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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, 01:10
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75% (hard)

Question Stats:

52% (01:39) correct 48% (01:41) wrong based on 929 sessions

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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, 01:10
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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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21 Feb 2014, 02:03
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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, 06:36
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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, 23:05
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, 11:00
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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09 Dec 2015, 12:30
1
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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Re: A certain clock marks every hour by striking a number of tim  [#permalink]

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25 May 2017, 19:42
Bunuel wrote:
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

There are 6 clock strikes and 5 intervals between strikes. 6+5 = 11 periods throughout the 22 seconds.

22/11 = 2 seconds/period.

At 12:00, there will be 12 clock strikes and 11 intervals 23*2 = 46 seconds total.
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Re: A certain clock marks every hour by striking a number of tim  [#permalink]

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31 May 2017, 19:11
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Bunuel wrote:
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

We are given that 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.

Since at 6:00 the lapse between the beginning and the last stroke is 22 seconds, we can create the following equation in which x = the time between strokes = the time for each stroke. Since there are 6 strikes at 6:00, we have:

strike - lapse - strike - lapse - strike - lapse - strike - lapse - strike - lapse - strike

There are 6 strikes and 5 lapses, and thus:

6x + 5x = 22

11x = 22

x = 2 seconds

So, at 12:00 there will be 12 strikes and 11 lapses. Thus, the total time will be:

12(2) + 11(2) = 24 +22 = 46 seconds.

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

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31 Jan 2018, 08:16
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1
Bunuel wrote:
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

In some regards, this is more of a Reading Comprehension question than a Quantitative question

... the time required FOR a stroke is exactly equal to the time interval BETWEEN strokes.
So, we have moments of silence and moments where the clock is ringing. Each period of silence is the same duration as each period of noise.

So, for example, at 3:00, we have (RING)(silence)(RING)(silence)(RING)

At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds
So, at 6:00, we have (RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)
Notice that, if we count RINGS and silences, we have a total of 11 periods.
If the entire event takes 22 seconds, we can conclude that each period is 2 seconds long.

At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
We can conclude that this event will include 12 RINGS and 11 silences for a total of 23 periods.
Since each each period is 2 seconds long, the entire event will take 46 seconds

Aside: If you're not convinced that there will be 12 RINGS and 11 silences, you can always write it out . ..
At 12:00, we have (RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)

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

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29 Apr 2018, 00:52
Bunuel wrote:
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

12 strokes and 11 intervals in between,
22 seconds for 6 strokes and 5 intervals.
so 12s for strokes and 10s for intervals. As 1 strokes = 1 intervals.
so for 12 strokes and 11 intervals we need = (24+22)s = 46s
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Re: A certain clock marks every hour by striking a number of tim  [#permalink]

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16 May 2018, 13:23
Bunuel wrote:
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.

Bunuel
how did you find out this --> 6 strokes + 5 intervals between strokes
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A certain clock marks every hour by striking a number of tim  [#permalink]

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16 May 2018, 22:10
1
dave13 wrote:
Bunuel wrote:
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.

Bunuel
how did you find out this --> 6 strokes + 5 intervals between strokes

At 6:00, we have (RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)
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