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2002 AMC 10B Problems/Problem 7

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Problem

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 \m...

Solution

Writing the first four fractions with a common denominator, we have \frac{41}{42}+\frac{1}{n}, hence n=42 is a solution. Thus, our answer is \boxed{(E)}.

See Also

2002 AMC 10B (ProblemsResources)
Preceded by
Problem 6
Followed by
Problem 8
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