M10-28

Question

The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel? (The circumference of a circle is \(2\pi r\))

A. \(\frac{250}{\pi}\)
B. \(\frac{500}{\pi}\)
C. 250
D. 500
E. 750

Show Answer

Official Answer

D

A.  \frac{250}{\pi} 
B.  \frac{500}{\pi} 
C. 250
D. 500
E. 750

Bunuel · Accepted Answer

Official Solution:

The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel? (The circumference of a circle is \(2\pi r\))

A. \(\frac{250}{\pi}\)
B. \(\frac{500}{\pi}\)
C. 250
D. 500
E. 750

Show Answer

Official Answer

D

A.  \frac{250}{\pi} 
B.  \frac{500}{\pi} 
C. 250
D. 500
E. 750

We actually do not need to use any formulas here - just need to understand how the calculations work for the circumference. Since the radius of the rear wheels is twice the radius of the front wheels, the circumference of the rear wheels is also twice that of the front wheels, making it 2 meters. To calculate the number of revolutions made by each rear wheel when traveling 1,000 meters, divide the total distance by the circumference: (1,000 meters)/(2 meters) = 500 revolutions.
 
Note that this is not a Geometry question. While it uses basic knowledge of lines and figures, it is a Word Problem question. There are 8 questions within GMAT Prep Focus Edition that use similar principles.  Here is one example .

Answer: D

b2bt · Answer

I thought we have to divided the distance i.e. 1000 meters with circumference i.e. 4 {\pi}  and hence the answer should be  \frac{250}{{\pi}} 
but I guess in the solution you have divided the the distance with radius. Is it so?

Bunuel · Answer

No. We are given that the  circumference  of the front wheels is 1 meter and the radius of the front wheels is half that of the rear wheels.

Thus, the  circumference  of the front wheels is  2\pi{r}=1  and the  circumference  of the rear wheels is  2\pi{(2r)}=2*2\pi{r}=2 .

So, we  are  dividing the distance with the circumference.

Hope it's clear.

Emiliya43 · Answer

are basically tryimg to find how many circumferences in the distance the cart travelled? So is resolution a full 360 degree circum?

thanks

Bunuel · Answer

One 360-degree revolution = the distance of one circumference.

buddyisraelgmat · Answer

What is the basic relation between Distance, Revolution, Circumference?

Is it  Distance = No of Revolutions * Circumference  ? Is this correct?

Bunuel · Answer

Yes, that;s correct. Check 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 what-is-the-number-of-360-degree-rotations-that-a-bicycle-wh-166668.html the-circumference-of-the-front-wheel-of-a-cart-is-30-ft-long-90588.html Hope it helps.

pacifist85 · Answer

I guess it needs less math thinking than rational thinking. Hope I will explain well enough. Let's put the information we have together:

Radius of front wheel: r
Radius of rear wheel: 2r

This means that when the front wheel makes 1 whole revolution, the rear one makes 2. That because its diameter (2 radii) is twice as large, so it covers twice the distance of the front wheel at the same time (if the weels were not attached, when the front wheel covers 5 meters, the back would cover 10). Put differently, since the wheels are actually attached to the same vehicle, the distance the rear wheel has covered in the same amount of time with the front is half the distance of the front (if the front wheel covered 10 meters, the read wheel covered 5).

Now, we know that the circumference is 1 meter (so, in 1 meter the cart makes 1 revolution) and that the cart covered 1 
km.

In others words:
1 revolution in 1 meter
x revolutions in 1000 meters?
x = 1000 for the front wheel, so x = 500 for the rear wheel.

JLAR2107 · Answer

Distance = Revolutions*Circumference ---> Revolutions = Distance/Circumference = 1km/Circumference

We need to find the circumference of the back tire using a relation to the circumference of the front tire.

Radius of front wheel (Rf): 1 meter = 2*Pi*Rf ---> Rf = 1/(2*Pi) meters
Radius of back wheel (Rb): 2*Rf = 1/Pi meters since it is stated that the radius of the back tire is twice that of the front
Circumference of back wheel (Cb) = 2*Pi*Rb = 2 meters

Revolutions = 1km/2 meters = 1*10^3 meters/2 meters =  500 meters

bharat9995 · Answer

Nice question, you don't even have to lift the pen to answer it. :-D

Madhavi1990 · Answer

Very cool - its like being tricked with word changes. The question talks about radius first and then mentions (*casually*) the circumferences. I was busy trying to calculate the 2 pi R; whereas its already there! :D

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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M10-28

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