GMAT Problem Solving - 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds

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

“4 Bells toll together at 9:00 A.M. They toll after 7, 8, 11 and 12 seconds” - this is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

With the given case scenario, it can be identified that 4 bells toll together at the interval of 7, 8, 11 and 12 seconds respectively. They have a toll together at 9 am as well. To find the number of times the bell would toll in the next 3 hours, it is essential to solve the problem.

Accordingly, it is firstly important to find the Lowest Common Multiple or LCM of the seconds of interval in which the bell tolls. This includes the LCM of 7, 8, 11 and 12 seconds.

The value derived from the LCM of these numbers is 1848/60.

Accordingly, this value needs to be added to 9.00 AM. This implies-

9.00AM + 1848/60 = 9.00AM + 30.80

Based on the above value, the sequence of the tolling of the bell that can be arranged and found includes- 9:00 AM , 9:31 AM , 10 : 02 AM , 10:33 AM, 11:04 AM , 11: 35 AM

Therefore, the above timing of the bell for tolling has been placed for the next three hours. Accordingly, in the next 3 hours, the bell will toll again five times. Hence, the correct answer is option C with 5 times.

Correct Answer: C

Approach Solution 2:

In order to find the time taken by 4 bells to toll together again after 9 AM, in the next three hours, it is important to find the lowest common multiple. This is for the seconds of intervals in which the bells toll. Certainly, the results of the LCM would help in finding the time taken by the bells to toll in the next three hours. Hence, the LCM to be found is for 7, 8, 11 and 12 seconds respectively. This can be equated as follows.

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

This equals to the time taken for the bells to toll is 30.8 mins

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

Certainly, the given question needs to find the number of times the bells will toll in the next 3 hours. So in every 30.8 minutes, the number of times the bells would toll is 3 times of 60 divided by the time taken for the bells to toll. This can be equated as-

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

Hence, the number of times the 4 bells would toll in the next 3 hours is 5 times and thus, option C is the right answer.

Correct Answer: C

Approach Solution 3:

Case 1: To find at what time duration all the bells will rang together, we are require to find their LCM
LCM of 7,8,11,12 =1848
This signifies that after every 1848 seconds, all the bells will toll together.

Case 2: To ccalculate the number of times the bells will ring together in the next 3 hours
So, the no. of seconds in three hours = 3×60×60=10800 secs
Therefore all the bells will toll together every 1848 sec.
Number of times they toll together in 10800 seconds = 10800/1848​=5

Hence, the number of times the 4 bells would toll in the next 3 hours is 5 times and thus, option C is the right answer.

Correct Answer: C

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