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21 Feb 2019, 15:59
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C
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69% (02:18) correct
31%
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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
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
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.
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.
22 Feb 2019, 06:43
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fskilnik
\(?\,\,\,:\,\,\,{\rm{approx}}.\,\,{\rm{degrees - rotation}}\,\,\,{\rm{in}}\,\,\,{\rm{1}}\,\,{\rm{min}}\)
\(360\,\,{\rm{degrees - rotation}}\,\,\,\, \leftrightarrow \,\,\,\,2 \cdot \pi \cdot 300\,\,{\rm{meters}}\,\,\,\,\,\,\left( {1\,\,{\rm{lap}}} \right)\)
\(10\,\,{\rm{meters}}\,\,\,\, \leftrightarrow \,\,\,\,1\,\,\sec \,\,\,\,\left( {{\rm{speed}}} \right)\)
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...
