khandelwal.ab wrote:Can any expert help me with an efficient solution and sound reasoning for this problem?
Q. An alarm is set in three watches for 6:00 AM. The alarms ring for 20, 50 and 60 seconds, respectively and then go off to snooze mode for 2, 5 and 6 minutes respectively. At what time will the alarms start ringing simultaneously for the second time?
A) 6:30 AM
B) 6:42 AM
C) 6:35 AM
D) 7:12 AM
E) 7:30 AM
[spoiler]
OA: C
[/spoiler]
Thanks in advance!
The alarms first go off at 6am.
The cycle for the longest alarm = 60 seconds + 6 minute snooze = 7 minutes.
Thus, the time needed must be a multiple of 7.
The only viable answer choices are B (6:42 implies that 42 minutes are needed) and C (6:35 implies that 35 minutes are needed).
Since the earlier time is 6:35am, let's see whether the other two alarms will go off at this time.
Answer choice C: 35 minutes
The cycle for the first alarm = 20 seconds + 2 minute snooze = 7/3 minutes.
Total time/cycle time = 35/(7/3) = 15 cycles.
The cycle for the second alarm = 50 seconds + 5 minute snooze = 35/6 minutes.
Total time/cycle time = 35/(35/6) = 6 cycles.
Success!
In 35 minutes, the first alarm will complete 15 cycles, the second alarm will complete 6 cycles, and the third alarm will complete 5 cycles (since 35/7 = 5 cycles), implying that all 3 alarms will go off at 6:35am.
The correct answer is
C.
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