Number System - many times do they flash together per hour

StrawberryCow wrote:How do you solve this.

A blue light flashes four times per minute and an orange light flashes five times per minute at regular intervals. If both the lights start flashing at the same time, how many times do they flash together per hour?
Answer Choices

A. 42
B. 120
C. 60
D. 36
E. 80

Thanks,StrawberryCow

Hi,
Is Answer C
This is how I did,
1 hour = 3600 sec.
Blue light flashes once in 15 sec(60/4)
Orange light flashes once in 12 sec(60/5)

Find LCM for 15 and 12 = 60

Now find how many 60's are there in 3600 =3600/60 = 60
Hence Answer is 60

Regards,
Uva.

Blue light flash once in 60/4 = 15 sec
Orange light flash once in 60/5 = 12 sec

Blue and orange light will flash together = LCM of 15 and 12 = 60 sec -> 1 min (after every)

So, after an hour blue and orange light will flash together = 60 times..

One way to do this if you're stuck on the test is to see how many times the lights flash simultaneously in one minute, then to multiply that by 60 to find out how many times they flash simultaneously per hour. (This won't always work, but it happens to work here for reasons I'll detail at the end of the post ... and it can't hurt to learn a practical alternative!)

Say we start our minute at 00:00 (minutes : seconds). The blue light flashes at 00:15, 00:30, 00:45, 1:00. The orange light flashes at 00:12, 00:24, 00:36, 00:48, 1:00. Since the only time they flash together is at 1:00, they only flash together once per minute, giving us 60 times per hour.

We could get in trouble if the lights don't both flash at 1:00 (as they might go into different cycles in the second minute), but here we don't have to worry about that - as soon as we see that the cycle is the same every minute, we're fine. If the problem had some other cycle, we'd just have to determine when the cycle repeats, then generalize that from minutes to hours.