A Simple LCM question

[sarathsasikumar]

Question : At a book store, "ABC BOOK STORE" the name is flashed using neon lights. The words are individually flashed at intervals of 2,4, and 5 seconds respectively and each word is put off after a second. What is the least time after which the full name of the book store can be read again ?

To me this looks like a simple LCM problem. The LCM of 2,4 and 5 is 20 seconds. So I believe that the name can be read after 20 seconds. The name will stay lit from the the 20th second to the 21st second.

The book (CAT - Arun Sharma) says that the answer is 30 seconds. The author seems to have added 1 second to each of the numbers 2,4 and 5 and says that the answer is the LCM of 3,5 and 6, which is 30 seconds.

In my opinion, When the clock ticks "30 seconds", only the words ABC and STORE will be lit.

What do you guys think ?

Thanks,
Sarath

[sarathsasikumar]

C'mon guys...someone pls answer !!

[jssaggu.tico]

Three words will be switching off after one second transition.Also, each word stays on for 1 sec.We need to find out at what time they ALL will be in ON state or end of which second they ALL will be switched OFF for first time.

For example, "ABC" switches ON at 2nd sec and gets OFF at 3rd sec.Hence, it is 3rd sec during which it is ON, not 2nd sec because it switches ON after the 2nd sec finishes or at the end of 2nd sec.(We have to add '1' in every second) -->Note Please.

So, each of them get switched off at the end of (t+1)th second, where 't' is the second after when they first switched on.

So, L.C.M of 2+1, 4+1 & 5+1 will yield the answer.(Ans=30)
Hence, at 30th second they will be all ON.

[RonPurewal]

Three words will be switching off after one second transition.Also, each word stays on for 1 sec.We need to find out at what time they ALL will be in ON state or end of which second they ALL will be switched OFF for first time.

For example, "ABC" switches ON at 2nd sec and gets OFF at 3rd sec.Hence, it is 3rd sec during which it is ON, not 2nd sec because it switches ON after the 2nd sec finishes or at the end of 2nd sec.(We have to add '1' in every second) -->Note Please.

So, each of them get switched off at the end of (t+1)th second, where 't' is the second after when they first switched on.

So, L.C.M of 2+1, 4+1 & 5+1 will yield the answer.(Ans=30)
Hence, at 30th second they will be all ON.

yep - this is it.

nicely done.