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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 $f(100)$?

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

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Official solution

We are given $3 = f(500) = f(100 \times 5) = \frac{f(100)}{5}$, so $f(100) = 3 \times 5 = 15$.

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