4 Bells toll together at 9:00 A.M. They toll after 7, 8, 11 and 12 sec

Question

4 Bells toll together at 9:00 A.M. They toll after 7, 8, 11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?
(A) 3 
(B) 4
(C) 5 
(D) 6
(E) 7

Kurtosis · Answer

All 4 bells toll together at LCM(7, 8, 11, 12) = 1848 secs

3 hours = 3600 * 3 = 10800 secs

Number of times = 10800/1848 --> 5 times

Answer: C

Abhishek009 · Answer

9:00 AM + LCM ( 7, 8, 11 & 12 )

=> 9:00 AM + 1848/60 Min = 9:00 AM +30.80 min

So, The sequence will be 9:00 AM , 9:31 AM , 10 : 02 AM , 10:33 AM, 11:04 AM , 11: 35 AM...

Thus, in the 3 hours, the bells will toll together 5 times...
  
Hence, answer will be (C) 5

rishit1080 · Answer

This is not a sub-600 level question I'm afraid. To find the LCM of 7, 8, 11, and 12 makes this question roughly an 800 level question. Easy processing but finding the LCM for these 4 numbers is immensely difficult. Reminder: think before you post question difficulty and follow the guidelines

matthewsmith_89 · Answer

Another approach to solve this
The LCM of 7, 8, 11 and 12 seconds is 1848 seconds

Therefore 1848/60 = 30.80

180/30.80 is obviously lower than 6 since 180/30 = 6

Therefore, the answer is C

KrishnakumarKA1 · Answer

They will toll again after every LCM (7,8,11,12) = 1848 second

no. of times the bell will ring in 3 hrs = 10800 seconds = 10800/1848 = 5.8 or 5 times
adding the first time we get the total no as 6 times.

CrackverbalGMAT · Answer

In order to find the time taken by 4 bells to toll together again after 9 AM, we need to find LCM of (7,8,11,12) secs.

Time taken = LCM of (7,8,11,12) =7*11*24 secs =(7*11*24)/60 minutes = (7*11*2)/5 = 154/5 = 30.8 mins

That means, After 9 AM , all 4 bells will toll together after every 30.8 mins .

Number of times , the bells will toll together again in the next 3 hours = (3*60)/30.8

Since the answer should be an integer, we can approximate it as an integer less than 6 i.e 5

Option C is the answer.

Thanks,
Clifin J Francis
GMAT SME

Greg1234 · Answer

How does one find the LCM of these four numbers?

inciduntveniam · Answer

How did you guys figure out that the LCM needs to be taken out here? Like when I read the question, this did not cross my mind. How do i improve this ?

egmat · Answer

Hi inciduntveniam,

Great question, because this is exactly the kind of recognition that comes from spotting a  pattern type , not from the numbers themselves.

Look at what the posted solutions (Kurtosis, Abhishek) jumped to: LCM. Here's the reasoning they skipped over.

Why LCM is the tool

Think about  one  bell at a time. The bell with a  7 -second period tolls at  7 ,  14 ,  21 ,  28  ... seconds - i.e. at every  multiple of 7 . The  8 -second bell tolls at every multiple of  8 . And so on.

Now ask: at what moment do  all four  toll at once again? It has to be a time that is  simultaneously  a multiple of  7 , of  8 , of  11 , and of  12  - in other words, a  common multiple  of all four periods.

There are infinitely many common multiples, but the  first  time they re-coincide is the  smallest  one. "Smallest common multiple of several numbers" is literally the definition of  LCM . That's the whole link.

The trigger to memorize

Whenever several things repeat on their own fixed cycles and you're asked  when they next line up together , that's an  LCM  situation - bells tolling, lights blinking, runners meeting at a start line, gears returning to position. (The mirror-image cue - "largest size that divides several quantities evenly" - points to  GCD  instead.)

Lock it in with a tiny version

Forget the ugly numbers. Suppose two bells toll every  2  and  3  seconds:
- 2-bell:  2 ,  4 ,  6 ,  8 ,  10 ,  12  ...
- 3-bell:  3 ,  6 ,  9 ,  12  ...

List them by hand and you'll  see  them first meet at  6  seconds - which is exactly LCM( 2 ,  3 ). Once you feel why  6  is the answer here, the  1848  in the original is the same idea, just with bigger numbers.

So the skill to build isn't computing LCM - it's recognizing "independent cycles, when do they coincide?" - LCM.

Answer: C

inciduntveniam · Answer

Thankyou so much, understood

4 Bells toll together at 9:00 A.M. They toll after 7, 8, 11 and 12 sec

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4 Bells toll together at 9:00 A.M. They toll after 7, 8, 11 and 12 sec

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