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

It is currently 20 Aug 2014, 05:01

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 107
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 14 [1] , given: 63

If m > 0 and n > 0, is (m+x)/(n+x) > m/n? [#permalink] New post 26 Jul 2011, 20:58
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

59% (02:28) correct 41% (00:40) wrong based on 51 sessions
If m > 0 and n > 0, is (m+x)/(n+x) > m/n?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-0-and-n-0-is-m-x-n-x-m-n-93967.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jul 2012, 04:21, edited 5 times in total.
Edited the question.
Kaplan Promo CodeKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
2 KUDOS received
Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 549
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 60

Kudos [?]: 272 [2] , given: 11

Re: M versus N [#permalink] New post 26 Jul 2011, 21:18
2
This post received
KUDOS
Revision:
(C) is the correct answer.

Please see ~fluke's solution below. Thanks.
_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

Get a free detailed MBA profile evaluation

Top MBA Rankings and MBA Admissions blog


Image


Last edited by GyanOne on 01 Aug 2011, 23:40, edited 4 times in total.
Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 107
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 14 [0], given: 63

Re: M versus N [#permalink] New post 27 Jul 2011, 05:47
Don't we need to know if X is positive or negative before multiplying both sides by (N + X)?
What if N is negative so that N + X < 0? This would call for us to change the sign of the inequality when we take the 1st step you did above in restating the question.
Intern
Intern
User avatar
Joined: 08 Feb 2010
Posts: 46
Concentration: Leadership, International Business
Schools: INSEAD Jan '13
GMAT 1: 670 Q50 V31
WE: Project Management (Energy and Utilities)
Followers: 1

Kudos [?]: 5 [0], given: 1

GMAT Tests User
Re: M versus N [#permalink] New post 27 Jul 2011, 07:36
I would go for C

(1) Gives us that any side could be greated depending on sign of X
(2) Gives us condition on X being +ve.

Hence combine together and we get C as answer.
Intern
Intern
User avatar
Joined: 08 Feb 2010
Posts: 46
Concentration: Leadership, International Business
Schools: INSEAD Jan '13
GMAT 1: 670 Q50 V31
WE: Project Management (Energy and Utilities)
Followers: 1

Kudos [?]: 5 [0], given: 1

GMAT Tests User
Re: M versus N [#permalink] New post 27 Jul 2011, 07:37
Hey please ingnore my earlier ans. B is the right answer.

Just check with the numbers. eg 4/3 < 3/2.
Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 107
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 14 [0], given: 63

Re: M versus N [#permalink] New post 27 Jul 2011, 07:42
GyanOne is correct. The OA is A. I just don't understand why we don't need to know that X is positive.

Revision:

GyanOne is incorrect. The OA is C. We do need to know the sign of X.

Last edited by Yalephd on 27 Jul 2011, 08:48, edited 2 times in total.
1 KUDOS received
Intern
Intern
avatar
Joined: 27 Jul 2011
Posts: 1
Followers: 0

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

Re: M versus N [#permalink] New post 27 Jul 2011, 07:51
1
This post received
KUDOS
This is why answer IS NOT B:

II) x>0
Case 1: let m=2, n=3 and x=1
(2+1)/(3+1) = 3/4 and 3/4 > 2/3

Case 2: let m=3, n=2 and x=1
(3+1)/(2+1) = 4/3 and 4/3 < 3/2

Since we can find find values to make the statement true and false, II is not sufficient.

From I) we know that m<n, also, not sufficient on it's own because X can be either positive or negative.

However, taking I and II together we can answer the question, so the answer is C.
Intern
Intern
avatar
Joined: 08 Jul 2011
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: M versus N [#permalink] New post 27 Jul 2011, 08:22
Yalephd wrote:
GyanOne is correct. The OA is A. I just don't understand why we don't need to know that X is positive.


I second this. GyanOne's algebra seems correct. And apparently OA is A. However what about cases 1. x=1, m=1, n=2; and 2. x=-1, m= 1, n=2. First case resolves to 2/3, which is greater than 1/2. Second case resolves to 0, which is less than 1/2. Insufficient.

So what am I missing?
Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 107
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 14 [0], given: 63

Re: M versus N [#permalink] New post 27 Jul 2011, 08:42
elementbrdr, you're right. We definitely need to know the sign of X. I have to go back and check the OA. Maybe I made a mistake. It looks like it has to be C.

M < N tells us that this is a proper fraction. If we add the same number to the numerator and the denominator, the fraction increases. If we subtract the same number from the numerator and the denominator, the fraction decreases. Hence, we need to know whether M < N and whether X < 0.

Last edited by Yalephd on 27 Jul 2011, 08:45, edited 1 time in total.
Intern
Intern
avatar
Joined: 08 Jul 2011
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: M versus N [#permalink] New post 27 Jul 2011, 08:57
Yalephd wrote:
OA is C


Well that makes sense based on plugging numbers. I still don't see what is wrong with GyanOne's algebra though...
3 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2048
Followers: 128

Kudos [?]: 898 [3] , given: 376

GMAT Tests User
Re: M versus N [#permalink] New post 27 Jul 2011, 09:00
3
This post received
KUDOS
\frac{m+x}{n+x} > \frac{m}{n}

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

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

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

1. m<n

Thus, n-m>0

Now, if x>0; the fraction will be greater than 0.
If x<0 but |x|<n; the fraction will be less than 0.

2. x>0

If x>0;
m<n; the fraction will be greater than 0
m>n; the fraction will be less than 0

Together;
The fraction is greater than 0.

Ans: "C"
********************************************************************

Since, we don't know the sign of x; we can't cross multiply as x can be negative and |x|>n
***********************************************************************
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 18 Sep 2009
Posts: 374
Followers: 3

Kudos [?]: 55 [0], given: 2

GMAT Tests User
Re: M versus N [#permalink] New post 28 Jul 2011, 06:56
After plug-in various numbers for m,n,x .I will go with c.
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 422
WE 1: Business Development
Followers: 7

Kudos [?]: 33 [0], given: 161

GMAT ToolKit User GMAT Tests User
Re: M versus N [#permalink] New post 31 Jul 2011, 09:08
fluke wrote:
\frac{m+x}{n+x} > \frac{m}{n}

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

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

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

1. m<n

Thus, n-m>0

Now, if x>0; the fraction will be greater than 0.
If x<0 but |x|<n; the fraction will be less than 0.

2. x>0

If x>0;
m<n; the fraction will be greater than 0
m>n; the fraction will be less than 0

Together;
The fraction is greater than 0.

Ans: "C"
********************************************************************

Since, we don't know the sign of x; we can't cross multiply as x can be negative and |x|>n
***********************************************************************



Shouldnt the divisor should be n(n+x) or am i missing something with the N?

how did you get rid of it after combining n+x and n?

thanks.
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 549
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 60

Kudos [?]: 272 [1] , given: 11

Re: M versus N [#permalink] New post 01 Aug 2011, 23:39
1
This post received
KUDOS
144144,

As n>0, we can exclude n from the divisor.
_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

Get a free detailed MBA profile evaluation

Top MBA Rankings and MBA Admissions blog


Image

Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 422
WE 1: Business Development
Followers: 7

Kudos [?]: 33 [0], given: 161

GMAT ToolKit User GMAT Tests User
Re: M versus N [#permalink] New post 02 Aug 2011, 00:09
tnx.
i did it at around 2am so i was "floating"... +1
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 107
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 14 [0], given: 63

Re: M versus N [#permalink] New post 02 Aug 2011, 04:50
How do we go from this
\frac{m+x}{n+x}-\frac{m}{n} > 0

to this
\frac{mn+nx-mn-mx}{n+x}> 0

I don't see how we dropped the N from the denominator.

"As n>0, we can exclude n from the divisor. " Why is that?
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 422
WE 1: Business Development
Followers: 7

Kudos [?]: 33 [0], given: 161

GMAT ToolKit User GMAT Tests User
Re: M versus N [#permalink] New post 02 Aug 2011, 06:30
Yalephd wrote:
How do we go from this
\frac{m+x}{n+x}-\frac{m}{n} > 0

to this
\frac{mn+nx-mn-mx}{n+x}> 0

I don't see how we dropped the N from the denominator.

"As n>0, we can exclude n from the divisor. " Why is that?


because its positive, you are allowed to multiple both sides of the equation times N. when u multiple the right side it stays 0, when you multiple the left side, N cancels the denominator.

If we had no information about whether it is +ve or -ve, we couldnt do it bc this might change the > sign (If N was -ve)

hope this is clear.
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 549
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 60

Kudos [?]: 272 [1] , given: 11

Re: M versus N [#permalink] New post 02 Aug 2011, 06:35
1
This post received
KUDOS
If the product of two numbers is positive, they must either both be positive or both be negative.

Since n is > 0 (given in the question), (nx-mx)/(m+x) must also be > 0. Therefore we check only for the condition where (nx-mx)/(m+x) is > 0 as it will also make the entire expression > 0.
_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

Get a free detailed MBA profile evaluation

Top MBA Rankings and MBA Admissions blog


Image

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 422
WE 1: Business Development
Followers: 7

Kudos [?]: 33 [1] , given: 161

GMAT ToolKit User GMAT Tests User
Re: M versus N [#permalink] New post 02 Aug 2011, 06:44
1
This post received
KUDOS
GyanOne wrote:
If the product of two numbers is positive, they must either both be positive or both be negative.

Since n is > 0 (given in the question), (nx-mx)/(m+x) must also be > 0. Therefore we check only for the condition where (nx-mx)/(m+x) is > 0 as it will also make the entire expression > 0.



GyanOne - I can say from a user of this amazing forum for few month now, we are very happy to have you here with us. Your answers are clear and very helpful. Thanks. +1
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 107
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 14 [0], given: 63

Re: M versus N [#permalink] New post 02 Aug 2011, 06:54
Got it. Thanks, guys. +1
Re: M versus N   [#permalink] 02 Aug 2011, 06:54
    Similar topics Author Replies Last post
Similar
Topics:
If m>0, n>0, is (m+x)/(n+x) > m/n? viveksharma 4 25 Aug 2008, 02:41
If m > 0 and n > 0, is (m+x)/(n+x) > m/n 1) m < xALIx 2 22 Jun 2008, 12:33
If m>0 and n>0, is (m+x)/(n+x) > m/n? (1) m is less above720 8 23 Aug 2007, 17:44
If m>0 and n>0, is m+x/n+x > m/n? ggarr 4 09 Jun 2007, 21:14
3 Experts publish their posts in the topic If m > 0 and n > 0, is (m+x)/(n+x) > m/n? kook44 7 12 Mar 2006, 19:18
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 25 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| 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®.