A circular rim 28 inches in diameter rotates...

Expert replies

AAPL: Moderator; Posts: 2749; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Sun Jan 28, 2018 2:24 pm

A circular rim 28 inches in diameter rotates the same number of inches per seconds as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minutes does the larger rim make in terms of x?

$$A.\ 48\pi x$$
$$B.\ 75x$$
$$C.\ 48x$$
$$D.\ 24x$$
$$E.\ \frac{x}{75}$$

The OA is C.

I don't have clear this PS question.

I know that the 2 rims have the same revolutions per seconds but I don't know how can I represent it to solve it. I appreciate if any expert explain it for me. Thank you so much.

Source: Beat The GMAT — Problem Solving | Sun Jan 28, 2018 2:24 pm

M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Mon Jan 29, 2018 2:40 am

Hello AAPL.

Let's take a look at your question.

We know that circumference*(rev/min) of 28 = circumference*(rev/min) of 35.

We have to calculate z on the following equation: $$28\pi\cdot x=35\pi\cdot z\ \Leftrightarrow\ \ z=\frac{4}{5}\cdot x\ \frac{\text{inches}}{\sec}.$$ But, we are asked how many revolutions per MINUTE... Hence, $$z=\frac{4}{5}x\ \frac{\text{inches}}{\sec}\cdot\frac{60\sec}{1\ \min}=48x\ \frac{\text{inches}}{\min}.$$ Therefore, the correct answer is the option C.

I hope this answer can help you.

Feel free to ask me again if you have any doubt.

Regards.

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Jan 30, 2018 10:37 am

AAPL wrote:A circular rim 28 inches in diameter rotates the same number of inches per seconds as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minutes does the larger rim make in terms of x?

$$A.\ 48\pi x$$
$$B.\ 75x$$
$$C.\ 48x$$
$$D.\ 24x$$
$$E.\ \frac{x}{75}$$

The smaller rim rotates at a rate of 28Ï€x inches per second. Since the larger rim rotates the same number of inches per second, it rotates at a rate of 28Ï€x inches per second also, and, in one minute, it rotates 28Ï€x * 60 inches.

Since 1 rotation of the larger rim = its circumference = 35Ï€, the number of rotations made by the larger rim will thus be:

(28Ï€x * 60)/35Ï€

(4x * 60)/ 5

4x * 12

48x

Answer: C

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