2002 AMC 10B Problem 7

Let n be a positive integer such that \frac{1}{2}+\frac{1}{3}+\frac{1}{7}+\frac{1}{n} is an integer. Which of the following statements is not true?

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.