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The rate of spin of a certain gyroscope doubled every 10 seconds from

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Carcass
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The rate of spin of a certain gyroscope doubled every 10 seconds from [#permalink] New post   14 May 2021, 05:50
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The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 400 meters per second, what was the speed, in meters per second, when the stopwatch was started?

A) 25/3
B) 25/4
C) 25/8
D) 25/16
E) 25/32
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E
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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from [#permalink] New post   14 May 2021, 06:40
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Carcass wrote:
The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 400 meters per second, what was the speed, in meters per second, when the stopwatch was started?

A) 25/3
B) 25/4
C) 25/8
D) 25/16
E) 25/32


This can be answered within a reasonable time frame by just charting each 10-second period.

- After 90 seconds: 400 meters/second
- After 80 seconds: 200 meters/second
- After 70 seconds: 100 meters/second
- After 60 seconds: 50 meters/second
- After 50 seconds: 25 meters/second
- After 40 seconds: 25/2 meters/second
- After 30 seconds: 25/4 meters/second
- After 20 seconds: 25/8 meters/second
- After 10 seconds: 25/16 meters/second
- START: 25/32 meters/second

Answer: E


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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from [#permalink] New post   14 May 2021, 09:33
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Carcass wrote:
The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 400 meters per second, what was the speed, in meters per second, when the stopwatch was started?

A) 25/3
B) 25/4
C) 25/8
D) 25/16
E) 25/32


let, at present be \(x\)
speed 10 seconds before = \(\frac{x}{2}\)
speed 20 seconds before = \(\frac{x}{4}\) ....

Lets count the number of jumps: 0-10-20-30-40-50-60-70-80-90 i.e. 9 jumps

Therefore speed 1.5 minutes before = \(\frac{x}{2^9} = \frac{400}{512} = \frac{25}{32}\)

Hence, option E
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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from [#permalink]
14 May 2021, 09:33
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