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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure above, AB represents a ramp and the circle represents a 23 Nov 2017, 23:29
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25% (medium)

Question Stats:

74% (01:22) correct 26% (01:33) wrong based on 47 sessions

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In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

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2017-11-23_2026_001.png
2017-11-23_2026_001.png [ 6.52 KiB | Viewed 2126 times ]
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A
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In the figure above, AB represents a ramp and the circle represents a 24 Nov 2017, 01:09
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Bunuel
[img]https://gmatclub.com/forum/download/file.php?id=38810[img][/img][/img]
In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

Show Spoiler
Attachment:
2017-11-23_2026_001.png
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Circumference of circle = 2 * pie * r = 3* pie
Distance = 15
Revolutions = 15/3*pie = 35/22 = ~1 2/3

A
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In the figure above, AB represents a ramp and the circle represents a 24 Nov 2017, 10:11
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Bunuel
[img]https://gmatclub.com/forum/download/file.php?id=38810[img][/img][/img]
In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

Show Spoiler
Attachment:
2017-11-23_2026_001.png
Show more
In distance, D, problems with wheels and number of revolutions:

D = (circumference, c) * (# of revolutions), so

# of revolutions = \(\frac{D}{c}\)

D = ramp AB length = hypotenuse
The 3x-4x-5x right triangle has multiplier of 3:
(5*3)= 15 = ramp AB length = D*

Circumference of wheel A
2πr = 2π(1.5) = 3π
\(c = (3)(3.14)\approx{9.4}\)

# revolutions =
\(\frac{D}{c}=\frac{15}{9.4}\approx{1.59}\), or \(1.6\)

Answer A

Bunuel , the first image of the figure does not show up, though the one in the spoiler does. I tried two browsers.

*OR Pythagorean theorem, \(9^2 + 12^2 = h^2\)
\(81 + 144 = 225 = h^2\)
\(\sqrt{h^2}=\sqrt{225}\) , so \(h=15\)
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In the figure above, AB represents a ramp and the circle represents a 24 Nov 2017, 10:14
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genxer123
Bunuel
[img]https://gmatclub.com/forum/download/file.php?id=38810[img][/img][/img]
In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

Show Spoiler
Attachment:
2017-11-23_2026_001.png
In distance, D, problems with wheels and number of revolutions:

D = (circumference, c) * (# of revolutions), so

# of revolutions = \(\frac{D}{c}\)

D = ramp AB length = hypotenuse
The 3x-4x-5x right triangle has multiplier of 3:
(5*3)= 15 = ramp AB length = D*

Circumference of wheel A
2πr = 2π(1.5) = 3π
\(c = (3)(3.14)\approx{9.4}\)

# revolutions =
\(\frac{D}{c}=\frac{15}{9.4}\approx{1.59}\), or \(1.6\)

Answer A

Bunuel , the first image of the figure does not show up, though the one in the spoiler does. I tried two browsers.

*OR Pythagorean theorem, \(9^2 + 12^2 = h^2\)
\(81 + 144 = 225 = h^2\)
\(\sqrt{h^2}=\sqrt{225}\) , so \(h=15\)
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_______________
Edited. Thank you.
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