Maths Olympiad Prep

Library / UKMT Senior Kangaroo /102 of 139

UKMT Senior Kangaroo, 2025

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

A teacher works out the number of different ways, WW, she can choose two students from Class A. She also works out the number of different ways, VV, she can choose two students from Class B. Class A has four more students in it than class B. She notices that W=3VW = 3V. How many students are there in class A?

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.