What is the number of 360-degree rotations that a bicycle wh : GMAT Data Sufficiency (DS)
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# What is the number of 360-degree rotations that a bicycle wh

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

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26 Jan 2014, 09:44
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 59
Category: Geometry Circles
Page: 157
Difficulty: 600

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

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26 Jan 2014, 09:45
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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.

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a-circular-rim-28-inches-in-diameter-rotates-the-same-number-65106.html
two-wheels-are-connected-via-a-conveyor-belt-the-larger-133697.html
how-long-in-minutes-did-it-take-a-bicycle-wheel-to-roll-130026.html
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Re: What is the number of 360-degree rotations that a bicycle wh [#permalink]

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26 Jan 2014, 10:40
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

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

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26 Jan 2014, 22:42
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
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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.

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

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01 Feb 2014, 08:30
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.

Similar questions to practice:
a-circular-rim-28-inches-in-diameter-rotates-the-same-number-65106.html
two-wheels-are-connected-via-a-conveyor-belt-the-larger-133697.html
how-long-in-minutes-did-it-take-a-bicycle-wheel-to-roll-130026.html
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19 Mar 2015, 08:15
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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!
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Re: What is the number of 360-degree rotations that a bicycle wh [#permalink]

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10 Jun 2016, 07:29
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
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Re: What is the number of 360-degree rotations that a bicycle wh   [#permalink] 10 Jun 2016, 07:29
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