Six bells commence tolling together and toll at intervals of 2, 4, 6,

Question

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

A. 10
B. 12
C. 15
D. 16
E. 4

RajatVerma1392 · Accepted Answer

The bells will toll together when there is one time interval which is divided by every single time interval.
Thus, we need to find the LCM of 2,4,6,8,10,12
LCM : 120

Thus, in 30 minutes = 30 * 60 seconds, they will toll together:

\frac{30*60}{120} 
= 15

IMO the answer is C.

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eakabuah · Answer

We need to find the LCM of the intervals at which the bells toll, i.e. 2,4,6,8,10,12
Prime factorization for the intervals are: 
2=2; 4=2^2; 6=2x3; 8=2^3; 10=2x5; 12=2^2 x 3
Hence LCM=2^3 x 3 x 5 = 120.
Number of times the bells toll together = 1+(30x60)/120 = 1+15 = 16.
You need to add one because the question stem says they commence tolling together. Meaning at time 0, they all tolled once.

The answer is therefore D.

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OC2910 · Answer

the all bells rang once at zeroth second 
next they will ring together at the LCM (all the fgiven individual times ) =120 second= 2mins

total interval 30 mins
number of times in 0 to 30 = 1+30/2
=16 times 
we need to count the first ringing

Archit3110 · Answer

total time = 30*60 ; 1800 sec
LCM for 2, 4, 6, 8 10 and 12 ; 120
so bells will toll together interval 120 sec 
1800/120 ; 15 times + 1 since they have tolled together at 0 sec
IMO D ; 16

ScottTargetTestPrep · Answer

The least common multiple (LCM) of 2, 4, 6, 8, 10, and 12 is 120. Thus, the bells toll together every 120 seconds (or 2 minutes), so in 30 minutes they will toll simultaneously 30/2 = 15 times. However, since they commence tolling together at the beginning (i.e., they are tolling together at the 0th second or the 0th minute), we need to add 1 to 15 and thus they toll together a total of 16 times.

Answer: D

SRSRS · Answer

The Initial Zero Hour condition is there to solve this question so that will be counted now,
The LCM of 2,4,6,8,10,12 is 120 hence 120 secs = 2 mins 
Now 30/2 = 15 times 
But the initial condition is also be added hence the answer is 15+1=16 
Option D

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CrackverbalGMAT · Answer

Solution:

The bells toll together for the first time at at a time

=LCM(2,4,6,8,10,12)

= 120 sec = 2min

30 min has 15 such 2 min and hence the bells must have tolled together for 15 min and add 1 to it to represent their tolling together for the first time at t=0 sec.

Hence 16 times(Option D)

Hope this helps

Devmitra Sen(Quants GMAT Expert)

bumpbot · Answer

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