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Problem 85

Number theory Difficulty 1.2 Multiple choice CEMC Gauss (Grade 8) · Canada · 2023

Tallulah is playing a game in which she rolls a single standard
die once. If the number rolled is $1,2,3$ , or $4$ , then she wins. If the number rolled is
5 or 6, then she loses. What is the probability that she loses?

Pick one

Official solution

Since the perimeter of $PQRS$
is 40 cm and $SR=16$ cm, then the
combined length of the remaining three sides is $40 \text{ cm}-16 \text{ cm}=24$ cm.

Each of the remaining three sides is equal in length, and so $PQ=\dfrac{24 \text{ cm}}{3}=8$ cm.

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