A lighthouse blinks regularly 5 times a minute. A neighboring lighthou GMAT Problem-Solving

Question: A lighthouse blinks regularly 5 times a minute. A neighboring lighthouse blinks regularly 4 times a minute. If they blink simultaneously, after how many seconds will they blink together again?

A. 20
B. 24
C. 30
D. 60
E. 300

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with basic math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Assuming they both blink once every zero seconds. It turns out that the start time must be 0*.
How long does it take for them to blink together again?
Five times every minute, Lighthouse #1 blinks.
60 seconds make up a minute.
L #1 blinks every 12 seconds (60 secs /5)
Four times every minute, Lighthouse #2 blinks.
Every 15 seconds, L #2 blinks: 60 seconds divided by four equals 15 seconds.
Given that there are only 60 seconds in a minute and the LCM of 12 and 15 is 60.
To meet both requirements (that #1 and #2 blink 5 and 4 times per minute AND that they blink again concurrently), we must start at 0.
The LCM is start time 0 and end time 60, or 60 seconds in 1 minute.
After 60 seconds, #1 and #2 will blink in unison once more.
Correct option: D

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with geometry. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
300 seconds is 5 cycles; this is random. Assume that at 12 the first two strikes have been recorded.
#1: 12, 24, 36, 48, 60 (cycle 1)
12, 24, 36, 48, 60 (cycle 2 ..)
12, 24, 36, 48, 60 (cycle 5)
#2 12, 27, 42, 57 (cycle 1)
12, 27, 42, 57 (cycle 2)
12, 27, 42, and 57 (cycle 5) never cross paths. If we set the start time to 0 they will meet (a multiple of 60). at 60, the second simultaneous blink.
Correct option: D

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with geometry. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
The first lighthouse blinks every 1/5 minutes, or 12 seconds. The second lighthouse blinks every 1/4 minutes, or 15 seconds.
We want to find the least common multiple of 12 and 15, which is the smallest time at which both lighthouses will blink simultaneously again.
The prime factorization of 12 is 2² * 3, and the prime factorization of 15 is 3 * 5. The least common multiple of 12 and 15 is therefore 2² * 3 * 5 = 60.
Therefore, both lighthouses will blink together again after 60 seconds, or 1 minute.
Correct option: D

“A lighthouse blinks regularly 5 times a minute. A neighboring lighthou" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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