2001 AMC 12 Problem 9 — Solution | LIVE by Po-Shen Loh

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2001 AMC 12 Problem 9

Attempt Problem 9 of the 2001 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

9.

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

$1$

$2$

$\dfrac{5}{2}$

$3$

$\dfrac{18}{5}$

Answer: C

Concepts:functional equation substitution

Difficulty rating: 1440

Solution:

Choose $x = 500$ and $y = \dfrac{6}{5}$ so that $xy = 600.$ Then $f(600) = \dfrac{f(500)}{6/5} = \dfrac{3}{6/5} = \dfrac{5}{2}.$

Thus, the correct answer is C.

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