Clearly both 1 and 5 are possible remainders, as are 7 and 11. There's something wrong with the question. What's the source?

Carol wrote: the numerator must be greater than the dominator, for the quotient won't be zero!

There's nothing wrong with having a quotient of zero in this question. All we know is that N is greater than 3. Unless some information is missing from the question itself, or something has been mistranscribed, there isn't enough information here to give a unique answer- there are four possible answers (1, 5, 7, 11). If you replace the number '12' in the question with a '2', however, then the answer would be B, since you'd know N was odd. That's the only quick adjustment I can think to make to the question if we want the question to make any sense.