GMAT Problem Solving - Lamp A Flashes Every 6 seconds, Lamp B Flashes Every 8 seconds, Lamp C Flashes Every 10 seconds

Question - Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 2 minutes after that how many times will exactly two lamps flash?

1. 5
2. 6
3. 9
4. 12
5. 15

“Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

This model answer has only 1 approach to solve the problem.

We have followed the LCM method to find the solution to the problem.
Given:
Lamp A flashes every 6 secs,
Lamp B flashes every 8 secs,
Lamp C flashes every 10 secs.
At certain time three flashes simultaneously.
Find out:
Then the three lamps flashes simultaneously in a span of 2 minutes.
Now, let us take the L.C.M of three 6,8,10 sec
The result is 120 secs.
Hence, exactly after 2 minutes it flashes simultaneoulsy.
The problem statement asks exactly two lamps falshes at the same time. .
We will take the lcm of a and b .
6 and 8 is 24 secs.
Now, we will divide 120/25 to get the number of times.
So two lamp flashes 5 times in 2 minutes.
We will take the lcm of b and c .
8 and 10 secs is 40 secs.
Now, we will divide 120/40 to get the number of times.
So both flashes 3 times in 2minutes.
lcm of c and a.
6 and 10 secs is 30 secs.
Now, we will divide 120/30 to get the number of times.
So two lamp flashes 4 times in 2 minutes.
Since, all three pairs flashes simultaenoulsy at 2 minutes. we have to minus one from all three pairs.
then 12-3=9.
so option C is correct.

Correct Answer: C

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