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Problem 100

Geometry Difficulty 1.2 Multiple choice CEMC Fermat · Canada · 2024

Square $PQRS$ is divided into
$16$ smaller congruent squares, as
shown.

What fraction of $PQRS$ is
shaded?

Pick one

Official solution

Square $PQRS$ is made up of
$16$ equal-sized small squares.

Of these, $2$ are fully shaded and
$8$ are half-shaded.

This shading is equivalent to fully shading $2 + 8 \cdot \frac{1}{2} = 2 + 4 = 6$ of
the $16$ small squares.

Thus, square $PQRS$ is $\frac{6}{16} = \frac{3}{8}$ shaded.

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