A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
A. 100xy
B. 100y - x
C. 100x - y
D. 100y / x
E. 100x / y
[spoiler]Source: majortests.com[/spoiler]
and a second wheel
- sanju09
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- kvcpk
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A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
Diameter is x
Hence perimeter = pi * x
for Second wheel pi*y
(pi*x)*100 = d
(pi*y)*number = d
(pi*y)*number = (pi*x)*100
number = 100x/y
pick E
Diameter is x
Hence perimeter = pi * x
for Second wheel pi*y
(pi*x)*100 = d
(pi*y)*number = d
(pi*y)*number = (pi*x)*100
number = 100x/y
pick E
good explanation!kvcpk wrote:A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
Diameter is x
Hence perimeter = pi * x
for Second wheel pi*y
(pi*x)*100 = d
(pi*y)*number = d
(pi*y)*number = (pi*x)*100
number = 100x/y
pick E
- kvcpk
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Thanks Blasterblaster wrote:good explanation!kvcpk wrote:A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
Diameter is x
Hence perimeter = pi * x
for Second wheel pi*y
(pi*x)*100 = d
(pi*y)*number = d
(pi*y)*number = (pi*x)*100
number = 100x/y
pick E
thanks it helped blaster:Dblaster wrote:good explanation!kvcpk wrote:A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
Diameter is x
Hence perimeter = pi * x
for Second wheel pi*y
(pi*x)*100 = d
(pi*y)*number = d
(pi*y)*number = (pi*x)*100
number = 100x/y
pick E
- Taran
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I solved it by picking numbers
First Wheel: Let x (dia) = 12 inches => Radius of first wheel = 6 inches
Circumference of first wheel = 2 Pi r = 2 Pi 6 = 12 Pi inches or Pi feet
Second Wheel: let y (dia) = 6 inches => Radius = 3 inches
Circumference of second wheel = 2 Pi r = 2 Pi 3 = 6 Pi inches or Pi/2 feet
Now, first wheel covers Pi feet in one revolution, so will cover 100 Pi feet in 100 revolutions (i.e d = 100 Pi feet)
Second Wheel covers Pi/2 feet in 1 revolution or covers 1 feet in 2/Pi revolutions. Thus it will cover d = 100 Pi feet in 100 Pi x 2/Pi revolutions. Solve it to get 200 revolutions.
Now your answers, when plugged with x = 12 and y = 6, should yield 200. Only E does that, hence is correct answer.
First Wheel: Let x (dia) = 12 inches => Radius of first wheel = 6 inches
Circumference of first wheel = 2 Pi r = 2 Pi 6 = 12 Pi inches or Pi feet
Second Wheel: let y (dia) = 6 inches => Radius = 3 inches
Circumference of second wheel = 2 Pi r = 2 Pi 3 = 6 Pi inches or Pi/2 feet
Now, first wheel covers Pi feet in one revolution, so will cover 100 Pi feet in 100 revolutions (i.e d = 100 Pi feet)
Second Wheel covers Pi/2 feet in 1 revolution or covers 1 feet in 2/Pi revolutions. Thus it will cover d = 100 Pi feet in 100 Pi x 2/Pi revolutions. Solve it to get 200 revolutions.
Now your answers, when plugged with x = 12 and y = 6, should yield 200. Only E does that, hence is correct answer.
- Bharadwaj Charan
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Distance traveled by first wheel is 100pi*x, the second wheel travels the same distance
so 100*pi*x/pi*y (which is the perimeter) --> so it is 100*x/y(pi cancels pi)
E is the answer.
this is my first post on Beat the GMAT...
so 100*pi*x/pi*y (which is the perimeter) --> so it is 100*x/y(pi cancels pi)
E is the answer.
this is my first post on Beat the GMAT...
- sanju09
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your most welcome, Bharadwaj Charan, and E is the right answer, hence congratulations tooBharadwaj Charan wrote:Distance traveled by first wheel is 100pi*x, the second wheel travels the same distance
so 100*pi*x/pi*y (which is the perimeter) --> so it is 100*x/y(pi cancels pi)
E is the answer.
this is my first post on Beat the GMAT...
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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Radius of the first wheel is x/2sanju09 wrote:A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
A. 100xy
B. 100y - x
C. 100x - y
D. 100y / x
E. 100x / y
[spoiler]Source: majortests.com[/spoiler]
So circumference of the wheel ( distance covered in one rotation ) = 2 * pi * ( x/2)
So in 100 revolutions it covers
2 *pi * ( x ) *100 = d
Now , the radius of the second wheel will be y / 2
So distance covered in 1 rotation will be
2* pi * y/2
Turns made by this wheel be " t " { Say }
So distance covered is :
2 * pi * y/2 * t
Now the same distance is covered by both ....
2 *pi * y/2 *t = 2 * pi * x/2 *100
y * t = 100 x
So t = 100 x / y
Option E.
Abhishek
- ronnie1985
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