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What is the greatest common divisor of positive integers m

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

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New post 18 Aug 2014, 08:02
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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
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Re: What is the greatest common divisor of positive integers m  [#permalink]

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New post 18 Aug 2014, 08:52
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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.

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

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New post 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.

Answer: D.





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

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New post 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
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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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