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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] New post 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] New post 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.

Answer: D.
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Re: A certain clock marks every hour by striking a number of tim [#permalink] New post 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] New post 22 Feb 2014, 05:36
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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.

Answer: D.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A certain clock marks every hour by striking a number of tim [#permalink] New post 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] New post 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?
Re: A certain clock marks every hour by striking a number of tim   [#permalink] 17 Oct 2014, 10:00
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