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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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)
_________________

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.

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.
_________________

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

Show Tags

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.
_________________

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

Show Tags

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)

gmatclubot

Re: If m>0 and n>o, is (m+x)/(n+x) greater than m/n ?
[#permalink]
26 Dec 2015, 18:31

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...