 i.e. farther from 1 than 1/2
Say 3/2 = 1.5
I add -1 to both numerator and denominator, it becomes 2/1 i.e. farther from 1

Once you understand this, the question takes a few seconds.

1. m < n
The fraction m/n must be less than 1. So if x is positive, the fraction will increase and move towards 1. If x is negative, the fraction will decrease to move away from 1. Not sufficient.

2. x > 0
x is positive but we do not know whether the fraction is greater than 1 or less than 1. If m/n is greater than 1, it will decrease and move towards 1. If m/n is less than 1, it will increase and move towards 1.

Using both together, m/n is less than 1 and x is positive so we are adding the same positive number to both numerator and denominator. Hence (m+x)/(n+x) will be greater than m/n to move towards 1.
Answer (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 417
WE 1: Business Development
Followers: 7

Kudos [?]: 85 [0], given: 161

GMAT ToolKit User
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 15 Apr 2011, 12:20
great explanation. thanks karishma.
_________________

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 16 May 2011
Posts: 77
Followers: 0

Kudos [?]: 12 [0], given: 2

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 06 Mar 2012, 07:30
Why cant we cross multiply to get; mn + nx > mn + mx, simplify, resulting is n>m??
is this totally wrong?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33531
Followers: 5939

Kudos [?]: 73677 [1] , given: 9903

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 06 Mar 2012, 08:08
1
This post received
KUDOS
Expert's post
dchow23 wrote:
Why cant we cross multiply to get; mn + nx > mn + mx, simplify, resulting is n>m??
is this totally wrong?


Cross-multiplying (m+x)/(n+x)>m/n would be wrong, since we don't know whether n+x is positive or negative: if n+x>0 then we would have as you've written mn+nx>mn+mx BUT if n+x<0 then when multiplying by negative number we should flip the sign of the inequity and write mn+nx<mn+mx.

General rule: never multiply or divide inequality by a variable (or by an expression with variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6677
Location: Pune, India
Followers: 1829

Kudos [?]: 11136 [0], given: 219

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 06 Mar 2012, 11:17
Expert's post
dchow23 wrote:
Why cant we cross multiply to get; mn + nx > mn + mx, simplify, resulting is n>m??
is this totally wrong?


Yes, cross multiplying is incorrect here. We do not know whether (n+x) is positive or negative. We know that m and n are positive but we know nothing about x. When you multiply an inequality by a positive number, the inequality sign stays the same but when you multiply an inequality by a negative number, the inequality sign flips. So before you multiply/divide an inequality by a variable, you need to know whether the variable is positive or negative.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 22 Jan 2012
Posts: 6
Followers: 0

Kudos [?]: 8 [0], given: 1

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 07 Mar 2012, 10:53
@flute, thanks for the solution.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10218
Followers: 481

Kudos [?]: 124 [0], given: 0

Premium Member
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 26 Dec 2015, 18:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 16 Apr 2015
Posts: 30
Followers: 0

Kudos [?]: 12 [0], given: 115

Premium Member
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ? [#permalink]

Show Tags

New post 26 Dec 2015, 18:31
whichscore wrote:
If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?

(1) m < n
(2) x > 0



I think lot of folks have suggested great solution, but me not great with math followed following, which helped me get to the answer fairly quickly.

Really to solve this we needed to both about X and about relationship between M&N. So, I tried using number, since we were given X,Y>0 but not given if X>0 or X<0 or M>N or M<N.

case 1: M>N, say 5/4 = 1.25
now X>0 or X<0
for X>0, say 3
(5+3)/(4+3) = 1.143 (values comes down)

for x < 0, say -3
(5-3)/(4-3) = 2 (value goes up)

case 2: M<N, say 3/4 = 0.75
now X>0 or X<0
for X>0, say 3
(3+3)/(4+3) = .85 (value goes up)

for x < 0, say -2
(3-2)/(4-2) = 2 (values comes down)
Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?   [#permalink] 26 Dec 2015, 18:31
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If m ≠ 0 and n ≠ 0, is mn > 0? Bunuel 4 29 Apr 2016, 03:56
Experts publish their posts in the topic If m > 0, is m/n > m? Bunuel 6 01 Nov 2015, 09:21
11 If m > 0 and n > 0, is (m+x)/(n+x) > m/n? Yalephd 24 26 Jul 2011, 21:58
9 Experts publish their posts in the topic If m > 0 and n > 0, is (m+x)/(n+x) > m/n? LM 9 10 May 2010, 09:32
If m>0 and n >0, is ((m+x)/(n+x)) > (m/n) metallicafan 3 09 Mar 2010, 20:49
Display posts from previous: Sort by

If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.