Library / UKMT Junior Kangaroo /112 of 243

UKMT Junior Kangaroo, 2024

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

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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.