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Number theory Difficulty 2.0 Junior Find the answer United Kingdom

The positive integers $m$ , $n$ and $p$ satisfy the equation $3m + \dfrac{3}{n + \frac{1}{p}} = 17$ . What is the value of $p$ ?

(A) $2$ (B) $3$ (C) $4$ (D) $6$ (E) $9$

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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.