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2001 AMC 12 Problems/Problem 9

Revision as of 00:51, 8 February 2009 by Duelist (talk | contribs) (→Solution)

Problem

Let $f$ be a function satisfying $f(xy) = \frac{f(x)}y$ for all postitive real numbers $x$ and $y$, and $f(500) =3$. What is $f(600)$?

$(\mathrm{A})\ 1 \qquad (\mathrm{B})\ 2 \qquad (\mathrm{C})\ \frac52 \qquad (\mathrm{D})\ 3 \qquad (\mathrm{E})\ \frac{18}5$

Solution

$f(500\cdot\frac65) = \frac3{\frac65} = \frac25$, so the answer is $\mathrm{C}$.

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