If the diameter of each of the car's wheels is 20 inches, wh

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Wed Oct 05, 2016 7:26 pm

If the diameter of each of the car's wheels is 20 inches, what was the approximate average speed of the car in km/h if after the two-hour journey each wheel made 75,000 revolutions? (1 inch = 0.0254 meter)

A. 32
B. 41
C. 59
D. 74
E. 88

SPOILER C

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Source: Beat The GMAT — Problem Solving | Wed Oct 05, 2016 7:26 pm

MBA Challengers: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Fri Sep 09, 2016 11:59 pm; Thanked: 20 times

by MBA Challengers » Thu Oct 06, 2016 1:15 am

Hi richachampion,

This question involves some slightly tedious arithmetic calculations but since the options are well spaced out, suggest you use some approximations:

Conceptually, we are looking at the circumference of the wheel as a synonym for the revolution.

So, start with calculating how many inches are covered with 1 revolution of the wheel:

Pi * diameter = 3.14 * 20 (For convenience and paucity of time, round off pi to 3). This results in 60 inches travelled per revolution

Each inch = 0.0254 metres. Round it off to 0.025 metres per inch. Convert the inch/revolution to metre/revolution by multiplying 60 * 0.025 to result in 1.5. So, each wheel travels ~1.5 metres per revolution.

In 2 hours, the car's wheels have turned 75,000 revolutions. This implies that the car has covered 75000 * 1.5 metres in 2 hours. Since, we need to calculate km/hr only calculate 75 * 1.5.
75 * 1.5 = 112.5. So, the car has travelled 112.5 km in 2 hours.

However, speed is calculated on a km/hr basis. When you divide this by 2, you get 56.25. Since you were anyway working on approximations, the closest answer which you will pick would be 59 km/hr which is option C.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Oct 06, 2016 2:51 am

richachampion wrote:If the diameter of each of the car's wheels is 20 inches, what was the approximate average speed of the car in km/h if after the two-hour journey each wheel made 75,000 revolutions? (1 inch = 0.0254 meter)

A. 32
B. 41
C. 59
D. 74
E. 88

1 revolution = 1 circumference = Ï€d = 20Ï€ inches â‰ˆ 60 inches.
75,000 revolutions = 75000*60 inches.
(75000 revolutions)/(2 hours) = (75000*60 inches)/(2 hours) * (254/10000 meters)/(1 inch) * (1 kilometer)/(1000 meters) = (75*6*254)/(2*1000) â‰ˆ (75*3*250)/1000= (75*3)/4 = 225/4 = somewhat more than 50.

The correct answer is C.

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