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# A certain clock marks every hour by striking a number of

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Joined: 28 Dec 2005
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A certain clock marks every hour by striking a number of [#permalink]

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28 Mar 2006, 18:10
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A certain clock marks every hour by striking a number of time equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds. At the 12:00, how many seconds elapse between th beginning of the first stroke and the end of the last stroke?

A. 72
B. 50
C. 48
D. 46
E. 44
VP
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Re: PS -110 from OG work Quan workbook [#permalink]

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28 Mar 2006, 18:40
46.

At 6, there are 6 strokes and there are 5 intervals between strokes.
Let t = time required for a stroke = time interval between strokes.
Thus, the 6t + 5t = 22 => t =2.

At 12, 12 strokes and 11 intervals => 12t + 11t = 23t = 23(2) -46.

myc2004 wrote:
A certain clock marks every hour by striking a number of time equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds. At the 12:00, how many seconds elapse between th beginning of the first stroke and the end of the last stroke?

A. 72
B. 50
C. 48
D. 46
E. 44
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5045
Location: Singapore
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31 Mar 2006, 11:21
time between strokes = time of each stroke

6 pm --> 6 strokes

Stroke 1 -> n seconds
n seconds between stroke 1 and 2
Stroke 2 -> n seconds
n seconds between stroke 2 and 3
Stroke 3 -> n seconds
n seconds between stroke 3 and 4
Stroke 4 -> n seconds
n seconds between stroke 4 and 5
Stroke 5 -> n seconds
n seconds between stroke 5 and 6
Stroke 6 -> n seconds

Total: 11 n seconds = 22 seconds, n = 2

12 -> 12 strokes + 11 in-betweens. Number of seconds = 12n + 11n = 23n = 46 seconds
VP
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31 Mar 2006, 17:44
If d is the duration of the stroke == duration of the pause between stroke. The total duration (start to end) at every hour :

(2n -1 )d = Total Duration

where n is the hour.

At 6:

(2x6 -1) d = 22

Therefore, d=2

So when n ==12

(2x12 -1)2 = 23 x 2 = 46
31 Mar 2006, 17:44
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