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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The product of two positive integers is equal to twice their sum. This product is also equal to six times the difference between the two integers. What is the sum of these two integers?

(A) $6$ (B) $7$ (C) $8$ (D) $9$ (E) $10$

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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.