Maths Olympiad Prep

Library / /119 of 213

, 2023

Geometry Difficulty 1.5 Junior Find the answer Canada

Bindu’s bike tires have a radius of 30 cm. She rides her bike far
enough that the tires rotate exactly five times. How far does Bindu’s
bike travel?

Pick one

Solution

The given list, 2,9,4,n,2n2,9,4,n,2n
contains 5 numbers.

The average of these 5 numbers is 6, and so the sum of the 5 numbers is
5×6=305\times 6=30.

That is, 2+9+4+n+2n=302+9+4+n+2n=30 or 15+3n=3015+3n=30, and so 3n=153n=15 or n=5n=5.

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.