PRACTICE Aptitude

Описание: The video focuses on aptitude practice, specifically covering concepts related to HCF (Highest Common Factor) and LCM (Least Common Multiple).

The instructor begins by motivating students (1:02) and emphasizing that no part of an exam is inherently easy or hard, advising against such a mindset (2:06).

Key topics and problems discussed include:
Finding the longest rod in a rectangle and a cuboid (3:54). For a rectangle with sides 15m and 20m, the longest rod can be placed diagonally, calculated using the Pythagorean theorem, resulting in 25m (4:03). For a cuboid with dimensions 20cm (l), 15cm (b), and 25cm (h), the longest rod is found using the formula √(l² + b² + h²) (5:07).
Finding the greatest four-digit number that leaves a remainder of four when divided by 16, 24, and 36 (6:22). The method involves finding the LCM of the divisors, dividing the greatest four-digit number by this LCM, subtracting the remainder, and then adding the desired remainder (9:38).
Finding the greatest five-digit number divisible by 15, 20, 24, 27, 32, and 36, with an additional condition that it "must be added" to 8321 to equal this number (14:45). This problem extends the previous concept by requiring a final subtraction to find the value that needs to be added.
Solving problems involving intervals, such as trains starting at different intervals (22:59). The instructor explains that for such problems (which also apply to clocks or bells), the LCM of the intervals should be calculated. An example is given for trains starting at 10, 30, 50, 60, and 90-minute intervals, with the first train starting at 2 PM, to find when they will meet again (23:03).
Calculating the LCM and HCF of fractions (28:34). The formulas are presented:
LCM of fractions: (LCM of numerators) / (HCF of denominators) (28:34)
HCF of fractions: (HCF of numerators) / (LCM of denominators) (29:04)
Examples are worked through, such as finding the LCM and HCF of 1/3, 5/6, 2/9, and 4/27 (29:58).

The instructor also provides tips for maintaining speed during exams (31:54) and discusses the potential use of scientific calculators (45:00) for complex calculations. The chapter concludes with the completion of these topics (40:25)