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505-555 (Easy)|   Geometry|      
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Bunuel
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A bicycle has two wheels of different sizes, how wide in feet is the 02 Sep 2018, 22:20
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C
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87% (00:54) correct 13% (00:52) wrong based on 59 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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C
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sumit411
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A bicycle has two wheels of different sizes, how wide in feet is the 02 Sep 2018, 23:20
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Bunuel
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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Imho, answer is C
Attachment:
IMG_20180903_115134.jpg
IMG_20180903_115134.jpg [ 98.07 KiB | Viewed 2665 times ]

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rahulkashyap
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A bicycle has two wheels of different sizes, how wide in feet is the 02 Sep 2018, 23:32
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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
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PKN
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A bicycle has two wheels of different sizes, how wide in feet is the 03 Sep 2018, 19:42
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rahulkashyap
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
Show more

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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A bicycle has two wheels of different sizes, how wide in feet is the 03 Sep 2018, 19:52
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PKN
rahulkashyap
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)
Show more

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
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A bicycle has two wheels of different sizes, how wide in feet is the 03 Sep 2018, 19:56
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Although I got the correct answer, should I be concerned that I visualised the bicycle with the rear small wheel? :lol:
A Kudos to you for this hand drawn diagram and a quick solution!
sumit411
Bunuel
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.
Imho, answer is C
Attachment:
IMG_20180903_115134.jpg

Thank you = Kudos
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A bicycle has two wheels of different sizes, how wide in feet is the 03 Sep 2018, 20:50
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rahulkashyap
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rahulkashyap
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
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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.
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sumit411
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A bicycle has two wheels of different sizes, how wide in feet is the 04 Sep 2018, 05:00
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abhinav770
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
Bunuel
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.
Imho, answer is C
Attachment:
IMG_20180903_115134.jpg

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

Thanks for the kudos :)

Thank you = Kudos
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