Gmatstudent2017 wrote:
Hi Bunuel,
I tried to solve this problem by picking numbers. So what I did was found the LCM between 40 and 32 since both wheels cover the same distance. 40*32 = 1280 so that means the bigger wheel must rotate 1280/40 = 32 times per minutes. That means in 60 minutes it'll rotate 1,920 times. Since the smaller wheel also rotates the same distance that is 1,920/32 = 60. So now the the target I'm looking for in the answer choice is 60 when r equals 32. When I plug in r equals to 32, I don't get the target answer of 60 anywhere. Can you tell me what I did wrong please?
Thank you!
The diagram above shows two wheels that drive a conveyor belt. The larger wheel has a diameter of 40 centimeters; the smaller wheel has a diameter of 32 centimeters. In order for the conveyor belt to run smoothly, each wheel must rotate the exact same number of centimeters per minute. If the larger wheel makes r revolutions per minute, how many revolutions does the smaller wheel make per hour, in terms of r?
(A) 1280π/3
(B) 75r
(C) 48r
(D) 24r
(E) 64π/3
Hi Gmatstudent2017,
In your approach, you lost track of the 'units' that each number represented. To start, the LCM of 40 and 32 is actually 160 (not 1280), but we can use 1280 when solving this question. To be mathematically accurate though, it's actually 1280pi (since we're dealing with the circumference of each of the circles - and they're 40pi and 32pi).
Since the larger circle has a circumference of 40pi, then it will travel 1280pi/40pi = 32 REVOLUTIONS per MINUTE, so R = 32.
The smaller circle will also travel that SAME distance, so it will travel 1280pi/32pi = 40 REVOLUTIONS per MINUTE.
We're asked how many revolutions the smaller circle will make in 1 HOUR though, so that is (60 minutes)(40 revolutions/min) = 2400 revolutions per HOUR.
In this example, we are looking for an answer that equals 2400 when R = 32. Only one answer matches.
GMAT assassins aren't born, they're made,
Rich