Circle Rotation Paradox

September 1, 2020

[P6 Maths and beyond: Circles]

 

The following question is a tricky question from 1982 that a lot of people got wrong.

 

 

It's deceptive (and tempting) to use the large circle B as the point of reference when answering this question. Sure, the circumference of Circle A makes three rounds around Circle B, but that is in relation to the circumference of Circle B as opposed to position of Circle A.

 

In Maths, we must be rigorous with the question and the answer. The question specifies "How many times will Circle A revolve in total", which means the point of reference we must look at is Circle A and how many times it completes a revolution. (in this case, the number of times a point of reference cycles 360 degrees around itself)

 

However many times it may revolve around Circle B does not matter. That simply shows the ratio of A's circumference to B's circumference. It does not solve the question of [# of Circle A revolutions] even though it's intuitive to think so.

 

Be wary of counter-intuitive questions like these. They are especially popular in both PSLE exams, and Express test papers.

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