remainder

Statement (1) is clearly insufficient. N could be 13, 38, 63, or 88.

Statement (2) implies that N is the intersection of two sets: those numbers that satisfy the given condition (an extension of the above four numbers) and the set of {3, 23, 43, 63, 83...} This is not sufficient, however, as these sets cross at 63, 163, 263, 363, and so on.

Both statements combined limits the intersection to 63, and thus is sufficient. The answer is C.