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2001 AMC 12 Problems/Problem 9

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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 \boxed{\mathrm{C}}.

See Also

2001 AMC 12 (ProblemsResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
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