Number Properties and Number Theory is a topic from which you should expect 4 to 7 questions in the GMAT quant section - in both variants viz., problem solving and data sufficiency. This is a very important topic.
The GMAT Syllabus in Number properties, number systems, and number theory include a wide array of concepts that range from simple questions on LCM, HCF, to questions on factors, remainders, remainder theory, factorial, unit digits, number of factors, sum of factors, and polynomial division rules . Wizako's GMAT Math Lesson Book in this hard math topic covers the following concepts in Number Properties & Number Theory.
Here is a typical solved example in Wizako's GMAT Book from this chapter
A green light flashes thrice in a minute and a red light flashes 4 times in 2 minutes at regular intervals. If the two lights start flashing together, how often will they flash together in an hour?
The green light flashes thrice in a minute.
Therefore, the green light will flash once every 20 seconds.
The red light flashes 4 times in 2 minutes
Therefore, the red light will flash once every 30 seconds.
Starting from the 0th second, the green light will flash at multiples of 20 seconds. i.e., at 0, 20, 40, 60, 80 ... seconds.
Starting from the 0th second, the red light will flash at multiples of 30 seconds. i.e., at 0, 30, 60, 90, 120 ... seconds.
Hence, the two lights will flash together at time intervals that are multiples common to both 20 and 30.
The smallest and first common multiple of 20 and 30 is the LCM of the two numbers.
The Least Common Multiple (LCM) of 20 and 30 = 2 × 3 × 10 = 60.
i.e., the two lights will flash together every 60 seconds or 1 minute.
Therefore, they will flash together 60 times in an hour.
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