M08-25

Official Solution:

If during a two-hour journey, a bicycle wheel with a diameter of 20 inches (1 inch = 0.0254 meters) made 75,000 360-degree rotations in a straight line without slipping, what was the approximate average speed of the wheel in kilometers per hour? (The circumference of a circle is \(2\pi r\))

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


It's important to note that the problem asks for an approximate average speed, and the answer options are well spread out, so we can use reasonable approximation.

To begin, we can calculate the circumference of the wheel. The radius of the wheel is half the diameter, which is \(\frac{20}{2} = 10\) inches or 0.254 meters (since 1 inch = 0.0254 meters). Therefore, the circumference is \(2\pi r = 2π(0.254) ≈ 0.5π ≈ 0.5*3 ≈1.5\) meters.

Since the wheel travels a distance equal to its circumference in one complete rotation, during 75,000 complete rotations, the wheel will cover a total distance of \(75,000*\frac{1.5}{1000} = 75*1.5 = 112.5 \approx 113\) kilometers.

Therefore, the average speed of the bicycle wheel during the two-hour journey is \(\frac{113}{2} = 56.5 \) kilometers per hour, which is closest to option C.

Note that this is not a Geometry question. While it uses basic knowledge of figures, it is actually a Distance/Rate question. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.


Answer: C