Problem Solving

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

Sorry, I do not have the different answers.

28pi/X = 35pi/y

y= 35pi X / 28pi

y= 5X/4 = 5X/4 *60 = 75X

parallel_chase wrote:28pi/X = 35pi/y

y= 35pi X / 28pi

y= 5X/4 = 5X/4 *60 = 75X

i did the same way as chase... go 75X as well..

I think errors are due to sentences.

the same number of inches per second; number of inches is equal to the circumference times the number of rotate per second.

y the revolutions per second for the 35 one rime
28pi*x=35pi*y
28x=35y
y=28/35x

Now per minutes:
60y=60*(28/35)x
60y=48x

The answer is 48x
I didn't like this question at first sight, the rim and the revolutions are not usual I think in gmat questions.

pepeprepa wrote:I think errors are due to sentences.

the same number of inches per second; number of inches is equal to the circumference times the number of rotate per second.

y the revolutions per second for the 35 one rime
28pi*x=35pi*y
28x=35y
y=28/35x

Now per minutes:
60y=60*(28/35)x
60y=48x

The answer is 48x
I didn't like this question at first sight, the rim and the revolutions are not usual I think in gmat questions.

yes this question is not fun.... but i dont understand how with this equation:
28pi*x=35pi*y

if x and y are the same (same rev per second) why are you assigning 2 different variables?

if bigger rim revolves y times per seconds then according to the given condition:

2*pi*28*x = 2*pi*35*y

y = .8x

now we need to give the total revolution per minute hence answer = 60*(.8x) = 48x

A simple way to do it is af follows. It will take a little more time but can be solved within 2 minutes if the other methods are not very clear.

The smaller rim makes 'x' rev/ sec
or, in 1 sec it makes 'x' revolutions
In a revolution, distance = (2)(pi)(14)........................................ circumference = 2(pi)r
or, in 'x' rev., distance = (2)(pi)(14)(x)

The larger rim crosses equal distance in equal time
so, in 1 sec distance = 28(pi)(x)
or, in 60 sec(1 min), distance = 28(pi)(x) * 60
or, revolution in 1 min = distance / circumference
= 28(pi)(x)*60 / 2(pi)(35/2)
= 48 x

I would probably use plugging in for this question, but I'll need the answers.
The problem states that the rims travel the same number of inches per second - not the same number of revolutions. In order to wrap your head around this, try a numerical example. Let's say that both rims travel 140 inches per second (140 chosen because its a multiple of both 28 and 35. - since both numbers are multiples of 7, I moved in batches of 70 until I found a number that works for both).
Small rim of 28 inches travels 140 inches per second: 140/28 = equals five revolutions per second, so x=5.
large rim of 35 inches travels the same 140 inches per second, but here there are only 140/35=4 revolutions per second.
Transition to minute: 4 revolutions per second for the larger rim means 4*60=240 revolutions per minute.

so the right answer should equal to 240 for x=5: 48x = 48*5 = 240 works, and will probably be the only answer choice which does.
While not necessarily faster, this way is safer - if you're plugging in x=5 and looking for a 240, there's just no way you'll choose 75X - it's just too big. Using numbers is a way to wrap your head around a tricky problem and make sure you don't make any mistakes in interpreting it.

I noticed that I had ignored the pi here, but we can always use 140pi instead and reduce it out - as long as we reach 5 revolutions and 4 revolutions, the problem is solved.

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

a)48/x
b)75x
c)48x
d)24x
e)x/75

The ratio of the circumferences is smaller:larger = 28pi:35pi = 4:5.
To simplify the math, let's plug in that the smaller circumference = 4 inches and that the larger circumference = 5 inches.

Plug in that the smaller rim makes x=2 revolutions/second.
Thus, the smaller rim rotates 2*4 = 8 inches/second.
In a minute, the smaller rim rotates 60*8 = 480 inches.
Thus, in a minute the larger rim makes 480/5 = 96 revolutions. This is our target answer.

Now we plug x=2 into all the answers choices to see which gives us our target answer of 96.

Only answer choice C works:
48x = 48*2 = 96.

The correct answer is C.