AMC 12 2002b Problem 4

Let $n$ be a positive integer such that $\frac 12 + \frac 13 + \frac 17 + \frac 1n$ is an integer. Which of the following statements is '''not''' true:

$\mathrm{(A)}\ 2\ \text{divides\ }n \mathrm{(B)}\ 3\ \text{divides\ }n \mathrm{(C)}\ 6\ \text{divides\ }n \mathrm{(D)}\ 7\ \text{divides\ }n \mathrm{(E)}\ {n > 84}$