What is the number of 360-degree rotations that a bicycle wh

Question

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.

Bunuel · Accepted Answer

SOLUTION

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

1 revolution of a circle = circumference of that circle. So, we basically asked to find the value of 100/(circumference).

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter. We can get the circumference. Sufficient.

(2) The wheel made twenty 360-degree rotations per minute. We cannot get the circumference. Not sufficient.

Answer: A.

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kinjiGC · Answer

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.

Hence Option A)

AKG1593 · Answer

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

Cosmas · Answer

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

So the number of rotations=100/( pi d) 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.

Answer A

blendercroix · Answer

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!

rishi02 · Answer

blendercroix

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.

Hope you understood

Basshead · Answer

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.

Since we know the diameter, we can determine the number of 360-degree rotations. If we actually solved: 0.5 * 3.14 = 1.57
100 / 1.57 = approximately 63.7 rotations.

SUFFICIENT.

(2) The wheel made twenty 360-degree rotations per minute.

Clearly not enough information -- time is irrelevant. INSUFFICIENT.

Answer is A.

woohoo921 · Answer

Bunuel 
Out of curiosity, is 400pie the answer to statement 1? Thank you!

woohoo921 · Answer

Also, where does 100/(circumference) come from? The official guide has this for the answer "Given either the circumference of the wheel or the means to calculate its circumference, it is thus possible to determine the number of times the circumference of the wheel was laid out along the straight-line path of 100 meters" and I am just confused as to where the "laid out" is coming from. Thanks again.

Bunuel · Answer

If the circumference of the wheel is say 10 meters, then to cover 100 meters the wheel should make 100/10 = 10 rotations (10 rotations * each is 10 meters = 100 meters). So, here we need to find the value of 100/(circumference). I'll let you calculate the value of (circumference) given the diameter is 0.5 meters.

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What is the number of 360-degree rotations that a bicycle wh

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