p is multiple of q means p=nq where n is an integer. or p/q = n
a) p/3q is an integer -> p/q = integer*3 = n (where n is an integer)
True
b) 3p/7q is an integer. or p/q = 7*integer/3. Now it is possible that integer is not multiple of 3, and thus p/q is not an integer. It is also possible that integer is multiple of 3, and p/q is an integer. thus insufficient.
IMO A

The prompt asks, is p=q*i, where i is some integer

In statement 1, we have p/3q = integer. This means that p should at least have a factor of both 3 and q in order to be divisible by 3q. Therefore, p/q=3*integer. If you substitute this back in to the main equation, is p=q*i, we get, Is 3*integer=i ?. Sufficient

In statement 2, we have 3p/7q = integer. Using the same reasoning, p should at least have a factor of 7 and q in order to be divisible by 7q. Therefore, p=7/3*integer. Substituting this back in to the main equation, we get, Is 7/3*integer =i ? If the integer is a multiple of 3, the result will be an integer, whereas, if it is a non-multiple of 3, the result will be a fraction. Insufficient

Thanks for the reasoning. It helped me !