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Problem 121

Combinatorics Difficulty 1.3 Find the answer CEMC Gauss (Grade 8) · Canada · 2025

Each of Mrs. Myer’s students voted exactly once for their
favourite season.

Which of the following statements about the results in the graph
shown is false?

Five students voted for Fall.
Winter received more votes than Spring.
Thirty-five students participated in this survey.
More than half of the students voted for Summer.
Fall and Spring received the same number of votes.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Reading from the graph, $5$
students voted for Spring, $15$ voted
for Summer, $5$ voted for Fall, and
$10$ voted for Winter.

Therefore, (A) Fall and Spring received the same number of votes, (B)
Winter received more votes than Spring, (C) $35$ students participated in the survey,
and (E) $5$ students voted for Fall,
are all true statements.

Since $15$ students voted for Summer
and $15$ is less than half of $35$ , then (D) is the statement that is
false.

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