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# A bicycle has two wheels of different sizes, how wide in feet is the

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Math Expert
Joined: 02 Sep 2009
Posts: 53069
A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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02 Sep 2018, 21:20
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Difficulty:

25% (medium)

Question Stats:

88% (01:07) correct 12% (01:00) wrong based on 37 sessions

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A bicycle has two wheels of different sizes, how wide in feet is the diameter of the smaller wheel?

(1) The larger wheel makes half as many rotations per second as the smaller wheel.
(2) The larger wheel has a circumference of 1.5 meters.

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Re: A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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02 Sep 2018, 22:20
2
Bunuel wrote:
A bicycle has two wheels of different sizes, how wide in feet is the diameter of the smaller wheel?

(1) The larger wheel makes half as many rotations per second as the smaller wheel.
(2) The larger wheel has a circumference of 1.5 meters.
Attachment:

IMG_20180903_115134.jpg [ 98.07 KiB | Viewed 575 times ]

Thank you = Kudos
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Manager
Joined: 08 Oct 2015
Posts: 241
A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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02 Sep 2018, 22:32
I think the ans should be E.
It only gives the ratio of their rps and the bigger dia

Posted from my mobile device

If we assume that dist of larger wheel equals that of the smaller, then the ans should be c. But I'm not sure whether we should assume that
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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03 Sep 2018, 18:42
rahulkashyap wrote:
I think the ans should be E.
It only gives the ratio of their rps and the bigger dia

Posted from my mobile device

If we assume that dist of larger wheel equals that of the smaller, then the ans should be c. But I'm not sure whether we should assume that

Hi rahulkashyap,

It's a cycle, 2 wheels rotate at the same instant.

As per st1, 2-full rotations of smaller wheel=1-full rotation of bigger while.
So, distance covered by smaller wheel in 2 rotations=distance covered by bigger wheel in 1 rotations
Or, $$2*2\pi*r=2\pi*R$$
Or, 2d=D
Or, $$d=\frac{D}{2}$$-----(1)

From st2, $$\pi*D=1.5$$
Or, $$D=\frac{1.5}{\pi}$$---(2)

We can determine 'd' from (1) and (2).
Sufficient.

Ans. (C)
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Posts: 241
Re: A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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03 Sep 2018, 18:52
PKN wrote:
rahulkashyap wrote:
I think the ans should be E.
It only gives the ratio of their rps and the bigger dia

Posted from my mobile device

If we assume that dist of larger wheel equals that of the smaller, then the ans should be c. But I'm not sure whether we should assume that

Hi rahulkashyap,

It's a cycle, 2 wheels rotate at the same instant.

As per st1, 2-full rotations of smaller wheel=1-full rotation of bigger while.
So, distance covered by smaller wheel in 2 rotations=distance covered by bigger wheel in 1 rotations
Or, $$2*2\pi*r=2\pi*R$$
Or, 2d=D
Or, $$d=\frac{D}{2}$$-----(1)

From st2, $$\pi*D=1.5$$
Or, $$D=\frac{1.5}{\pi}$$---(2)

We can determine 'd' from (1) and (2).
Sufficient.

Ans. (C)

Well what you've said is what I have mentioned myself. But nowhere in the statement does it say that the cycle is moving on the ground. So hence the confusion whether we are allowed to make the assumption that the distance covered by the 2 wheels is the same
Manager
Joined: 10 May 2018
Posts: 124
Concentration: Finance, Sustainability
Re: A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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03 Sep 2018, 18:56
Although I got the correct answer, should I be concerned that I visualised the bicycle with the rear small wheel?
A Kudos to you for this hand drawn diagram and a quick solution!
sumit411 wrote:
Bunuel wrote:
A bicycle has two wheels of different sizes, how wide in feet is the diameter of the smaller wheel?

(1) The larger wheel makes half as many rotations per second as the smaller wheel.
(2) The larger wheel has a circumference of 1.5 meters.
Attachment:
IMG_20180903_115134.jpg

Thank you = Kudos

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
Re: A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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03 Sep 2018, 19:50
rahulkashyap wrote:
PKN wrote:
rahulkashyap wrote:
I think the ans should be E.
It only gives the ratio of their rps and the bigger dia

Posted from my mobile device

If we assume that dist of larger wheel equals that of the smaller, then the ans should be c. But I'm not sure whether we should assume that

Hi rahulkashyap,

It's a cycle, 2 wheels rotate at the same instant.

As per st1, 2-full rotations of smaller wheel=1-full rotation of bigger while.
So, distance covered by smaller wheel in 2 rotations=distance covered by bigger wheel in 1 rotations
Or, $$2*2\pi*r=2\pi*R$$
Or, 2d=D
Or, $$d=\frac{D}{2}$$-----(1)

From st2, $$\pi*D=1.5$$
Or, $$D=\frac{1.5}{\pi}$$---(2)

We can determine 'd' from (1) and (2).
Sufficient.

Ans. (C)

Well what you've said is what I have mentioned myself. But nowhere in the statement does it say that the cycle is moving on the ground. So hence the confusion whether we are allowed to make the assumption that the distance covered by the 2 wheels is the same

I think revolutions per second is the key phrase.

The larger wheel makeshalf as many rotations per second as the smaller wheel.
"The larger wheel makes" means when it undergoes motion.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 07 Oct 2017
Posts: 258
Re: A bicycle has two wheels of different sizes, how wide in feet is the  [#permalink]

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04 Sep 2018, 04:00
abhinav770 wrote:
Although I got the correct answer, should I be concerned that I visualised the bicycle with the rear small wheel?
A Kudos to you for this hand drawn diagram and a quick solution!
sumit411 wrote:
Bunuel wrote:
A bicycle has two wheels of different sizes, how wide in feet is the diameter of the smaller wheel?

(1) The larger wheel makes half as many rotations per second as the smaller wheel.
(2) The larger wheel has a circumference of 1.5 meters.
Attachment:
IMG_20180903_115134.jpg

Thank you = Kudos
Well, that's a big concern why you want to sit on that type of cycle!

Thanks for the kudos

Thank you = Kudos
_________________

Thank you =Kudos
The best thing in life lies on the other side of the pain.

Re: A bicycle has two wheels of different sizes, how wide in feet is the   [#permalink] 04 Sep 2018, 04:00
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