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

It is currently 17 Oct 2019, 03:48

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 and n are consecutive positive integers, is m greater than n ?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58428
If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 02:04
1
13
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:21) correct 22% (01:46) wrong based on 400 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If m and n are consecutive positive integers, is m greater than n ?

(1) m-1 and n+1 are consecutive positive integers.
(2) m is an even integer.

Data Sufficiency
Question: 86
Category: Arithmetic Properties of numbers
Page: 158
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58428
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 02:04
SOLUTION

If m and n are consecutive positive integers, is m greater than n?

(1) m-1 and n+1 are consecutive positive integers --> m>n, if m were less than n than m-1 (integer less than m) and n+1 (integer more than n) wouldn't be consecutive. Sufficient.

Or look at this in another way: stem says that the distance between m and n is 1. Now, if m<n then the distance between m-1 and n+1 would be 3 and they couldn't be consecutive as (1) states. Thus it must be true that m>n.

(2) m is an even integer. Clearly insufficient.

Answer: A.
_________________
Most Helpful Community Reply
Current Student
avatar
B
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5
GMAT ToolKit User
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 11:36
6
The question states that \(m\) &\(n\) are consecutive positive integers. The question can then be boiled down to whether the order is \(m,n\) or \(n,m\).

(1) m-1 and n+1 are consecutive positive integers.

We know that \(m-1\) and \(n+1\)are consecutive positive integers. If the order is \(m,n\) then this statement clearly fails. If the order is \(n,m\) then this statement is true, hence \(A\) is sufficient.

(2) m is an even integer.

If \(m\) is an even integer, \(n\) must be odd. \(n\) can still fall to the left or right of \(m\), and therefore statement (2) is insufficient.

Answer: A
General Discussion
Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 116
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 05:12
1
St1: m-1 and n+1 are consecutive positive integers.

Case 1:
m is even, n is odd and m < n
Let m = 2, n = 3
m-1 = 1, n+1 = 4 -> not consecutive positive integers.

Case 2:
m is even, n is odd and m > n
Let m = 2, n = 1
m-1 = 1, n+1 = 2 -> consecutive positive integers.

Case 3:
m is odd, n is even and m < n
Let m = 3, n = 4
m-1 = 2, n+1 = 5 -> not consecutive positive integers.

Case 4:
m is odd, n is even and m > n
Let m = 3, n = 2
m-1 = 2, n+1 = 3 -> consecutive positive integers.

Not sufficient. Dow to B, C or E.

St2: m is an even integer. Not sufficient. If m = 2 and n = 1 -> m > n but if m = 2 and n = 3 -> m < n.

St 1 + St2: Not sufficient as illustrated by case 1 and case 2.

Answer (E).
Intern
Intern
avatar
Joined: 30 Nov 2013
Posts: 20
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 08:56
2
Donnie84 wrote:
St1: m-1 and n+1 are consecutive positive integers.

Case 1:
m is even, n is odd and m < n
Let m = 2, n = 3
m-1 = 1, n+1 = 4 -> not consecutive positive integers.

Case 2:
m is even, n is odd and m > n
Let m = 2, n = 1
m-1 = 1, n+1 = 2 -> consecutive positive integers.

Case 3:
m is odd, n is even and m < n
Let m = 3, n = 4
m-1 = 2, n+1 = 5 -> not consecutive positive integers.

Case 4:
m is odd, n is even and m > n
Let m = 3, n = 2
m-1 = 2, n+1 = 3 -> consecutive positive integers.

Not sufficient. Dow to B, C or E.

St2: m is an even integer. Not sufficient. If m = 2 and n = 1 -> m > n but if m = 2 and n = 3 -> m < n.

St 1 + St2: Not sufficient as illustrated by case 1 and case 2.

Answer (E).


I think you are making a mistake somewhere !! Well from the different cases you have illustrated it is clear that "A" is sufficient !! Because both cases where m-1,n+1 were consecutive you had m>n therefore statement "1" is clearly sufficient. Hope that helped ;)
Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 116
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 10:09
Zatmah wrote:
Donnie84 wrote:
St1: m-1 and n+1 are consecutive positive integers.

Case 1:
m is even, n is odd and m < n
Let m = 2, n = 3
m-1 = 1, n+1 = 4 -> not consecutive positive integers.

Case 2:
m is even, n is odd and m > n
Let m = 2, n = 1
m-1 = 1, n+1 = 2 -> consecutive positive integers.

Case 3:
m is odd, n is even and m < n
Let m = 3, n = 4
m-1 = 2, n+1 = 5 -> not consecutive positive integers.

Case 4:
m is odd, n is even and m > n
Let m = 3, n = 2
m-1 = 2, n+1 = 3 -> consecutive positive integers.

Not sufficient. Dow to B, C or E.

St2: m is an even integer. Not sufficient. If m = 2 and n = 1 -> m > n but if m = 2 and n = 3 -> m < n.

St 1 + St2: Not sufficient as illustrated by case 1 and case 2.

Answer (E).


I think you are making a mistake somewhere !! Well from the different cases you have illustrated it is clear that "A" is sufficient !! Because both cases where m-1,n+1 were consecutive you had m>n therefore statement "1" is clearly sufficient. Hope that helped ;)


Thanks Zatmah! Great catch! Using both the statements, we are down to case 2 only in which m > n.

Answer is (C).
Current Student
avatar
B
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5
GMAT ToolKit User
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 11:41
1
Donnie84 wrote:
St1: m-1 and n+1 are consecutive positive integers.

Case 1:
m is even, n is odd and m < n
Let m = 2, n = 3
m-1 = 1, n+1 = 4 -> not consecutive positive integers.

Case 2:
m is even, n is odd and m > n
Let m = 2, n = 1
m-1 = 1, n+1 = 2 -> consecutive positive integers.

Case 3:
m is odd, n is even and m < n
Let m = 3, n = 4
m-1 = 2, n+1 = 5 -> not consecutive positive integers.

Case 4:
m is odd, n is even and m > n
Let m = 3, n = 2
m-1 = 2, n+1 = 3 -> consecutive positive integers.

Not sufficient. Dow to B, C or E.

St2: m is an even integer. Not sufficient. If m = 2 and n = 1 -> m > n but if m = 2 and n = 3 -> m < n.

St 1 + St2: Not sufficient as illustrated by case 1 and case 2.

Answer (E).



You're almost correct; look at your statement 1 possibilities. Both of the possibilities that show m, n as consecutive integers also have m>n. Therefore statement A is sufficient.
Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 116
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 12:12
speedilly wrote:
Donnie84 wrote:
St1: m-1 and n+1 are consecutive positive integers.

Case 1:
m is even, n is odd and m < n
Let m = 2, n = 3
m-1 = 1, n+1 = 4 -> not consecutive positive integers.

Case 2:
m is even, n is odd and m > n
Let m = 2, n = 1
m-1 = 1, n+1 = 2 -> consecutive positive integers.

Case 3:
m is odd, n is even and m < n
Let m = 3, n = 4
m-1 = 2, n+1 = 5 -> not consecutive positive integers.

Case 4:
m is odd, n is even and m > n
Let m = 3, n = 2
m-1 = 2, n+1 = 3 -> consecutive positive integers.

Not sufficient. Dow to B, C or E.

St2: m is an even integer. Not sufficient. If m = 2 and n = 1 -> m > n but if m = 2 and n = 3 -> m < n.

St 1 + St2: Not sufficient as illustrated by case 1 and case 2.

Answer (E).



You're almost correct; look at your statement 1 possibilities. Both of the possibilities that show m, n as consecutive integers also have m>n. Therefore statement A is sufficient.


Thanks speedilly! Got it finally. Gosh, this question was really challenging :oops:
Manager
Manager
User avatar
B
Joined: 09 Nov 2013
Posts: 61
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 12 Feb 2014, 23:46
Zatmah wrote:
Donnie84 wrote:
St1: m-1 and n+1 are consecutive positive integers.

Case 1:
m is even, n is odd and m < n
Let m = 2, n = 3
m-1 = 1, n+1 = 4 -> not consecutive positive integers.

Case 2:
m is even, n is odd and m > n
Let m = 2, n = 1
m-1 = 1, n+1 = 2 -> consecutive positive integers.

Case 3:
m is odd, n is even and m < n
Let m = 3, n = 4
m-1 = 2, n+1 = 5 -> not consecutive positive integers.

Case 4:
m is odd, n is even and m > n
Let m = 3, n = 2
m-1 = 2, n+1 = 3 -> consecutive positive integers.

Not sufficient. Dow to B, C or E.

St2: m is an even integer. Not sufficient. If m = 2 and n = 1 -> m > n but if m = 2 and n = 3 -> m < n.

St 1 + St2: Not sufficient as illustrated by case 1 and case 2.

Answer (E).


I think you are making a mistake somewhere !! Well from the different cases you have illustrated it is clear that "A" is sufficient !! Because both cases where m-1,n+1 were consecutive you had m>n therefore statement "1" is clearly sufficient. Hope that helped ;)


Indeed, A is sufficient ,:)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58428
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 17 Feb 2014, 01:48
1
SOLUTION

If m and n are consecutive positive integers, is m greater than n?

(1) m-1 and n+1 are consecutive positive integers --> m>n, if m were less than n than m-1 (integer less than m) and n+1 (integer more than n) wouldn't be consecutive. Sufficient.

Or look at this in another way: stem says that the distance between m and n is 1. Now, if m<n then the distance between m-1 and n+1 would be 3 and they couldn't be consecutive as (1) states. Thus it must be true that m>n.

(2) m is an even integer. Clearly insufficient.

Answer: A.
_________________
Intern
Intern
avatar
Joined: 02 Jan 2014
Posts: 10
Schools: INSEAD Jan '15
GMAT ToolKit User
Re: If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 23 Feb 2014, 11:46
1
Hi - I have another (slightly different way) that works better and faster for me


If m and n are consecutive positive integers, is m greater than n?

(1) m-1 and n+1 are consecutive positive integers.
For M > N to be consecutive and true,
M = N + 1 and N = M -1
stem (1) give us precisely the algebraic expression we require to prove M > N is true

(2) m is an even integer
Insufficient. For example, if M = 4, N could be 3 or 5.

Hence A alone is sufficient.
Senior Manager
Senior Manager
User avatar
B
Joined: 10 Mar 2013
Posts: 467
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
If m and n are consecutive positive integers, is m greater t  [#permalink]

Show Tags

New post 14 Jun 2015, 02:52
1
Statement 1) Let's pick some consecutive numbers

Case 1
m=15 , n=14
m-1=14, n+1=15

Case2
m=14, n=15
M-1=13 n+1=16 --> not sonsecutive --> m>n (see first case, m&n can be consecutive ONLY in case M>N )


Statement 2) clearly not sufficient
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660
Intern
Intern
avatar
Joined: 18 Nov 2015
Posts: 5
If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 24 Feb 2016, 02:52
If m and n are consecutive positive integers, is m greater than n ?

(1) m -1 and n + 1 are consecutive positive integers.
(2) m is an even integer.




Arithmetic Properties of numbers
For two integers x and y to be consecutive, it is
both necessary and sufficient that I x - y I = 1.
(1) Given that m-1 and n + 1 are consecutive
integers, it follows that ~ m - 1)- ( n + 1 ~ = 1,
or lm - n - ~ = 1. Therefore, m - n - 2 = 1 or
m - n - 2 = -1. The former equation implies
that m- n = 3, which contradicts the fact
that m and n are consecutive integers.
Therefore, m - n - 2 = -1, or m = n + 1,
and hence m > n; SUFFICIENT.
(2) If m = 2 and n = 1, then m is greater than n.
However, if m = 2 and n = 3, then m is not
greater than n; NOT sufficient

I know all of the topics of the question. But my confusion is that question describes m and n are consecutive positive integers, so why we need
I x - y I = 1. Why we use absolute for positive integers. Would any one like to explain me please.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7962
Re: If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 24 Feb 2016, 02:58
1
Bahadur wrote:
If m and n are consecutive positive integers, is m greater than n ?

(1) m -1 and n + 1 are consecutive positive integers.
(2) m is an even integer.




Arithmetic Properties of numbers
For two integers x and y to be consecutive, it is
both necessary and sufficient that I x - y I = 1.
(1) Given that m-1 and n + 1 are consecutive
integers, it follows that ~ m - 1)- ( n + 1 ~ = 1,
or lm - n - ~ = 1. Therefore, m - n - 2 = 1 or
m - n - 2 = -1. The former equation implies
that m- n = 3, which contradicts the fact
that m and n are consecutive integers.
Therefore, m - n - 2 = -1, or m = n + 1,
and hence m > n; SUFFICIENT.
(2) If m = 2 and n = 1, then m is greater than n.
However, if m = 2 and n = 3, then m is not
greater than n; NOT sufficient

I know all of the topics of the question. But my confusion is that question describes m and n are consecutive positive integers, so why we need
I x - y I = 1. Why we use absolute for positive integers. Would any one like to explain me please.


Hi,
we take ABSOLUTE MOD because we are not aware whether x is big or y is big..
if x is bigger, x-y=1..
if y is bigger, x-y=-1..
so |x-y|=1..

_________________
Intern
Intern
avatar
Joined: 18 Nov 2015
Posts: 5
Re: If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 24 Feb 2016, 03:07
chetan2u wrote:
Bahadur wrote:
If m and n are consecutive positive integers, is m greater than n ?

(1) m -1 and n + 1 are consecutive positive integers.
(2) m is an even integer.




Arithmetic Properties of numbers
For two integers x and y to be consecutive, it is
both necessary and sufficient that I x - y I = 1.
(1) Given that m-1 and n + 1 are consecutive
integers, it follows that ~ m - 1)- ( n + 1 ~ = 1,
or lm - n - ~ = 1. Therefore, m - n - 2 = 1 or
m - n - 2 = -1. The former equation implies
that m- n = 3, which contradicts the fact
that m and n are consecutive integers.
Therefore, m - n - 2 = -1, or m = n + 1,
and hence m > n; SUFFICIENT.
(2) If m = 2 and n = 1, then m is greater than n.
However, if m = 2 and n = 3, then m is not
greater than n; NOT sufficient

I know all of the topics of the question. But my confusion is that question describes m and n are consecutive positive integers, so why we need
I x - y I = 1. Why we use absolute for positive integers. Would any one like to explain me please.


Hi,
we take ABSOLUTE MOD because we are not aware whether x is big or y is big..
if x is bigger, x-y=1..
if y is bigger, x-y=-1..
so |x-y|=1..


thank you I have overcome my confusion. thank you.
Intern
Intern
avatar
Joined: 25 Jun 2014
Posts: 42
GMAT 1: 690 Q48 V37
WE: Operations (Computer Software)
Re: If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 24 Feb 2016, 03:16
1
(1) m - 1 and n + 1 are consecutive positive integers.
(2) m is an even integer.



Statement I : Sufficient

Lets take the help of numbers here.

m = 3 and n = 2
m-1 = 2 and n + 1 = 3 ( m-1 and n+1 are consecutive integers).

m = 2 and n = 3
m-1 = 1 and n + 1 = 4 ( m-1 and n+1 are not consecutive integers).

Generalize it,

m = x

n = x + 1

m - 1 = x - 1

n + 1 = x + 2

In this case, m-1 and n+1 are not consecutive positive integers.

Now,

m = x + 1

n = x

m - 1 = x

n + 1 = x + 1

In this case, m-1 and n+1 are consecutive positive integers.

Hence m > n


Statement II: Not Sufficient.


Answer A
_________________
Did I Help You..If Yes.. Then Kudos Please.. :-)
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 922
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User
Re: If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 29 Jun 2017, 14:42
If m and n are consecutive positive integers, is m greater than n ?

(1) m-1 and n+1 are consecutive positive integers.

Lets check by substituting some values

\(I - m > n\)

\(m = 4 & n = 3\)

\(m - 1 = 4 - 1 = 3\)

\(n + 1 = 3 + 1 = 4\)

\(I - m > n\) - Satisfies the Equation as we are getting two consecutive integers 3 & 4 (Also you can check by plugging in other values like 7 & 8)

\(II - m < n\)

\(m = 3 & n = 4\)

\(m - 1 = 3 - 1 = 2\)

\(n + 1 = 4 + 1 = 5\)

\(II - m < n\) - This does not satisfy the Equation as we are not getting two consecutive equations. (Also you can check by plugging in other values like 8 & 7)

Hence, we see that in order to satisfy the Eq. (1), m has to be greater than n.

Hence (1) =====> is SUFFICIENT

(2) m is an even integer.

m is even, this does not give us any information about n, n can be consecutive integer which is higher than m or consecutive integer which is lower than m.

Hence, (2) =====> is NOT SUFFICIENT

Hence, Answer is A
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Senior Manager
Senior Manager
avatar
P
Joined: 27 Dec 2016
Posts: 309
CAT Tests
Re: If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 29 Jun 2017, 17:58
I have one small confusion. The question says that "if m and n are consecutive positive integers..." Doesn't this imply automatically that the order is m and then n? How are we unsure that its not m and n rather it could be n and m? Please help me.

Thanks!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58428
Re: If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 29 Jun 2017, 23:52
csaluja wrote:
I have one small confusion. The question says that "if m and n are consecutive positive integers..." Doesn't this imply automatically that the order is m and then n? How are we unsure that its not m and n rather it could be n and m? Please help me.

Thanks!


If it were the way you are saying, we won't have this question. So, x and y are consecutive integers does NOT necessarily mean that y > x.

P.S. Also, note that this is an official question.
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13214
Re: If m and n are consecutive positive integers, is m greater than n ?  [#permalink]

Show Tags

New post 24 Sep 2018, 19:02
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 Bot
Re: If m and n are consecutive positive integers, is m greater than n ?   [#permalink] 24 Sep 2018, 19:02
Display posts from previous: Sort by

If m and n are consecutive positive integers, is m greater than n ?

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





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