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What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter. (2) The wheel made twenty 360-degree rotations per minute.

Statement 1) We have the diameter, we can determine circumference. From there we can determine the number of full 360 rotations by using the formula = Distance traveled/circumference - Hence Sufficient.

Statement 2) We just know it makes full 360 - degree rotation every one minute. We don't know what is the time taken by the bicycle to travel the distance. Not Sufficient.

Re: What is the number of 360-degree rotations that a bicycle wh [#permalink]

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26 Jan 2014, 22:42

1

This post received KUDOS

From S1:diameter=circumference of wheel=distance covered in one rotation total dist.=100 metres=>no. of rotations =total dist/dist. covered in one rotation.Hence,sufficient From S2:20 rotations=1 min.But we don't know the speed of the wheel(time taken to cover 100 metres).Hence,insufficient. Ans.A

Re: What is the number of 360-degree rotations that a bicycle wh [#permalink]

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28 Jan 2014, 01:35

From Statement (1), we can get the circumference of the wheel. Circumference=pid=0.5pi, where d is the diameter.

So the number of rotations=100/(pid) Sufficient

From statement (2), we need to know the wheel's speed for the entire 100m or the total time it took rolling for 100m to be able to calculate the number of rotations.

Re: What is the number of 360-degree rotations that a bicycle wh [#permalink]

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02 Oct 2015, 21:55

I'm still curious how to do the calculation for both statements:

Statement 1: DIAMETERwheel = 0.5 meter To find circumference = phi x D = phi.0.5 then what is the next step after I find the circumference? Am i supposed to divide 360 rotation by phi 0.5?

Statement 2: 20 rotations/ minute. Does this statement refer to "Rate = Distance/ Time" formula? 20 rotations/ minute = 100 meters/time minute time = 1/5 rotations. meter/ minute and then what is the next step? How to find circumference from this formula? Thanks!

Statement 1 : You have to divide the distance traveled ( = 100m ) by the circumference to know how many 360 degree rotations the wheel completed

Statement 2: You know how many 360 degree rotations the wheel completes in a minute but since you do not know the time taken for bicycle to complete 100m of distance you cant say how many rotations it made. You do not need to apply the s= d/t concept anywhere.

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24 Aug 2017, 16:47

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