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Problem 593

AMC 10/12, early questions

Geometry Difficulty 3.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2017

In the diagram, $\triangle PQR$ is equilateral and has side length 6 cm.

Each of the shaded triangles is equilateral and has side length 2 cm. What fraction of the area of $\triangle PQR$ is shaded?

Pick one

Official solution

The positive divisors of 20 are: $1,2,4,5,10,20$ .

Of the 20 numbers on the spinner, 6 of the numbers are divisors of 20.

It is equally likely that the spinner lands on any of the 20 numbers.

Therefore, the probability that the spinner lands on a number that is a divisor of 20 is $\frac{6}{20}$ .

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