Very nice question and answer is indeed "B". I picked "D" initially.

Explanation, The whole question boils down to --> n/m = integer or not. We know, 3<m<13.

1. Given, 3n/m= integer, it CAN NOT be refered that n/m is interger because 3<m<13.

Check this - if n=14 and m=6. This condition is invalid. Hence insuff.

2. Given, 13n/m= integer, it CAN be refered that n/m is interger because m<13 & m is PRIME number.

Hence suff.

Hence B is the answer.

Cheers.

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