Problem 20 · 2021 Math Kangaroo
Stretch
Spatial & Visual Reasoning
transformations
The picture beside shows two cogs, each with a black tooth. Where will the black teeth be after the small cog has made one full turn?
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Answer: C
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Hint 1 of 3
When two cogs touch, they push the same number of teeth past the meeting point.
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Hint 2 of 3
The small cog makes one whole turn, so its black tooth comes right back to where it started.
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Hint 3 of 3
The big cog has more teeth, so it only turns part way around, not all the way.
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Approach: track each cog's black tooth after one small turn
- One full turn of the small cog brings its black tooth back to its starting spot.
- The big cog is pushed the same number of teeth, but since it has more teeth it turns only part way.
- Putting both black teeth in their new spots matches option C.
Mark:
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