# Difference between revisions of "2001 AMC 12 Problems/Problem 9"

## Problem

Let $f$ be a function satisfying $f(xy) = \frac{f(x)}y$ for all positive real numbers $x$ and $y$. If $f(500) =3$, what is the value of $f(600)$?

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

## Solution

$f(500\cdot\frac65) = \frac3{\frac65} = \frac52$, so the answer is $\mathrm{C}$.