Difference between revisions of "2002 AMC 12P Problems/Problem 6"

Revision as of 00:17, 30 December 2023

Problem

Participation in the local soccer league this year is $10\%$ higher than last year. The number of males increased by $5\%$ and the number of females increased by $20\%$ . What fraction of the soccer league is now female?

$\text{(A) }\frac{1}{3} \qquad \text{(B) }\frac{4}{11} \qquad \text{(C) }\frac{2}{5} \qquad \text{(D) }\frac{4}{9} \qquad \text{(E) }\frac{1}{2}$

Solution

If $\log_{b} 729 = n$ , then $b^n = 729$ . Since $729 = 3^6$ , $b$ must be $3$ to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of $b \Longrightarrow \boxed{\mathrm{E}}$ .

2002 AMC 12P (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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 == Problem ==
-Participation in the local soccer league this year is <math>10</math>% higher than last year. The number of males increased by <math>5</math>% and the number of females increased by <math>20</math>%. What fraction of the soccer league is now female?
+Participation in the local soccer league this year is <math>10\%</math> higher than last year. The number of males increased by <math>5\%</math> and the number of females increased by <math>20\%</math>. What fraction of the soccer league is now female?
 <math>

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Difference between revisions of "2002 AMC 12P Problems/Problem 6"

Revision as of 00:17, 30 December 2023

Problem

Solution

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