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# G, M, and N are integers, M=X+6; G is the greatest common

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Senior Manager
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G, M, and N are integers, M=X+6; G is the greatest common [#permalink]  06 May 2006, 02:43
G, M, and N are integers, M=X+6; G is the greatest common factor of M and N. G=?

1) N=2531
2) N=X+7
Director
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From A) 2531 is a prime so M=q* 2531. Since 2531 is the GREATEST common factor, or G, then G-2531 so A SUF

From B) seems that M and N are consecutive integers and their GCF is 1 so B is SUFF

Tough Q
Intern
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It is C.

1 Not suff - We donot know what is X. X can be 2525 in which case G will be 2531 or X can be other than 2525 in which case G will be 1.

2 Not suff - We donot know what is M and N.

Combine together. we have M = X + 6 and N = X + 7. 2 consecutive numbers and hence G is 1.
VP
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narsi wrote:
It is C.

1 Not suff - We donot know what is X. X can be 2525 in which case G will be 2531 or X can be other than 2525 in which case G will be 1.

2 Not suff - We donot know what is M and N.

Combine together. we have M = X + 6 and N = X + 7. 2 consecutive numbers and hence G is 1.

Why do u think B is not sufficient? I think B is! It shows that they are consecutive, hence relatively prime!
Manager
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BG wrote:
From A) 2531 is a prime so M=q* 2531. Since 2531 is the GREATEST common factor, or G, then G-2531 so A SUF

How do you quickly determine if a number is prime?
Manager
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trick question. I agree with B
VP
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BG wrote:
From A) 2531 is a prime so M=q* 2531. Since 2531 is the GREATEST common factor, or G, then G-2531 so A SUF

From B) seems that M and N are consecutive integers and their GCF is 1 so B is SUFF

Tough Q

beautiful work. but how do you know that, in a, gcf is 2531? m could also be 2531. so gcf could be 1 or 2531.

agree with B.
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shevy wrote:
BG wrote:
From A) 2531 is a prime so M=q* 2531. Since 2531 is the GREATEST common factor, or G, then G-2531 so A SUF

How do you quickly determine if a number is prime?

Does anyone have any answer to this? I wouldn't be able to tell just by looking at the problem that 2531 is a prime number. Any shortcuts to calculate this?

Thanks!
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Definitely 'B'.

M=X+6; from 2) N=X+7.
M=N-1, so we have 1 as GCF.

Guys please remember me the rule when the digit is divided by 3, when by 4, by 6, by 7, by 8, by 9.
I forgot it. Just remember something like when the sum of the last 2 digits of any number is divided by 4 the number is divided by 4.

Thank you.
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