AoPSWiki
Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.

2002 AMC 10B Problems/Problem 7

From AoPSWiki

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
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
Trying to get to the USAMO in 2010? Our AIME Problem Series can help you get there! Click here to enroll today!
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us