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Current Student B
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]

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6 00:00

Difficulty:   25% (medium)

Question Stats: 68% (01:08) correct 32% (01:03) wrong based on 159 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 V
Joined: 02 Sep 2009
Posts: 56300
Re: What is the greatest common divisor of positive integers m  [#permalink]

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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.

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Current Student B
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]

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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 V
Joined: 02 Aug 2009
Posts: 7764
What is the greatest common divisor of positive integers m  [#permalink]

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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
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Re: What is the greatest common divisor of positive integers m  [#permalink]

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_________________ Re: What is the greatest common divisor of positive integers m   [#permalink] 27 Dec 2018, 03:17
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