Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So

EDIT: corrected explanation.

Questions dealing with number properties can almost always be solved logically, with very little calculation.
We'll look for such an answer, a Logical approach.

(1) If we were told that n were an integer, than this would be sufficient, as 3 and 14 are mutually prime. Since it is not, we can manipulate things however we like. For example, choosing 3n/14 = 1, would give n/14 = 1/3, which is not an integer while choosing 3n/14 = 3 would give n/14 = 1, which is
Insufficient.

(2) this implies that n/7 is an integer which in turn implies that n is an integer divisible by 7. If n has 2 in its prime factors, then n/14 is an integer and if it does not, it is not.
Insufficient.

Combined.
From (2) we learn that n is an integer. Therefore, based on the observation that 3 and 14 are mutually prime, (1) implies that n/14 must be an integer.
Sufficient.

(C) is our answer