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The volume of a cube is $V$ cm$^3$. The surface area of the cube is $2V$ cm$^2$. What is the value of $V$?

(A) $8$ (B) $16$ (C) $27$ (D) $64$ (E) $128$

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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, ordering) added by this project. Solutions are the publisher's, linked not copied.