GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 Jan 2020, 06:12

### 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

# What is the greatest common divisor of positive integers m

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34
WE: Engineering (Energy and Utilities)
What is the greatest common divisor of positive integers m  [#permalink]

### Show Tags

18 Aug 2014, 08:02
1
6
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:11) correct 32% (01:05) wrong based on 165 sessions

### HideShow timer Statistics

What is the greatest common divisor of positive integers m and n ?

(1) m-n and n are co-prime
(2) m and n are consecutive integers

Source: 4Gmat
Math Expert
Joined: 02 Sep 2009
Posts: 60687
Re: What is the greatest common divisor of positive integers m  [#permalink]

### Show Tags

18 Aug 2014, 08:52
2
4
What is the greatest common divisor of positive integers m and n ?

(1) m-n and n are co-prime. This means that the greatest common divisor of m-n and n is 1. Now, if m and n had greatest common divisor greater than 1, then m-n would also share the same factor (if x is a factor of both m and n, then x must also be a factor of m-n), thus in this case m-n and n would have that factor as the greatest divisor not 1. Therefore m and n do not share any factor greater than 1. Sufficient.

(2) m and n are consecutive integers. Consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). Thus the greatest common divisor of m and n is 1. Sufficient.

_________________
##### General Discussion
Current Student
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34
WE: Engineering (Energy and Utilities)
Re: What is the greatest common divisor of positive integers m  [#permalink]

### Show Tags

18 Aug 2014, 22:24
Bunuel wrote:
What is the greatest common divisor of positive integers m and n ?

(1) m-n and n are co-prime. This means that the greatest common divisor of m-n and n is 1. Now, if m and n had greatest common divisor greater than 1, then m-n would also share the same factor (if x is a factor of both m and n, then x must also be a factor of m-n), thus in this case m-n and n would have that factor as the greatest divisor not 1. Therefore m and n do not share any factor greater than 1. Sufficient.

(2) m and n are consecutive integers. Consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). Thus the greatest common divisor of m and n is 1. Sufficient.

When you explain it, it seems quite easy , but while working it out, it doesn't seem to be that way. One reason is because, I don't necessarily think in that same line

Any suggestions ?
Math Expert
Joined: 02 Aug 2009
Posts: 8331
What is the greatest common divisor of positive integers m  [#permalink]

### Show Tags

12 Jun 2016, 04:41
alphonsa wrote:
What is the greatest common divisor of positive integers m and n ?

(1) m-n and n are co-prime
(2) m and n are consecutive integers

Source: 4Gmat

Hi,

(1) m-n and n are co-prime
what ever common factors m and n have , m-n, m+n, m and n will also have same factors..

Reason - say m and n have x in common.... so $$m = xa$$ and $$n = xb.$$...
so $$m-n = xa-xb = x(a-b)..................m+n = x(a+b)................m=xa$$ .............n=xb......mn = xa*xb...........
BUT not$$\frac{m}{n}$$
thus all five of them have same common factors..

so IF m-n and n are co-primes or both do not have any factor in common, so m and n will also be co-prime..
Suff

(2) m and n are consecutive integers
consecutive integers do not have any factor other than 1 in common.....
Suff

D
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 14007
Re: What is the greatest common divisor of positive integers m  [#permalink]

### Show Tags

27 Dec 2018, 03:17
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: What is the greatest common divisor of positive integers m   [#permalink] 27 Dec 2018, 03:17
Display posts from previous: Sort by