A certain clock marks every hour by striking a number of times equal

Question

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

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Bunuel · Accepted 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 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

The Official Guide For GMAT® Quantitative Review, 2ND Edition

(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.

KarishmaB · Answer

I guess your generation has had no exposure to the clocks of the old days. In the old days, the clocks used to strike at the hour i.e. at 2 o clock, you would hear 2 strikes. There would be a small interval between two strikes. The point was that watches/clocks were not common and often there was a single clock for a whole village. There would be loud strikes at every hour to inform everyone of the time. People could count the strikes to know what time it is. Check out this youtube video of big ben to understand what a clock strike is: https://www.youtube.com/watch?v=rkXy20fUoic at 6'o clock, there would be 6 strikes. First strike, then a short interval, the second strike, then a short interval and so on till the 6th strike. So there would be in all 5 intervals between 6 strikes. Similarly, between 12 strikes, there would be 11 intervals. According to the question, the time spent in the strike and the interval is same. At 6'o clock, the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs. At 12'o clock, the 12 strikes and 11 intervals will take 2*(12+11) = 46 secs

Manofsteel · Answer

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)

Bunuel · Answer

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.

GyanOne · Answer

Let x = time required for each stroke = time interval between strokes

Therefore when the clock strikes 6:00pm, the time requires for the six strokes = 6x (for the strokes) + 5x (for the interval between the strokes) = 11x = 22 secs
=> x = 2 seconds

Therefore at 12:00, time between the beginning of the first stroke and end of the last = 23x (12x+11x) = 46 seconds or option (D).

alphabeta1234 · Answer

Dear lord

Can someone explain what the question is even asking!

What the heck does this even mean!

"A certain clock marks every hour by striking a number of times equal to the hour"

Please can someone elaborate. Why does GMAC phrase questions like this?

Bunuel · Answer

It just means that at 1:00 the clock strikes once, at at 2:00 the clock strikes twice, at 3:00 the clock strikes 3 times, ...

Hope it's clear.

bicu17 · Answer

I don't understand the interval part in the explanations. How do you come up with 5 intervals? Why do you add them together?
Thanks.

Raihanuddin · Answer

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 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

The Official Guide For GMAT® Quantitative Review, 2ND Edition

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made,
Rich

JeffTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

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 Answer: D 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

dave13 · Answer

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

Bunuel · Answer

Please read the whole thread: https://gmatclub.com/forum/a-certain-cl ... l#p2007220 At 6:00, we have (RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)(silence)(RING)

TheUltimateWinner · Answer

Hi  EMPOWERgmatRichC 
Is it necessary to be the time integer?
Thanks for your nice explanation...

EMPOWERgmatRichC · Answer

Hi Asad,

To answer your immediate question: No, whatever "unit" of time that a question is based around doesn't necessarily have to be an integer - but the units often will be integers. In that same way, Quant questions in general don't have to be based on integers (and you'll see several questions on Test Day that aren't), but most questions often are based around integers (since the GMAT is NOT a Test of high-level calculation skills - it's a Test of critical thinking skills that involve some math - so complex, non-integers don't show up too often).

My response to Raihanuddin was really meant to point out that the 'hypothetical change' that he was making to the question would have made the question a bit more difficult (and step-heavy) and created an answer that wasn't as "nice" as the answers in the original prompt.

GMAT assassins aren't born, they're made,
Rich

energetics · Answer

We are given time stroke = time between strokes, the trap here is to assume they are equivalent and get messed up in calculating those numbers. However, it's stated that we are counting the "time between the first and last stroke" only; i.e. there is no interval on the last stroke.

This is a good question to draw a diagram:

x = stroke, o = interval

x-o-x-o-x-o-x-o-x-o-x
1---2---3---4---5----6

You can see there are 6 x's and only 5 o's, this means 22 secs is evenly divided by 11... 2 secs per stroke
Now, applying the same logic to 12, it would be double the number of strokes (24) minus 1 (for the cut-off at the end).

2*23 = 46, D.

dabaobao · Answer

At 6:00:
Total intervals = 11
Time for one interval = x
Time taken = 22
11x = 22 => x = 22/11 = 2

At 12:00
Total intervals = 23
Total time = 23*2 = 46

ANSWER: D

GMATGuruNY · Answer

Between each pair of strokes there is an interval.
Each interval lasts for the same amount of time as each stroke.
Let t = time per stroke/interval.

At 6pm:
6 strokes + 5 intervals = 11t.
11t = 22 seconds.
t = 2 seconds.

At 12pm:
12 strokes + 11 intervals = 23t = 23*2 = 46 seconds.

D

A certain clock marks every hour by striking a number of times equal

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