Maths Olympiad Prep

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Algebra Difficulty 1.5 Junior Find the answer Canada

The two equal-arm scales shown are balanced.

Figure 0

Of the following, 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 — 2

Solution 1

The first scale shows that [[IMAGE0]] has the same mass as [[IMAGE1]] .

The second scale shows that [[IMAGE2]] has the same mass as [[IMAGE3]] .

Therefore, the sum of the masses of [[IMAGE4]] and [[IMAGE5]] is equal to the sum of the masses of [[IMAGE6]] and [[IMAGE7]] .

That is, the equal-arm scale shown below is balanced.

[[IMAGE8]]

The left and right sides of this scale each contain a [[IMAGE9]] , and the scale remains balanced if one [[IMAGE10]] is removed from each side of the scale (since they are equal in mass).

That is, the equal-arm scale shown below is balanced.

[[IMAGE11]]

Therefore of the answers given, [[IMAGE12]] has the same mass as [[IMAGE13]] .

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Solution 2

On the spinner given, the prime numbers that are odd are 3,53,5 and 7. Since the spinner is divided into 8 equal sections, the probability that the arrow stops in a section containing a prime number that is odd is 38\frac38.

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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.