Question: There are five bells which start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively. In 36 minutes, how many times will the bells ring simultaneously?
(A) 13
(B) 12
(C) 6
(D) 5
(E) 4
Correct Answer: A
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- There are five bells which start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively.
Asked:
- In 36 minutes, find out the number of times the bells will ring simultaneously.
As per the condition of the question, five bells start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively. So we need to find the LCM of the time intervals to solve the problem.
Therefore, LCM of 3,6,9,12,15 =180 Sec
So the number of times the bell rings in 36 minutes = \((36 * \frac{60}{180}) +1\)
= \(\frac{36}{3} + 1\)
= 12 + 1
= 13 times
Approach Solution 2:
The problem statement states that:
Given:
- There are five bells which start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively.
Asked:
- In 36 minutes, find out the number of times the bells will ring simultaneously.
Five bells start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively.
Let’s find the LCM of the time intervals using prime factorization:
3 = 3 (prime number)
6 = 3 x 2
9 = 3 x 3
12 = 3 x 2 x 2
15 = 3 x 5
Therefore, LCM of 3,6,9,12,15 = 3 x 3 x 2 x 2 x 5 = 180
Therefore, bells ring after every 180 seconds i.e., 3 min
Hence, in 3 min bell will ring at 0 sec. as well
So the required number of times the bells will ring in 36 minutes = 1 + 36/3 = 1 + 12 = 13 times.
Approach Solution 3:
The problem statement suggests that:
Given:
- There are five bells which start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively.
Asked:
- In 36 minutes, find out the number of times the bells will ring simultaneously.
All bells will ring together after exactly 180 seconds (which is the L.C.M of 3, 6, 9, 12 and 15 seconds) or in 3 minutes.
So within 36 minutes, the bells will toll together 1 + 36/3 = 1 + 12 = 13 times.
“There are five bells which start ringing together at intervals of 3, 6”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. In order to solve GMAT Problem Solving questions, the candidates must hold a basic concept of mathematics. The candidates can practise several sorts of questions from GMAT Quant practice papers that will enable them to improve their mathematical understanding.
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