Question: 6 -

What is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22 ?

1436

1216

1286

1386

Answer:

1386

Solution:

LCM of 12, 14, 18 and 22 = 2772

Hence the least number which will be exactly divisible by 12, 14, 18 and 22 = 2772

2772 ÷ 2 = 1386

1386 is the number which when doubled, we get 2772 

Hence, 1386 is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22.

Question: 7 -

A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they again at the starting point ?

36m 22s

46m  22 s

36m 12s

46m 12s

Answer:

46m 12s

Solution:

LCM of 252, 308 and 198 = 2772

Hence they all will be again at the starting point after 2772 seconds.
i.e., after 46 minutes 12 seconds

Question: 8 -

Which of the following integers has the most number of divisors?

101

176

99

182

Answer:

176

Solution:

99 = 1 × 3 × 3 × 11
=> Divisors of 99 are 1, 3, 11, 9, 33 and 99
101 = 1 × 101
=> Divisors of 101 are 1 and 101
182 = 1 × 2 × 7 × 13
=> Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182
176 = 1 × 2 × 2 × 2 × 2 × 11
=> Divisors of 176 are 1, 2, 11, 4, 22, 8, 44, 16, 88, 176
Hence 176 has most number of divisors.

Question: 9 -

What is the greatest possible length which can be used to measure exactly the lengths 8 m, 4 m 20 cm and 12 m 20 cm?

30 cm

20 cm

25 cm

10 cm

Answer:

20 cm

Solution:

Required length 
= HCF of 800 cm, 420 cm, 1220 cm 
= 20 cm

Question: 10 -

The least number which should be added to 28523 so that, the sum is exactly divisible by 3, 5, 7 and 8 is

32

42

37

41

Answer:

37

Solution:

LCM of 3, 5, 7 and 8 = 840

28523 ÷ 840 = 33 remainder = 803

Hence the least number which should be added = 840 - 803 = 37