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2002 AMC 8 Problems/Problem 25

Revision as of 15:08, 3 July 2012 by Yunyun333 (talk | contribs)

Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have?

$\text{(A)}\ \frac{1}{10}\qquad\text{(B)}\ \frac{1}{4}\qquad\text{(C)}\ \frac{1}{3}\qquad\text{(D)}\ \frac{2}{5}\qquad\text{(E)}\ \frac{1}{2}$

Answer:

Since Ott gets equal amounts of money from each friend, we can say that he gets x dollars from each friend. This means that Moe has 5x dollars, Loki has 4x dollars, and Nick has 3x dollars. The total amount is 12x dollars, and since Ott gets 3x dollars total, 3x/12x=3/12=1/4=B.

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