Try Sample Questions with Detailed Explaination for SSC CHSL 2020, SSC CGL Tier I, SSC CGL Tier II and UPSC CDS 2020 Exam

Study the following questions carefully and choose the right answer:
1
The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case, is:
» Explain it
D
Given numbers are: 6, 9, 12, 15, 18
 
LCM of given numbers = 180
 
So, 180 + 2 = 182 is the number that leaves 2 as a remainder.

Hence, option D is correct.
 
2
The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be
» Explain it
A
Let two numbers are 98x and 98y. Then, 
 
Product of number = Product of HCF and LCM
 
98x × 98y = 98 × 2352
 
xy = 24
 
Let x = 8 and y = 3                 (As Co-prime factors of 24 be 8 and 3) 
 
Then, Sum of number = 98 × 8 + 98 × 3 = 98 (11) = 1078

Hence, option A is correct.
 
3
The LCM of two numbers is 2376 while their HCF is 33. If one of the numbers is 297, then the other number is
» Explain it
B
Given,

LCM of two numbers = 2376

HCF of two numbers = 33

One of the number = 297

∵    (HCF of two numbers) × (LCM of two numbers) = (First number) × (Second number)

     Second number =   33 × 2376  = 264
297

Hence, option B is correct.

4
The product of HCF and LCM of 18 and 15 is
» Explain it
D
HCF of 18 and 15 = 3
 
LCM of 18 and 15 = 90
 
∴    Product of HCF and LCM of both numbers = 3 × 90 = 270.

Hence, option D is correct,
 
5
Three planets revolve round the Sun once in 200, 250 and 300 days, respectively in their own orbits. When do they all come relatively to the same position as at a certain point of time in their orbits?
» Explain it
A
Given that, three planets revolves the Sun once in 200, 250 and 300 days, respectively in their own orbits.
 
∴     Required time = LCM of (200, 250 and 300) = 3000 days
 
Hence, after 3000 days they all come relatively to the same position as at a certain point of time in their orbits.

Hence, option A is correct.