HMMT November 2010 T9

A function $f(x, y, z)$ is linear in $x, y$ , and $z$ such that $f(x, y, z)=\frac{1}{x y z}$ for $x, y, z \in\{3,4\}$ . What is $f(5,5,5)$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{216}

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