If m and n are negative, is m/n less than 1? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 12:09

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Status: Current Student
Joined: 16 May 2010
Posts: 44
Schools: Darden '13
Followers: 0

Kudos [?]: 9 [1] , given: 4

If m and n are negative, is m/n less than 1? [#permalink]

### Show Tags

26 May 2010, 06:35
1
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

34% (02:57) correct 66% (01:34) wrong based on 220 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93552 [5] , given: 10578

### Show Tags

26 May 2010, 07:53
5
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

Hope it helps.
_________________
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

### Show Tags

26 May 2010, 08:04
1
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.
Intern
Status: Current Student
Joined: 16 May 2010
Posts: 44
Schools: Darden '13
Followers: 0

Kudos [?]: 9 [1] , given: 4

### Show Tags

26 May 2010, 10:19
1
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
Joined: 23 May 2010
Posts: 441
Followers: 5

Kudos [?]: 103 [0], given: 112

### Show Tags

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
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1712
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 97

Kudos [?]: 918 [0], given: 109

### Show Tags

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.

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: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 02 Sep 2010
Posts: 48
Followers: 3

Kudos [?]: 52 [0], given: 16

### Show Tags

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
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93552 [0], given: 10578

### Show Tags

05 Dec 2010, 04:34
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.
_________________
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 448

Kudos [?]: 1980 [0], given: 210

### Show Tags

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
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93552 [0], given: 10578

### Show Tags

05 Dec 2010, 23:31
Expert's post
1
This post was
BOOKMARKED
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 $$\frac{m}{n}<1$$.
_________________
Manager
Joined: 30 Aug 2010
Posts: 91
Location: Bangalore, India
Followers: 5

Kudos [?]: 160 [3] , given: 27

### Show Tags

05 Dec 2010, 23:37
3
KUDOS
2
This post was
BOOKMARKED
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.

Regards,
Murali.
Kudos?
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 448

Kudos [?]: 1980 [0], given: 210

### Show Tags

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
Joined: 31 Oct 2010
Posts: 32
Followers: 0

Kudos [?]: 61 [0], given: 25

### Show Tags

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
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93552 [0], given: 10578

### Show Tags

07 Dec 2010, 04:19
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).
_________________
Manager
Joined: 15 Mar 2012
Posts: 60
Location: United States
Concentration: Marketing, Strategy
Followers: 0

Kudos [?]: 18 [0], given: 19

### Show Tags

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13521
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If m and n are negative, is m/n less than 1? [#permalink]

### Show Tags

09 May 2014, 10:44
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 Club Legend
Joined: 09 Sep 2013
Posts: 13521
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If m and n are negative, is m/n less than 1? [#permalink]

### Show Tags

14 May 2015, 18:59
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 Club Legend
Joined: 09 Sep 2013
Posts: 13521
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If m and n are negative, is m/n less than 1? [#permalink]

### Show Tags

14 Jun 2016, 10:14
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 and n are negative, is m/n less than 1?   [#permalink] 14 Jun 2016, 10:14
Similar topics Replies Last post
Similar
Topics:
14 If r and s are negative, is r/s less than 1 ? 8 07 Mar 2012, 15:24
Are negative integers m and n both less than x? 4 11 Jan 2012, 22:03
If m and n are negative integers, what is the value of mn? 6 29 Dec 2011, 07:45
10 If m and n are negative integers what is the value of m*n 5 28 Jan 2011, 04:57
5 If m and n are negative, is m/n less than 1 ? (1) mn < 1 29 06 Sep 2009, 12:53
Display posts from previous: Sort by