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When I increase a certain number by 20%, I get twice as much as when I decrease 20 less than the number by 20%. What is that number?

(A) $40$ (B) $60$ (C) $80$ (D) $100$ (E) $120$

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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.