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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

A function $f$ satisfies $y^3 f(x) = x^3 f(y)$ and $f(3) \neq 0$ . What is the value of $\dfrac{f(20) - f(2)}{f(3)}$ ?

(A) $6$ (B) $20$ (C) $216$ (D) $296$ (E) $2023$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.