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Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

In the multiplication shown, $P$ , $Q$ and $R$ are all different digits so that $PPQ \times Q = RQ5Q$ What is the value of $P + Q + R$ ?

(A) $20$ (B) $13$ (C) $15$ (D) $16$ (E) $17$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.