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

1) m is a prime number

2) 2n=7m

(1) If m is a prime number, then it may or may not be a prime factor of n. Hence the greatest common divisor may be either m or m n. Moreover, m and n are also not known. Insufficient

(2) If twice of one positive integer is 7 times another positive integer, then the former must have 7 as its factor, or n has 7 as one of its factor, for sure, whereas, m may or may not have 7 as one of its factor. Also, that the later must have 2 as its factor, or m has 2 as one of its factor, for sure, whereas, n may or may not have 2 as one of its factor. So, if n = 7 p and m = 2 q for some positive integers p and q, then their greatest common divisor is the greatest common divisor of the positive integers p and q that we don't know. Insufficient

Taken together

If m is prime, then q is 1, and the greatest common divisor of p and 1 is p. We don't know what's p. Still insufficient

[spoiler]E[/spoiler]

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

1) m is a prime number

2) 2n=7m

1.) if m is a prime number the greatest common divisor of m and n can be either 1 or m
It is insufficient to conclude what is the gcd

2) 2n = 7m

N is a multiple of 7 and m is a multiple of 2 insufficient to calculate GCD

Now, If we combine these two

m=2 and n=7 and GCD is 1; Sufficient

C according to me

OA is C

ajith wrote: 1.) if m is a prime number the greatest common divisor of m and n can be either 1 or m
It is insufficient to conclude what is the gcd

2) 2n = 7m

N is a multiple of 7 and m is a multiple of 2 insufficient to calculate GCD

Now, If we combine these two

m=2 and n=7 and GCD is 1; Sufficient

Ajith,

Can you explain statements I and II with a bit more in detail? Esp., the concept behind it.

sanju09 wrote:

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

1) m is a prime number

2) 2n=7m

(1) If m is a prime number, then it may or may not be a prime factor of n. Hence the greatest common divisor may be either m or m n. Moreover, m and n are also not known. Insufficient

(2) If twice of one positive integer is 7 times another positive integer, then the former must have 7 as its factor, or n has 7 as one of its factor, for sure, whereas, m may or may not have 7 as one of its factor. Also, that the later must have 2 as its factor, or m has 2 as one of its factor, for sure, whereas, n may or may not have 2 as one of its factor. So, if n = 7 p and m = 2 q for some positive integers p and q, then their greatest common divisor is the greatest common divisor of the positive integers p and q that we don't know. Insufficient

Taken together

If m is prime, then q is 1, and the greatest common divisor of p and 1 is p. We don't know what's p. Still insufficient

[spoiler]E[/spoiler]

Oh yes!!

If m is prime, then q is 1, to allow us take m = 2, now; and also if 2 n = 7 m, n = 7, and the greatest common divisor of m and n is 1.

[spoiler]sorry...it's C[/spoiler]