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Number theory Difficulty 1.0 Junior Find the answer United Kingdom

What fraction of the integers from $1$ to $8000$ inclusive are cubes?

(A) $\dfrac{1}{1000}$ (B) $\dfrac{1}{800}$ (C) $\dfrac{1}{400}$ (D) $\dfrac{1}{200}$ (E) $\dfrac{1}{100}$

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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.