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Number theory Difficulty 2.0 Junior Find the answer United Kingdom

What is the smallest possible sum of two positive integers whose product is 240?

(A) $30$ (B) $31$ (C) $32$ (D) $34$ (E) $38$

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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.