A certain clock marks every hour by striking a number...

LUANDATO wrote:A certain clock marks every hour striking a number of times equal to the hour, and the time required for 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
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

LUANDATO wrote:A certain clock marks every hour striking a number of times equal to the hour, and the time required for 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 lapse between strokes = the time for each stroke. Since there are 6 strokes at 6:00, we have:

stroke - lapse - stroke - lapse - stroke - lapse - stroke - lapse - stroke - lapse - stroke

There are 6 strokes 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