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

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Math Expert
Joined: 02 Sep 2009
Posts: 57155
Six bells commence tolling together and toll at intervals of 2, 4, 6,  [#permalink]

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07 Aug 2019, 00:40
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Difficulty:

75% (hard)

Question Stats:

26% (01:08) correct 74% (01:43) wrong based on 54 sessions

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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

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Manager
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Six bells commence tolling together and toll at intervals of 2, 4, 6,  [#permalink]

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07 Aug 2019, 00:47
2
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

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Joined: 18 May 2019
Posts: 154
Six bells commence tolling together and toll at intervals of 2, 4, 6,  [#permalink]

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07 Aug 2019, 02:28
1
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.

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Manager
Joined: 04 Apr 2015
Posts: 218
Re: Six bells commence tolling together and toll at intervals of 2, 4, 6,  [#permalink]

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07 Aug 2019, 04:02
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
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Re: Six bells commence tolling together and toll at intervals of 2, 4, 6,  [#permalink]

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08 Aug 2019, 11:21
Bunuel wrote:
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

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
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Re: Six bells commence tolling together and toll at intervals of 2, 4, 6,  [#permalink]

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12 Aug 2019, 11:54
Bunuel wrote:
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

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.

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Re: Six bells commence tolling together and toll at intervals of 2, 4, 6,   [#permalink] 12 Aug 2019, 11:54
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