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

It is currently 24 Apr 2014, 03:06

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 and n are negative, is m/n less than 1?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
User avatar
Status: Current Student
Joined: 16 May 2010
Posts: 44
Schools: Darden '13
Followers: 0

Kudos [?]: 6 [1] , given: 4

If m and n are negative, is m/n less than 1? [#permalink] New post 26 May 2010, 06:35
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

32% (02:44) correct 67% (01:16) wrong based on 109 sessions
If m and n are negative, is m/n less than 1?

(1) mn<1
(2) m-n>n

I'm studying using Jeff Sackman's "Total GMAT Math" and I feel like one of the DS question answers is wrong in the answer guide.

[Reveal] Spoiler:
I say B. The guide says E. Can anyone explain?
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17394
Followers: 2889

Kudos [?]: 18492 [2] , given: 2361

GMAT Tests User CAT Tests
Re: Can anyone answer this DS question? [#permalink] New post 26 May 2010, 07:53
2
This post received
KUDOS
Expert's post
MateoLibre wrote:
I'm studying using Jeff Sackman's "Total GMAT Math" and I feel like one of the DS question answers is wrong in the answer guide. Here is the question:

If m and n are negative, is m/n less than 1?
(1) mn<1
(2) m-n>n

I say B. The guide says E. Can anyone explain?


Hi, welcome to the Gmat Club. Below is the solution for your question:

Given m<0 and n<0. Q: is \frac{m}{n}<1? --> is m>n? (when multiplying by negative n, switch the sign).

(1) mn<1. As both are negative --> 0<mn<1. Clearly insufficient to conclude which one is greater.

(2) m-n>n --> m>2n. If m=-3 and n=-2 answer is NO but if m=-3 and n=-4 answer is YES. Not sufficient.

(1)+(2) m=-0.2 and n=-1, both conditions satisfied --> m>n BUT m=-1.1 and n=-0.6, again both conditions satisfied --> m<n. Two different answers. Not sufficient.

Answer: E.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

1 KUDOS received
Intern
Intern
Joined: 11 Apr 2010
Posts: 48
Concentration: Marketing, Strategy
Schools: Indian School of Business (ISB) - Class of 2013
GMAT 1: 730 Q49 V41
WE: Other (Pharmaceuticals and Biotech)
Followers: 0

Kudos [?]: 10 [1] , given: 9

Re: Can anyone answer this DS question? [#permalink] New post 26 May 2010, 08:04
1
This post received
KUDOS
Hi Mateo,

Stem says m and n are neg or m<0 and n<0. It does not state that m and n are integers. It asks us whether m/n<1, which means whether |m|<|n|.

1. m*n<1

This can happen in 3 cases

I. |m|<1 and |n|<1 (eg |-0.25| and |-0.5| or |-0.5| and |-0.25|)---> presenting 2 cases |m|/|n|>1 or |m|/|n|<1

II. |m|<1 and |n|>1 (eg |-0.25| and |-1|)---> |m|/|n|>1

III. |m|>1 and |n|<1 (eg |-1| and |-0.25|)---> |m|/|n|<1

Hence Insufficient.

2. m-n>n
---> m-2n>0
This can only happen when |m|<2*|n|-----> |m|/|n|<2, which does not necessarily mean <1. Hence insufficient

Combining statements 1 and 2, we cannot get a solution since, |m|/|n| can be <2 but >1, or < 2 and <1.

Hence, E.
1 KUDOS received
Intern
Intern
User avatar
Status: Current Student
Joined: 16 May 2010
Posts: 44
Schools: Darden '13
Followers: 0

Kudos [?]: 6 [1] , given: 4

Re: Can anyone answer this DS question? [#permalink] New post 26 May 2010, 10:19
1
This post received
KUDOS
Bunuel-
Wow. Thanks for the quick response to that. I'm still new to DS questions. I'm only about a week and a half deep into my GMAT studying, so I have a long way to go. It makes more sense to me now. I feel like I'm making a lot of careless mistakes, especially when it comes to DS questions. I guess I need to just keep practicing. Anyway, seriously thanks.

Matt
Senior Manager
Senior Manager
Joined: 23 May 2010
Posts: 443
Followers: 5

Kudos [?]: 26 [0], given: 112

Re: Can anyone answer this DS question? [#permalink] New post 24 Sep 2010, 20:37
Hey Matt
All the best .. I read your post today and guess we are sailing in the same boat cheers !!!
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1732
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 60

Kudos [?]: 209 [0], given: 109

GMAT Tests User
Re: Can anyone answer this DS question? [#permalink] New post 30 Oct 2010, 20:17
Bunuel wrote:
MateoLibre wrote:
I'm studying using Jeff Sackman's "Total GMAT Math" and I feel like one of the DS question answers is wrong in the answer guide. Here is the question:

If m and n are negative, is m/n less than 1?
(1) mn<1
(2) m-n>n

I say B. The guide says E. Can anyone explain?


Hi, welcome to the Gmat Club. Below is the solution for your question:

Given m<0 and n<0. Q: is \frac{m}{n}<1? --> is m>n? (when multiplying by negative n, switch the sign).

(1) mn<1. As both are negative --> 0<mn<1. Clearly insufficient to conclude which one is greater.

(2) m-n>n --> m>2n. If m=-3 and n=-2 answer is NO but if m=-3 and n=-4 answer is YES. Not sufficient.

(1)+(2) m=-0.2 and n=-1, both conditions satisfied --> m>n BUT m=-1.1 and n=-0.6, again both conditions satisfied --> m<n. Two different answers. Not sufficient.

Answer: E.

Hope it helps.


I solved it, but it took me many minutes.
I still wondering how you know the right steps to solve it so fast :?
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

Intern
Intern
Joined: 02 Sep 2010
Posts: 48
WE 1: Business Development Manger
WE 2: Assistant Manager-Carbon Trading
WE 3: Manager-Carbon Trading
Followers: 2

Kudos [?]: 5 [0], given: 16

GMAT Tests User
Re: Can anyone answer this DS question? [#permalink] New post 05 Dec 2010, 04:00
Hi bunuel,

I could not understand statement 2 ; m>2n you have taken m=-3 and n =-2 this makes -3>-4 which will be 3<4 true and in second case you have taken m=-3 and n=-4 this will make -3>-8 3<8this is also true ..i could not understand Pleas explain
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17394
Followers: 2889

Kudos [?]: 18492 [0], given: 2361

GMAT Tests User CAT Tests
Re: Can anyone answer this DS question? [#permalink] New post 05 Dec 2010, 04:34
Expert's post
rite2deepti wrote:
Hi bunuel,

I could not understand statement 2 ; m>2n you have taken m=-3 and n =-2 this makes -3>-4 which will be 3<4 true and in second case you have taken m=-3 and n=-4 this will make -3>-8 3<8this is also true ..i could not understand Pleas explain


Given m<0 and n<0. Question: is m>n?

(2) m-n>n --> m>2n.
If m=-3 and n=-2, (these values satisfy both the stem and statement: both are negative and -3>2*(-2)), then as m=-3<-2=n the answer is NO;
If m=-3 and n=-4, (these values satisfy both the stem and statement: both are negative and -3>2*(-4)), then as m=-3>-4=n the answer is YES. Not sufficient.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Ms. Big Fat Panda
Ms. Big Fat Panda
User avatar
Status: Biting Nails Into Oblivion
Joined: 09 Jun 2010
Posts: 1857
Followers: 322

Kudos [?]: 1286 [0], given: 194

GMAT ToolKit User GMAT Tests User
Re: Can anyone answer this DS question? [#permalink] New post 05 Dec 2010, 18:24
I have a random question on this problem.

For the second statement, you're given that m - n > n, so why can't you just divide the whole thing out by n, in which case you get an expression with m/n? I can intuitively sense it's wrong but I can't place my finger on why.
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17394
Followers: 2889

Kudos [?]: 18492 [0], given: 2361

GMAT Tests User CAT Tests
Re: Can anyone answer this DS question? [#permalink] New post 05 Dec 2010, 23:31
Expert's post
whiplash2411 wrote:
I have a random question on this problem.

For the second statement, you're given that m - n > n, so why can't you just divide the whole thing out by n, in which case you get an expression with m/n? I can intuitively sense it's wrong but I can't place my finger on why.


It's not wrong at all, in fact it's a valid algebraic way to deal with statement (2).

Statement (2): m-n>n --> m>2n --> divide both parts by n (note that as given that n is negative then we should switch sign): \frac{m}{n}<2 --> but this is not sufficient to say whether \frac{m}{n}<1.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

1 KUDOS received
Manager
Manager
Joined: 30 Aug 2010
Posts: 93
Location: Bangalore, India
Followers: 3

Kudos [?]: 79 [1] , given: 27

Re: Can anyone answer this DS question? [#permalink] New post 05 Dec 2010, 23:37
1
This post received
KUDOS
Friends,

In GMAT, to avoid the confusion with the negative #s, i use my own and simple technique that is as below.

PLEASE NOTE THAT: DEALING WITH THE INEQUALITIES THAT CONTAIN +VE #s IS EASIER THAN DEALING WITH THOSE CONTAIN -VE#S.

Given: m and n are -ve #s
I take: x and y as +ve #s.

now i write m = -x and n = -y

FROM NOW ON I AM GONNA DEAL WITH THE +VE #S ONLY. I CAN NOT BE TRAPPED BY THE TESTMAKER.

qtn: is m/n less than 1? == > is -x/-y < 1 ==> is x/y<1 ==> is x < y (NOTE: as x and y both are +ve, i can safely cross multiply).

(1) mn<1

==> (-x)(-y)<1 ==> xy<1 : our qtn is "is x<y", why is y a greatest person than x or vice-versa. As their product is < 1 ==> means, they can always inerchange their values with out effecting thier product. So x could b < y or vice-versa. NOT SUFF.

(2) m-n>n

==> -x+y>-y ==> x-y<y ==> x< 2y ==> x/y < 2 (Again note that x and y both are +ve and hence i can safely cross multiply)

hence x/y is < 2, aren't there any other #s between 2 and 1, how can i say that x/y is < 1 knwoing that x/y is < 2....NOT SUFF.


1 & 2 together , xy<1 and x/y<2...Can't even be combined...NO LUCK...NOT SUFF.

ANSWER "E"

Regards,
Murali.
Kudos?
Ms. Big Fat Panda
Ms. Big Fat Panda
User avatar
Status: Biting Nails Into Oblivion
Joined: 09 Jun 2010
Posts: 1857
Followers: 322

Kudos [?]: 1286 [0], given: 194

GMAT ToolKit User GMAT Tests User
Re: Can anyone answer this DS question? [#permalink] New post 06 Dec 2010, 06:52
Ah, thanks Bunuel. The sign conversion was what tripped me up. Forgot to read the part that said they were negative numbers; should pay more attention.

@Murali: Good trick!
Intern
Intern
Joined: 31 Oct 2010
Posts: 33
Followers: 0

Kudos [?]: 6 [0], given: 25

Re: Can anyone answer this DS question? [#permalink] New post 06 Dec 2010, 21:48
Bunuel, I was wondering about the -.2 and -1 and the -1.1 and -.6. Did you use these particular figures for a purpose or were they just easy numbers you knew configured into a number less than 1. Allowing you to make M as big as possible then M as small as possible?
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17394
Followers: 2889

Kudos [?]: 18492 [0], given: 2361

GMAT Tests User CAT Tests
Re: Can anyone answer this DS question? [#permalink] New post 07 Dec 2010, 04:19
Expert's post
mmcooley33 wrote:
Bunuel, I was wondering about the -.2 and -1 and the -1.1 and -.6. Did you use these particular figures for a purpose or were they just easy numbers you knew configured into a number less than 1. Allowing you to make M as big as possible then M as small as possible?


Question asks is \frac{m}{n}<1? or is m>n?

From (1) we have: 0<mn<1, which is useless (whether alone or combined with 2) to answer which variable is greater.

From (2) we have: \frac{m}{n}<2, so \frac{m}{n} is less than 2 but we can not say whether it's less than 1, so again this statement is useless to answer the question.

So even not testing the numbers we could say that the answer is E. But to show this, to demonstrate that the answer is E I just picked 2 sets of numbers, first set m>n and the second m<n, also with little trial and error it's not hard to get the numbers to satisfy stem and the statements (remember on DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Manager
Manager
Joined: 15 Mar 2012
Posts: 60
Location: United States
Concentration: Marketing, Strategy
Followers: 0

Kudos [?]: 8 [0], given: 19

Re: Can anyone answer this DS question? [#permalink] New post 14 Feb 2013, 14:17
rite2deepti wrote:
Hi bunuel,

I could not understand statement 2 ; m>2n you have taken m=-3 and n =-2 this makes -3>-4 which will be 3<4 true and in second case you have taken m=-3 and n=-4 this will make -3>-8 3<8this is also true ..i could not understand Pleas explain


rite2deepti,

I thought the same, but you have to look at the question itself m>n?

Plugging m = -3 and n = -2 this yields -3 > -4 which is correct, however, the question is -3>-2 and this is incorrect, thats why its a NO.

For the second case m = -3 and n = -4 this yields -3 > -8 which is correct, and YES as an answer -3>-4. Having this, we can conclude its INSUFFICIENT, NO AND YES.
_________________

MV
"Better to fight for something than live for nothing.” ― George S. Patton Jr

Re: Can anyone answer this DS question?   [#permalink] 14 Feb 2013, 14:17
    Similar topics Author Replies Last post
Similar
Topics:
New posts Is mn < m/n (1) mn is a positive integer. (2) n is a saurya_s 6 29 Sep 2004, 03:43
New posts Is mn<m/n? 1) mn is a positive integer 2) n is a negative ruhi 6 17 Nov 2004, 11:19
New posts If m>0 and n>0, is (m+x)/(n+x) > m/n? (1) m is less above720 8 23 Aug 2007, 17:44
This topic is locked, you cannot edit posts or make further replies. New 3 Experts publish their posts in the topic If m and n are negative, is m/n less than 1 ? (1) mn < 1 ichha148 29 06 Sep 2009, 12:53
New posts 3 Experts publish their posts in the topic If m and n are negative integers what is the value of m*n rxs0005 4 28 Jan 2011, 04:57
Display posts from previous: Sort by

If m and n are negative, is m/n less than 1?

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.