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Problem 347

Number theory Difficulty 2.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2022

A positive number is divisible by both 3 and 4. The tens digit is
greater than the ones digit. How many positive two-digit numbers have
this property?

Pick one

Official solution

The side lengths of each of the three identical squares are
equal.

The perimeter of $WXYZ$ is 56 m and
is comprised of 8 such side lengths.

Thus, the length of each side of the three identical squares is $56 \text{ m}\div 8=7$ m.

The area of each of the three identical squares is $7 $\text{ m}\times 7 \text{}$ m}=49 $\text{}$
m}^2$.

Therefore, the area of $WXYZ$ is
$3 $\times 49 \text{}$ m}^2=147 $\text{}$
m}^2$.

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