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CEMC Gauss (Grade 8), 2020

Algebra Difficulty 1.7 Junior Find the answer Canada

XX is 20% of 50. 40 is 20% of YY. 40 is ZZ% of 50. What does X+Y+ZX+Y+Z equal?

Pick one

Solution

We begin by recognizing that there are 6 different symbols, and so each face of the cube contains a different symbol.

From left to right, let us number the views of the cube 1, 2 and 3.

Views 1 and 2 each show a face containing the symbol Figure 0 .

What symbol is on the face opposite to the face containing Figure 1  ?

In view 1, Figure 2 and Figure 3 are on faces adjacent to the face containing Figure 4 , and so neither of these can be the symbol that is on the face opposite Figure 5 .

In view 2, Figure 6 and Figure 7 are on faces adjacent to the face containing Figure 8 , and so neither of these can be the symbol that is on the face opposite Figure 9 .

There is only one symbol remaining, and so Figure 10 must be the symbol that is on the face opposite Figure 11 , and vice versa.
A net of the cube is shown below.

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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.