Circular disc, A rolls around another circular disc, B (without slippi

Question

Circular disc, A rolls around another circular disc, B (without slipping). It starts at the top of the disc B and continues until it reaches its starting position. How many revolutions does disc A make in total around its center, if radius of disc B is 4 times that of disc A.

A. 3
B. 4
C. 5
D. 6
E. 8

Show Answer

Official Answer

C

A. 3
B. 4
C. 5
D. 6
E. 8

CrackverbalGMAT · Accepted Answer

A tricky question.

If the radius of A is x, then radius of B = 4x

Circumference of B =  2\pi * 4x  =  8 \pi x  is the distance that has to be traveled by the smaller circle of circumference  2 \pi x .

Therefore the number of revolutions should be  \frac{8 \pi x}{2 \pi x} = 4

If this were a straight road instead of a circle, this answer would have been correct.

Since the disc is moving around the circle, there is a second movement happening with the revolution, which is a rotation.

One rotation of the smaller disc from the staring point to the end point is 1 extra revolution.

In general the total number of revolutions of a circular disc around another circle = n + 1, where n is the number of revolutions found by dividing the larger circumference by the smaller circumference the +1 accounts for the revolution due to the 1 rotation.

The Correct answer is  Option C

Arun Kumar

Fdambro294 · Answer

hmmm, you got me. Tricky question. Still trying to picture this in my head. Googling now, but any extra insight would be helpful (I guess finding a picture would be the most help)

EDIT: https://plus.maths.org/content/circles-rolling-circles

Playing with my coins now.....gotta love the GMAT

rocky620 · Answer

CrackVerbalGMAT 
Sir, is the generalization based on the assumption that another circle/disc is stationery?
If so, what will be the no. of revolutions when both discs are moving? Will it be n+1, n, n-1 or any other answer?

CrackverbalGMAT · Answer

Hello rocky620. This is based on the other disc being stationery. If 2 discs move, then direction of movement and speed will come into play and that's relative speed and some physics too. Don't worry, as it is outside the scope of GMAT and you will not get questions like that.

Arun Kumar

rocky620 · Answer

CrackVerbalGMAT 
Thanks sir, so by default the second disc will always be stationery?

vaibhav1221 · Answer

Look at the picture. There are three figures.

Figure 1: If it would've been a straight line rather than a circle.

Figure 2: If it would've applied Figure 1's logic to a circle.

Figure 3: How it would actually look.

Hope this helps.

Fdambro294 · Answer

I think the best way to visualize this is to think of the Circle A going around a Square instead of a Circle (both are 360 Degrees Total)

At each Corner/Vertex of the Square, Circle A will have to make a Rotation of 90 Degrees WITHOUT having made any headway around the Larger Square. Circle A will have to make this 90 Degree Rotation in order to change directions, NOT move forward around the Square.

Making this "in place" Rotation 4 Times at each Vertex = ONE 360 Degree Rotation Circle A makes without having added any Distance around the Square.

This same exact occurrence is happening around Circle B, just that it is spread out "smoothly" over the entire 360 Degrees of Circle B. There are no abrupt 90 Degree Rotations like there were in the Square situation.

That is the way I was able to finally visualize this in my head.

Circular disc, A rolls around another circular disc, B (without slippi

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Circular disc, A rolls around another circular disc, B (without slippi

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