A certain clock marks every hour by striking a number of tim : GMAT Problem Solving (PS)
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# A certain clock marks every hour by striking a number of tim

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A certain clock marks every hour by striking a number of tim [#permalink]

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21 Feb 2014, 00:10
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain clock marks every hour by striking a number of times 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 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

(A) 72
(B) 50
(C) 48
(D) 46
(E) 44

Problem Solving
Question: 110
Category: Arithmetic Operations on rational numbers
Page: 75
Difficulty: 600

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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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21 Feb 2014, 00:10
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A certain clock marks every hour by striking a number of times 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 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

(A) 72
(B) 50
(C) 48
(D) 46
(E) 44

At 6:00: 6 strokes + 5 intervals between strokes = 11 parts = 22 seconds. So, 1 stroke = 1 interval = 22/11 = 2 seconds;

At 12:00: 12 strokes + 11 intervals between strokes = 23 parts * 2 seconds for each = 46 seconds.

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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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21 Feb 2014, 01:03
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Very easy question once you figure out the meaning of - 'by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes'

What this means is that if it is 6 O Clock - then the clock will strike 6 times with 5 intervals in between those 6 strikes each interval time = to the time of each strike. Which basically means 11 same time gaps as seen below:-
Strike 1>interval time 1>Strike 2>Interval time 2>Strike 3>.....Interval time 5>Strike 6.

The question says that at 6 O Clock the time between begining of first stroke and end of last stroke = 22secs
since all time intervals and strike times are same total no of strikes+time intervals = 11
Time per strike = Time per interval = 22/11 = 2secs

Now at 12 O Clock there will be 12 strikes and 11 intervals, since each has the same time (2secs) the time elapsed from the begining of the first stroke to the end of the last stroke = (12+11)x2 = 46 seconds

Option (D)
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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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22 Feb 2014, 05:36
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SOLUTION

A certain clock marks every hour by striking a number of times 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 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

(A) 72
(B) 50
(C) 48
(D) 46
(E) 44

At 6:00: 6 strokes + 5 intervals between strokes = 11 parts = 22 seconds. So, 1 stroke = 1 interval = 22/11 = 2 seconds;

At 12:00: 12 strokes + 11 intervals between strokes = 23 parts * 2 seconds for each = 46 seconds.

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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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13 Mar 2014, 22:05
For 6:00 clock there, time elapsed = 22 seconds
So, to stroke 6, 5 empty time slots would be required
Total = 6 + 5 = 11 slots
So one slot will require = 22/11 = 2 seconds.

We can also generalize this information by putting in a formula:
For n time, it will be n + n-1 = (2n-1)

Time elapsed between First & Last Stroke = (2n-1) x 2 where
n = Time displayed

So for 12'o clock, it would be (24-1) x 2 = 46 = Answer = D

Bunuel, can you please tell if this approach is correct.
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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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17 Oct 2014, 10:00
Hi, Bunuel
If I change the question little bit what will be the answer?

A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly twice 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 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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08 Dec 2015, 14:08
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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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09 Dec 2015, 11:30
Hi Raihanuddin,

I'm not sure if you're still interested in this post (since it's from over a year ago), but here is the answer to your question:

The change that you've made to the prompt will lead to an answer that is NOT an integer, but here's how you would go about solving it. By making the interval between strokes TWICE the length of a single stroke, and keeping the fact that at 6:00 we have 22 seconds from the start of the first stroke to the end of the last stroke....

We have....
6 strokes x seconds per stroke
5 intervals @ 2X seconds per interval
6(X) + 5(2X) = 16X seconds

16X = 22 seconds
X = 22/16 = 11/8 seconds

So at 12:00, we have...
12 strokes x seconds per stroke
11 intervals @ 2X seconds per interval
12(X) + 11(2X) = 34X seconds

Plugging in the value of X, we have....

34(11/8) = 17(11/4) = 187/4 seconds = 46 3/4 seconds

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31 May 2016, 07:20
A certain clock marks every hour by striking a number of times 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 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

A. 72

B. 50

C. 48

D. 46

E. 44

I got E.
OA is D.

I am having a hard time comprehending the question. Can someone please explain in detail? Thanks in advance.
Math Expert
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Re: A certain clock marks every hour by striking a number of tim [#permalink]

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31 May 2016, 07:30
utengsolanki wrote:
A certain clock marks every hour by striking a number of times 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 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

A. 72

B. 50

C. 48

D. 46

E. 44

I got E.
OA is D.

I am having a hard time comprehending the question. Can someone please explain in detail? Thanks in advance.

Merging topics. Please refer to the discussion above.

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Re: A certain clock marks every hour by striking a number of tim   [#permalink] 31 May 2016, 07:30
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