Problem Solving

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
(8) 50
(C) 48
(0) 46
(E) 44

The correct answer is D

And Here is OG explanation:
[spoiler]At 6:00 there are 6 strokes and 5 intervals between strokes. Thus, there are 11 equal time intervals in the 22 seconds between the beginning of the first stroke and the end of the last stroke. Therefore, each time interval is ii = 2 seconds long. At 12:00 there are 12 strokes and 11 intervals between strokes. Thus, there are 23 equal 2-second time intervals, or 23 x 2 = 46 seconds, between the beginning of the first stroke and the end of the last stroke. [/spoiler]

amirhakimi wrote: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
(8) 50
(C) 48
(0) 46
(E) 44

The correct answer is D

Time required for a stroke = "_" = t
Time between strokes = "x" = t

At 6:00, the clock strikes exactly six times = "_x_x_x_x_x_" = 6t + 5t = 11t
11t = 22
t = 2

At 12:00, the clock strikes exactly twelve times = 12t + 11t = 23t
23t = 23 * 2 = 46 seconds

Choose D

Cheers