How often will five bells toll together in one hour if they start toge

Question

How often will five bells toll together in one hour if they start together and toll at intervals of 5, 6, 8, 12, 20 seconds, respectively?

(A) 29
(B) 30
(C) 31
(D) 41
(E) 120

thkkrpratik · Answer

Step 1: Find the LCM of 5,6,8,12,20.

LCM is 120 (this is the time in seconds when all bells toll together aka once every 2 minutes).

Thus, total times = 60/2 = 30 times.

Option B

chloe2m · Answer

No  Option C  is the correct answer (31). 
As you said in one hour they will toll together 30 times (3600/120) but since they start together you have to add +1.

Kinshook · Answer

How often will five bells toll together in one hour if they start together and toll at intervals of 5, 6, 8, 12, 20 seconds, respectively?

The time when five bells will toll together = LCM(5,6,8,12,20) = 2^3*3*5 = 120 seconds

The number of times when five bells will toll together in one hour = 60*60/120 = 30 times

IMO B

shwetakoshija · Answer

NOTE: In my opinion, this is not the best way to express the intended meaning of this question. Had I written it, I would have specified that "they start together at the start of the hour". Right now, who knows when the bells start tolling with respect to this one hour. Imagine the first joint toll 1 second before the start of this one-hour timer vs first joint toll right with the start of this one-hour timer. Answer would be 30 vs 31 in these situations.

For now, assuming the intended meaning that the first toll happened just as this one-hour timer started, below is the detailed solution:

Given : 
 
 5 bells toll at intervals of 5, 6, 8, 12, and 20 seconds, respectively.  
 They start together (imagine a timer starting with the first toll of all these bells).

To find : How many times all five bells toll together in one hour

Solution:

Step 1 : Find the LCM of the intervals
The LCM will tell us after how many seconds all the bells toll together again (for the first time after starting).

Prime factorizations:
 
 5 = 5 
 6 = 2 × 3 
 8 =  2^3  
 12 =  2^2  × 3 
 20 =  2^2  × 5

So, LCM =  2^3  × 3 × 5 = 120 seconds
This means all the bells toll together every 120 seconds, i.e.,  every 2 minutes .

Step 2 : Count how many such intervals fit in 1 hour
1 hour = 60 minutes 
So, there are 60 ÷ 2 =  30  such 2-minute intervals in 60 minutes.

Step 3 : Include the starting time
They toll together at  time 0 , and then after every 2 minutes
Thus, they toll together  31 times  in total in that one hour.

Correct Answer: (C)

Shweta Koshija  
 GMAT, GRE, SAT, AP Calculus Coach for 10+ years

Yosemite98 · Answer

I think it is not properly written. "How often" does not mean how many times...

How often will five bells toll together in one hour if they start toge

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How often will five bells toll together in one hour if they start toge

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