GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Sep 2018, 14:44

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.

Close

Request Expert Reply

Confirm Cancel

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

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

Hide Tags

Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 833
GMAT ToolKit User
If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post Updated on: 30 Jul 2012, 05:17
1
8
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:18) correct 35% (01:08) wrong based on 290 sessions

HideShow timer Statistics

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

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

Originally posted by LM on 10 May 2010, 09:32.
Last edited by Bunuel on 30 Jul 2012, 05:17, edited 1 time in total.
Edited the question and added the OA.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: DS4  [#permalink]

Show Tags

New post 10 May 2010, 14:38
3
3
If m>0 and n>0, is (m+x)/(n+x) > m/n?

(1) m < n. No info about x. Not sufficient.
(2) x >0. No info about m and n. Not sufficient.

(1)+(2) As from the above two statements nominators and denominator of both fractions are positive, we can crossmultiply --> is \(\frac{m+x}{n+x}>\frac{m}{n}\) --> is \((m+x)n>(n+x)m\) --> is \(mn+xn>mn+xm\) --> is \(x(n-m)>0\) --> as \(x>0\) and \(n>m\), then \(x(n-m)>0\) is true. Sufficient.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

General Discussion
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 833
GMAT ToolKit User
Re: DS4  [#permalink]

Show Tags

New post 10 May 2010, 21:01
Bunuel wrote:
If m>0 and n>0, is (m+x)/(n+x) > m/n?


(1) m < n. No info about x. Not sufficient.
(2) x >0. No info about m and n. Not sufficient.

(1)+(2) As from the above two statements nominators and denominator of both fractions are positive, we can crossmultiply --> is \(\frac{m+x}{n+x}>\frac{m}{n}\) --> is \((m+x)n>(n+x)m\) --> is \(mn+xn>mn+xm\) --> is \(x(n-m)>0\) --> as \(x>0\) and \(n>m\), then \(x(n-m)>0\) is true. Sufficient.

Answer: C.


Did you score 60 in the Quant or are you working with the GMAC!!! :-)

Awesome dexterity in giving the solutions.
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 436
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 17 Jan 2013, 03:57
1
LM wrote:
If m > 0 and n > 0, is (m+x)/(n+x) > m/n?

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


I used plug in...

1.
let m=3 and n=4 and x = 1
\(\frac{m}{n} = \frac{3}{4}\) while \(\frac{m+x}{n+x}= \frac{4}{5}\)
\(\frac{3}{4} < \frac{4}{5}\) YES!

let m=3 and n=4 and x=-1
\(\frac{m}{n} = \frac{3}{4}\) while \(\frac{m+x}{n+x}= \frac{2}{3}\)
\(\frac{3}{4} > \frac{2}{3}\) NO!

thus, INSUFFICIENT!

2. x > 0
From statement 1 we tested m=3 and n=4 and x=1 (see that x>0 here) and we got YES!

let m=4 and n=3
\(\frac{m}{n} = \frac{4}{3}\) while \(\frac{m+x}{n+x}= \frac{5}{4}\)
\(\frac{4}{3} > \frac{5}{4}\) NO!

thus, INSUFFICIENT!

Together, we combine and using statement 1 where when x>0 we get YES!

Answer: C
_________________

Impossible is nothing to God.

Director
Director
avatar
Joined: 29 Nov 2012
Posts: 802
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 26 Feb 2013, 04:02
Why can't we cross multiply in the original statement?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 26 Feb 2013, 04:07
1
1
fozzzy wrote:
Why can't we cross multiply in the original statement?


Never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know its sign.

We don't know whether n+x is positive or negative, thus don't know whether we should flip the sign or not.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 223
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 02 May 2014, 19:24
Hi Bunuel,

Why isn't the answer B given that in the below steps, (2) gives us the same information as in (1)?

(2)
Because we know that both m and n are positive and that x is positive, we can safely cross-multiply.
(m+x)*n > (n+x)*m
mn + xn > mn + xm
xn > xm
n > m
Because we now know that n > m, we can use the same steps that you used for C to answer the question and only (2) will be sufficient to answer the problem.
Please tell me where I am going wrong here.
Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 123
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 03 May 2014, 00:17
LM wrote:
If m > 0 and n > 0, is (m+x)/(n+x) > m/n?

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


Statement I is insufficient:

Let us say m = 4 and n = 5

Is (4+x)/(5+x) > 4/5?
(Take a hint from the second statement - Apply the negation test)

(4 - 4)/(5-4) is not greater than 4/5
(4 + 5)/(5+5) is greater than 4/5

Statement II is not sufficient:
(4 + 5)/(5+5) is greater than 4/5
(5 + 4)/(4 + 4) is not greater than 5/4

Combining is sufficient:
m > n and x is positive
Cross multiplying the inequality:
(mn + nx) > mn + mx
n > m which is true in statement I

Hence answer is C.
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 03 May 2014, 04:50
TooLong150 wrote:
Hi Bunuel,

Why isn't the answer B given that in the below steps, (2) gives us the same information as in (1)?

(2)
Because we know that both m and n are positive and that x is positive, we can safely cross-multiply.
(m+x)*n > (n+x)*m
mn + xn > mn + xm
xn > xm
n > m
Because we now know that n > m, we can use the same steps that you used for C to answer the question and only (2) will be sufficient to answer the problem.
Please tell me where I am going wrong here.


For (2) we don't know whether n>m.

The question asks whether (m+x)/(n+x) > m/n. For (2) when you simplify the question becomes is n>m? This is not given, that;s exactly what we need to find out.

Does this make sense?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 223
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 03 May 2014, 06:55
Yes, I realize this now, and that with (1), we know that the answer to this question statement is Yes.

Posted from my mobile device
Director
Director
User avatar
G
Joined: 26 Oct 2016
Posts: 649
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 26 Jan 2017, 20:12
Since we know m and n both are +ve, so we can cross multiply m and n in the question.
So,
the question becomes,
Is (m+x)/(n+x)> m/n?
Is n(m+x)>m(n+x) ?
Is nm + nx > mn + mx ?
cancel out mn from both sides, gives us

Is nx > mx ? or Is x(n-m) > 0 ?


Now St 1 only:
1. m < n We don't know anything abt x to answer our new re-phrased question. Insufficient.

St 2 only:
2. X> 0 relation between m and n not known. So Insufficient.

Now combined,
We know x > 0 i.e +ve and m < n so nx > mx answer is yes.

We can test values here too now to confirm,
x = 1, n = 3, m= 2, so nx > mx is 1.3 > 2.1 ie. 3>2 so yes.

So if x was -ve . i.e x< 0 then the inequality would have been revered. So both the stmts combined are sufficient.
Hence C.
_________________

Thanks & Regards,
Anaira Mitch

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8131
Premium Member
Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n?  [#permalink]

Show Tags

New post 01 Jul 2018, 23:28
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

Re: If m > 0 and n > 0, is (m+x)/(n+x) > m/n? &nbs [#permalink] 01 Jul 2018, 23:28
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.