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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

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

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: 1. Please provide your solutions to the questions; 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.

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.

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

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.

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?

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

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

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: 1. Please provide your solutions to the questions; 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.

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.

Answer: D
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