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Problem 304

Combinatorics Difficulty 2.4 Multiple choice CEMC Pascal · Canada · 2024

Glen, Hao, Ioana, Julia, Karla, and Levi participated in the 2023
Canadian Team Mathematics Contest. On their team uniforms, each had a
different number chosen from the list $11$ , $12$ , $13$ , $14$ , $15$ , $16$ . Hao’s and Julia’s numbers were even.
Karla’s and Levi’s numbers were prime numbers. Glen’s number was a
perfect square. What was Ioana’s number?

Pick one

Official solution

The perimeter of a rectangle is made up of two widths and two
lengths.

Since each length is twice the width, then two lengths is equivalent to
four widths, and so the perimeter is equal to $2+4=6$ times the width.

Since the perimeter of the rectangle is $120
$\text{}$ cm}, then the width of the rectangle is $\text{120}$ cm}}{6}=20 $\text{}$
cm}$.

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