GMAT Math

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 stoke 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

I think the wording is confusing (I've had many students ask me about it), but the math required to solve it is pretty straightforward. I'd say it's a 500-level math question.

Cheers,
Brent