Number System-Railway Maths Part V

Total Questions: 50

31. Find the value of D if 1216 - 32D = DDD is divisible by 8. [RRB NTPC 30/01/2021 (Morning)]

Correct Answer: (d) 8
Solution:

1216 - 32D = DDD
1216 is divisible by 8 so 32D should also be divisible by 8 then the result DDD will be divisible by 8.
For 32D, D should be equal to 8

32. A seven digit number 67843A2 is divisible by 11 where A is a single digit whole number. Find the value of A. [RRB NTPC 30/01/2021 (Morning)]

Correct Answer: (d) 8
Solution:

67843A2 is divisible by 11
Sum of odd place digits - the sum of even place digits = 0 or a multiple of 11 = 19 - (11 + A) = 8 - A = 0
So, A = 8

33. There are two numbers such that the big number is obtained by adding 5 to the other. If the total of the two numbers is 19, find the product of these numbers. [RRB NTPC 30/01/2021 (Evening)]

Correct Answer: (a) 84
Solution:

Let, small number = X and larger number = Y
ATQ, Y = X + 5 ⇒ Y -  X = 5-----(i)
X + Y = 19 (ii)
Solving the equation (i) & (ii)
We get the value of Y = 12 and X = 7
The product of these numbers
= XY = 12 × 7 = 84

34. A number is greater than 3 but less than 8, Also, it is greater than 6 but less than 10. The number is: [RRB NTPC 30/01/2021 (Evening)]

Correct Answer: (b) 7
Solution:

Let, number = x
A/Q
[3 < x < 8] and [6 < x < 10]
Only, [6 < x < 8] is possible
So that the number is 7

35. Find the least number by which 6250 should be multiplied, so that it becomes a perfect cube. [RRB NTPC 30/01/2021 (Evening)]

Correct Answer: (c) 20
Solution:

Factorization of 6250 = 2 × 5 × 5 × 5 × 5 × 5
When 6250 is multiplied by 2 × 2 × 5
then 6250 will be a perfect cube.
So, the required number = 2 × 2 × 5 = 20

36. In four consecutive prime numbers, the product of the last three is 7429 and that of the first three is 4199. The largest of these prime number is: [RRB NTPC 30/01/2021 (Evening)]

Correct Answer: (c) 23
Solution:
→ D/A = 23/13
So, the largest prime no. is 23.

37. How many factors of 2⁷ x 3³ x 5⁴ x 7 are even? [RRB NTPC 31/01/2021 (Morning)]

Correct Answer: (a) 280
Solution:

2⁷ × 3³ × 5⁴ × 7
Even number of factors =
7× (3 + 1)(4 + 1)(1 + 1)
= 7 × 4 × 5 × 2 = 280

38. The square root of 90 will lie between______.

Correct Answer: (a) 9 and 10
Solution:

9² = 81 and 10² = 100
And 90 lies between 81 and 100 so its square root must lie between 9 and 10.

39. The lowest value of x which makes 136/(x - 4) an integer is: [RRB NTPC 31/01/2021 (Morning)]

Correct Answer: (c)-132
Solution:

40. The sum of prime numbers between 50 and 60 is_____. [RRB NTPC 31/01/2021 (Morning)]

Correct Answer: (b) 112
Solution:

Prime numbers between 50 and 60 = 53, 59
Sum = 53 +59 = 112