Maths Olympiad Prep

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CEMC Gauss (Grade 8), 2015

Algebra Difficulty 1.2 Junior Find the answer Canada

The equal-arm scale shown is balanced.

Figure 0

One Figure 1 has the same mass as

Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

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

Solutions — 3

Solution 1

The equal-arm balance shows that 2 rectangles have the same mass as 6 circles.
If we organize these shapes into two equal piles on both sides of the balance, then we see that 1 rectangle has the same mass as 3 circles.

Solution 2

The equal-arm scale shows that 22 squares have the same mass as 44 circles.

If we split the 22 squares and the
44 circles each into two equal
groups, then 11 square has the same
mass as 22 circles.

Solution 3

The length of the side not labelled is equal to the sum of the two horizontal lengths that are labelled, or 2+3=52+3=5. Thus, the perimeter of the figure shown is 5+5+2+3+3+2=205+5+2+3+3+2=20.

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