It's good to realize that no two distinct prime numbers have a common divisor other than 1.


We are asked to find the greatest common divisor of m and n


(1) If m is a prime number, n may or may not be a multiple of m. If it is, then the GCD is m. Otherwise, it is 1.
NOT SUFF
(2) If 2n = 7m, we can say thay n and m are in a 7 to 2 ratio (i.e. n=7x and m=2x for some positive integer x. The GCD will be x, but we have no way of finding its value.
NOT SUFF
(T) M =2x is a prime number, so x=1 and thus the GCD is 1. SUFF


Alternatively, if 7m =2n , 7m is even and m (a prime number) must be 2. We can find the value for n and thus answer the question.

How come in posts like these i dont see the question in the first post? Is it in an attachment?

@madhan_dc It's embedded as an image from postimage.org. You might want to check your browser settings.