2002 AMC 10B Problems/Problem 7

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?

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

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 $\boxed{(E)}$ .

2002 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2002 AMC 10B Problems/Problem 7

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