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Brenda will test-drive a vintage motor car on a circular track with ra

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New post 21 Feb 2019, 15:59
1
5
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A
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C
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Difficulty:

  45% (medium)

Question Stats:

63% (02:25) correct 37% (02:32) wrong based on 41 sessions

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GMATH practice exercise (Quant Class 5)

Brenda will test-drive a vintage motor car on a circular track with radius 300 meters, at a constant speed of 10 meters per second. If her husband Jim is at rest, at the center of this track, to film the entire test-drive, which of the following values is closest to the approximate angle Jim will rotate his head during her 1-minute car ride?

(A) 75 degrees
(B) 90 degrees
(C) 115 degrees
(D) 140 degrees
(E) 155 degrees

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Re: Brenda will test-drive a vintage motor car on a circular track with ra  [#permalink]

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New post 21 Feb 2019, 23:39
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radius = 300 meters
Circumference = 2*300*π = 1800 (considering π as 3)
speed = 10m/s
distance in 1 minute = 600 meters.
Angle Jim will rotate = 600/1800*360 = 120.
A close approximation to 115.

C is the answer.
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New post 22 Feb 2019, 06:43
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fskilnik wrote:
GMATH practice exercise (Quant Class 5)

Brenda will test-drive a vintage motor car on a circular track with radius 300 meters, at a constant speed of 10 meters per second. If her husband Jim is at rest, at the center of this track, to film the entire test-drive, which of the following values is closest to the approximate angle Jim will rotate his head during her 1-minute car ride?

(A) 75 degrees
(B) 90 degrees
(C) 115 degrees
(D) 140 degrees
(E) 155 degrees

\(?\,\,\,:\,\,\,{\rm{approx}}.\,\,{\rm{degrees - rotation}}\,\,\,{\rm{in}}\,\,\,{\rm{1}}\,\,{\rm{min}}\)

\(360\,\,{\rm{degrees - rotation}}\,\,\,\, \leftrightarrow \,\,\,\,2 \cdot \pi \cdot 300\,\,{\rm{meters}}\,\,\,\,\,\,\left( {1\,\,{\rm{lap}}} \right)\)

\(10\,\,{\rm{meters}}\,\,\,\, \leftrightarrow \,\,\,\,1\,\,\sec \,\,\,\,\left( {{\rm{speed}}} \right)\)


Let´s use UNITS CONTROL, one of the most powerful tools of our method!


\(?\,\,\, = \,\,\,1\,\,\min \,\,\,\left( {{{60\,\,\sec } \over {1\,\,\min }}} \right)\,\,\,\left( {{{10\,\,{\rm{meters}}} \over {1\,\,{\rm{sec}}}}} \right)\,\,\,\left( {{{360\,\,{\rm{degrees - rotation}}} \over {2 \cdot \pi \cdot 300\,\,{\rm{meters}}}}} \right)\,\,\,\,\,\left[ {{\rm{degrees - rotation}}} \right]\)

\(\pi \cong {{22} \over 7}\,\,\,\, \Rightarrow \,\,\,\,? \cong {{60 \cdot 10 \cdot 360} \over {2 \cdot {{22} \over 7} \cdot 300}}\,\, = \,\,{7 \over {22}} \cdot {{30 \cdot 10 \cdot 6} \over 5}\,\, = \,\,{7 \over {22}} \cdot 360\)

\(? \cong {7 \over {22}} \cdot 360 = {7 \over {11}} \cdot \left( {110 + 66 + 4} \right) = 7\left( {16 + {4 \over {11}}} \right) = 112 + 2 + {6 \over {11}} \cong 115^\circ\)


The correct answer is (C).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

P.S.: there is an immediate alternate way: (60*10)metres/300metres = 2 radians (1 radian is 180/pi degrees and it´s done), but "radians" is out-of-GMAT´s scope...
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Re: Brenda will test-drive a vintage motor car on a circular track with ra  [#permalink]

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New post 25 Feb 2019, 08:44
fskilnik wrote:
GMATH practice exercise (Quant Class 5)

Brenda will test-drive a vintage motor car on a circular track with radius 300 meters, at a constant speed of 10 meters per second. If her husband Jim is at rest, at the center of this track, to film the entire test-drive, which of the following values is closest to the approximate angle Jim will rotate his head during her 1-minute car ride?

(A) 75 degrees
(B) 90 degrees
(C) 115 degrees
(D) 140 degrees
(E) 155 degrees


given
radius = 300 mts
total circumference = 600 pi
speed = 10 mtr per second i.e 600 mtr per minute
time taken to do 1 round ; 600 pi /600 = pi minutes
Jim will have to rotate his head ; 360/ pi times ~ 115 degress
IMO C
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Re: Brenda will test-drive a vintage motor car on a circular track with ra   [#permalink] 25 Feb 2019, 08:44
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