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| − | == Problem ==
| + | #REDIRECT[[2002 AMC 12B Problems/Problem 4]] |
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| − | Let <math>n</math> be a positive integer such that <math>\frac {1}{2} + \frac {1}{3} + \frac {1}{7} + \frac {1}{n}</math> is an integer. Which of the following statements is ''not'' true?
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| − | <math> \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 </math>
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| − | ==Solution==
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| − | Writing the first four fractions with a common denominator, we have <math>\frac{41}{42}+\frac{1}{n}</math>, hence <math>n=42</math> is a solution. Thus, our answer is <math>\boxed{(E)}</math>.
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| − | ==See Also==
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| − | {{AMC10 box|year=2002|ab=B|num-b=6|num-a=8}}
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| − | [[Category:Introductory Number Theory Problems]] | |
