When 14 is divided by 5 , the remainder is 4 . When 14 is divided by a positive integer $n$, the remainder is 2 . For how many different values of $n$ is this possible?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
When 14 is divided by $n$, the remainder is 2 , so $n$ must divide evenly into $14-2=12$. Therefore, $n$ could be $1,2,3,4,6$, or 12 .

But the remainder has to be less than the number we are dividing by, so $n$ cannot be 1 or 2 . Thus, $n$ can be $3,4,6$ or 12 , so there are 4 possible values of $n$.

ANSWER: (D)