Previous Year Topic Wise Questions With Solutions: HCF & LCM

Ans: (d)
Prime factorization of 1001 = 7 × 11 × 13
If the HCF of a set of numbers is 1, the numbers are relatively prime (i.e. coprime).
Some of the possible combinations of three numbers whose LCM is 1001 and HCF is 1 are:
7, 11, 13
1, 13, 77 (7 × 11)
1, 11, 91 (7 × 13)
1, 7, 143 (11×13)
13, 13, 77
11, 11, 91
7, 7, 143
1, 1, 1001
1, 1001, 1001
Also,
7, 11, 143
11, 13, 91
11, 13, 77
....and so on.
(Since the HCF is 1, each prime factor can appear only in one or two of the three numbers, not in all the three.)
Therefore, n is definitely more than 8.

Ans: (b)
Quantity of petrol contained in X = 399 litre 
Quantity of diesel contained in Y = 532 litres
By taking the factors of 399 and 532 
we get: 399 = 1 × 3 × 7 × 19
532 = 1 × 2 × 2 × 7 × 19
So, the possible bottle sizes are 1 litre, 7 litres, 19 litres and 133 litres. 
Therefore, the number of possible bottle sizes is 4.

Ans: (a)
Option (a) is correct: The passage highlights the significance of quality education in imparting foundations skills, and its contribution to the knowledge economy through the lines "the advent of the knowledge economy poses new challenges, and one of the severe consequences of having an uneducated workforce will be our inability to keep pace with the global economy". Thus the statement aligns with the message of the passage on the significance of quality education. 
Option (b) is incorrect: This statement is not supported by the passage directly. The passage only talks about the challenges posed by the knowledge economy. It does not explicitly state that India is not focusing on or promoting a knowledge economy. 
Option (c) is incorrect: The lines, "Like one learns to walk before running, similarly one picks up advanced skills only after picking the basic foundational skills." and "Without a strong learning foundation at the primary level, there can be no improvement in higher education or skill development" clearly emphasize the importance of school education rather than the higher education. 
Option (d) is incorrect: This statement is beyond the scope of the passage, as the passage does not talk about the literacy and awareness of the parents anywhere.

Ans: (c)
Let the number of pens with A be the LCM of 2, 3, 4, 5, and 6 = 60
Then the number of pens with B = 60/2 = 30
The number of pens with C = 60/3 = 20
The number of pens with D = 60/4 = 15 (an odd number)
The number of pens with E = 60/5 = 12
The number of pens with F = 60/6 = 10
To ensure that all get an even number of pens, we need to double the number of pens bought by A, i.e. 60 × 2 = 120
So, total number of pens bought by X = 120 + 60 + 40 + 30 + 24 + 20 = 294

Ans: (b)
Joseph visits the club every 5th day.
Harsh visits the club every 24th day.
Sumit visits the club every 9th day.
The next time they will meet again will be the LCM of these time-periods.
LCM (5, 24, 9) = 360
So, all the three will meet 360 days after Sunday. 
Now, we need not count 360 days. 
Rather we will use the concept of odd days.
Odd number of days in 360 = Remainder when 360 is divided by 7 = 3
So, they will meet again on Sunday + 3 = Wednesday