Maths Olympiad Prep

Library / UKMT Junior Kangaroo /78 of 243

UKMT Junior Kangaroo, 2018

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a plan of a town with various bus stops. There are four bus routes in the town. Route 1 goes C−D−E−F−G−H−CC-D-E-F-G-H-C and is 1717 km long. Route 2 goes A−B−C−F−G−H−AA-B-C-F-G-H-A and is 1212 km long. Route 3 goes A−B−C−D−E−F−G−H−AA-B-C-D-E-F-G-H-A and is 2020 km long. Route 4 goes C−F−G−H−CC-F-G-H-C. How long is route 4?

(A) 1010 km (B) 99 km (C) 88 km (D) 77 km (E) 66 km

Figure for this problem

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.