Maths Olympiad Prep

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Problem 108

Geometry Difficulty 1.3 Multiple choice CEMC Gauss (Grade 8) · Canada · 2019

The circumference of a circle is 100. The diameter of this circle is equal to

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Official solution

Solution 1

One third of 396 is 396÷3=132396\div3=132. Thus, Joshua has read 132 pages of the book.

To finish the book, Joshua has 396132=264396-132=264 pages left to read.

Solution 2

Joshua has read the first third of the book only, and so he has 113=231-\frac13=\frac23 of the book left to read.

Two thirds of 396 is 396×23=396×23=7923=264396\times\frac23=\frac{396\times2}{3}=\frac{792}{3}=264.

Joshua has 264 pages left to read.

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