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Number theory Difficulty 2.0 Junior Find the answer United Kingdom

The number 100 is multiplied by either 2 or 3. The result then has 1 or 2 added to it. Finally the new result is divided by either 3 or 4. The final result is an integer. What is this integer?

(A) $50$ (B) $51$ (C) $67$ (D) $68$ (E) More than one final answer is possible

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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.