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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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28 Mar 2012, 23:38

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

(1) m is a prime number.

(2) m and n are consecutive integers.

Spoiler: OA

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

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29 Mar 2012, 00:25

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

(1) m is a prime number. Not sufficient as no info about n.

(2) m and n are consecutive integers. Any two consecutive positive integers are co-prime, which means that they do not share any common factor but 1. For example: 3 and 4, 5 and 6, 100 and 101, are consecutive integers and they do not share any common factor but 1. So, the greatest common divisor of m and n is 1. Sufficient.

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

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Updated on: 01 Dec 2015, 20:44

Hi All,

This DS question can be solved by TESTing VALUES and/or a bit of logic.

We're told that M and N are both POSITIVE INTEGERS. We're asked for the greatest common divisor of M and N.

1) M is a prime number.

This Fact tells us nothing about N.

IF...
M = 2
N = 2
Then the answer to the question is 2

IF...
M = 2
N = 3
Then the answer to the question is 1
Fact 1 is INSUFFICIENT

2) M and N are CONSECUTIVE integers.

The second TEST from Fact 1 'fits' this Fact too...

IF...
M = 2
N = 3
Then the answer to the question is 1

Looking at this example, you might notice that when dealing with consecutive positive integers, the ONLY factor that will divide into both numbers is 1. If you 'TEST' 3 and 4, 4 and 5, 5 and 6, etc., you 'll get the SAME answer every time.
Fact 2 is SUFFICIENT

Final Answer:

Spoiler: ::

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Originally posted by EMPOWERgmatRichC on 29 Nov 2015, 15:26.
Last edited by EMPOWERgmatRichC on 01 Dec 2015, 20:44, edited 1 time in total.

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

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01 Dec 2015, 03:02

Here, we are given that m & n are Positive Integers, & we have to find Greatest Common divisor of m & n.

Statement 1 says: m is a prime number, but we don't know anything of n
Therefore insufficient

Statement 2 says: m and n are consecutive integers.
Now you may take any values of m & n, the greatest common divisor will always be 1

Therefore sufficient.

Answer is B.

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

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16 Mar 2016, 08:49

Using the rule that any two consecutive are co- primes we can say B is sufficient and GCD =1
hence B
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Re: What is the greatest common divisor of positive integers m [#permalink]

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11 Jul 2016, 08:27

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

Statement 1) M is a prime number. INSUFFICIENT
If M is prime and N is also prime then GCF=1 (Example 3 and 5 ; GCF=1)
If M is prime and N is a multiple of that prime then GCF=M (example 3 and 6; GCF=3)

Statement 2) SUFFICIENT
Any two conceptive integers will be a pair of ODD and EVEN. They will share no factor EXCEPT 1

THEREFORE B is sufficient GCF=always 1

eybrj2 wrote:

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

(1) m is a prime number.

(2) m and n are consecutive integers.

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

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29 Sep 2018, 21:50

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