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

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The rate of spin of a certain gyroscope doubled every 10 seconds from  [#permalink]

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New post 31 Dec 2015, 11:01
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  55% (hard)

Question Stats:

65% (02:05) correct 35% (02:04) wrong based on 284 sessions

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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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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from  [#permalink]

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New post 31 Dec 2015, 11:15
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duahsolo 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

For more on this straightforward technique, see our free video - http://www.gmatprepnow.com/module/gmat- ... /video/929

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Brent
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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from  [#permalink]

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New post 07 Jan 2016, 01:11
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duahsolo 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


Hi,
two ways you can do the Qs of this type..

1) working backwards..


here you will have to carry out HOW many steps- 90/10..
can be error prone, but the way would be..
after
    90 secs - 400..
    80 secs - 200.., keep dividing by 2
    70 secs - 100
    60 secs - 50
    50 secs - 25
    40 secs - 25/2
    30 secs - 25/4
    20 secs - 25/8
    10 secs - 25/16..
    initial - 25/32..

2) straight

..

an easier and better, and less time consuming method



let the initial speed be x ..
it doubles in 10 secs, or it increases 2 times every 10 secs..
total 10 secs period= 90/10=9..
so final speed after 90 secs= x*2*2...9 times
therefore \(x*2^9=400\)...
or \(x*2^9=400=2^4*25\)...
\(x=25*2^4/2^9=25/2^5=25/32..\)
ans E
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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from  [#permalink]

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New post 10 Jul 2017, 09:03
1
Long method, count backwards....

Shortcut, use Geometric Progression.
Nth term of a GP is, tn = a*r^n (where a is the first term of progression and r is the ratio of second term to first term)
We know, r = 2 (as speed doubles)
tn = 400 (speed at 90 sec)
n= 9 (since there will be 9 intervals of 10 sec in 90 sec)
so, substitute all these values in equation above.
400 = a * 2^9 or, 400 = a* 512
therefore, a = 400/512 = 25/32.

This method looks long but it only takes 10-15 sec to solve.
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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from  [#permalink]

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New post 23 Nov 2018, 11:36
utkarshthapak wrote:
Long method, count backwards....

Shortcut, use Geometric Progression.
Nth term of a GP is, tn = a*r^n (where a is the first term of progression and r is the ratio of second term to first term)
We know, r = 2 (as speed doubles)
tn = 400 (speed at 90 sec)
n= 9 (since there will be 9 intervals of 10 sec in 90 sec)
so, substitute all these values in equation above.
400 = a * 2^9 or, 400 = a* 512
therefore, a = 400/512 = 25/32.

This method looks long but it only takes 10-15 sec to solve.

Isn't geometric progression given by a*r^n-1?
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Re: The rate of spin of a certain gyroscope doubled every 10 seconds from   [#permalink] 23 Nov 2018, 11:36
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