Number System-Railway Maths Part V

Total Questions: 50

11. While solving a mathematical problem, Atul squared the initial number and then subtracted 15 from it. Pratul first subtracted 15 from the initial number and then squared the difference. If both obtained the same answer, what was the initial number? [RRB NTPC 23/01/2021 (Evening)]

Correct Answer: (a) 8
Solution:

Let the initial number = x
A/Q, x² 15 = (x - 15)²
⇒ x²- 15 = x² + 225 - 30x
⇒ 30x = 240 ⇒ x = 8

12. The sum of first 'n' natural numbers is. [RRB NTPC 23/01/2021 (Evening)]

Correct Answer: (a) n(n+1)/2
Solution:

The sum of first 'n' natural numbers = n(n + 1)/2

13. If a positive number N, when divided by 5 leaves a remainder 3, then the unit's place digit of N is: [RRB NTPC 25/01/2021 (Morning)]

Correct Answer: (c) 3 or 8
Solution:

A / Q
N ÷ 5 = 3
Example, 8 ÷ 5 = 3, 13 ÷ 5 = 3

14. Instead of multiplying a number by 2, Rahul divided it by 2 and got the answer as 2. What should be the actual answer? [RRB NTPC 25/01/2021 (Morning)]

Correct Answer: (c) 8
Solution:

Let number = x
A/Q, ⇒ x/2 = 2 ⇒ x = 4
actual answer = 2x = 2 × 4 = 8

15. How many numbers are there between 200 to 1000 that are completely divisible by 7? [RRB NTPC 25/01/2021 (Morning)]

Correct Answer: (c) 114
Solution:

Difference between 1000 and 200 = 800
800 is divided by 7 then we get 114 as complete value and the remainder is 2 so that 114 numbers between 200 to 1000 are completely divisible by 7.

16. 41⁴³ +43⁴³) is is divisible by which of the following? [RRB NTPC 25/01/2021 (Evening)]

Correct Answer: (a) 84
Solution:

We know that when 'm' is an odd number (xᵐ + aᵐ) is divisible by (x + a).
Each one is divisible by (41 + 43).
So Common factor = (41 + 43) = 84.

17. Find the difference between the place value and face value of 6 in 516372? [RRB NTPC 25/01/2021 (Evening)]

Correct Answer: (a) 5994
Solution:

In 516372, face value of 6 = 6 and place value of 6 = 6000
Difference between the place value and face value of 6 in 516372 = 6000 - 6 = 5994

18. The difference between the greatest and the smallest number of six digit is: [RRB NTPC 27/01/2021 (Morning)]

Correct Answer: (b) 899999
Solution:

Greatest six digits number = 999999
Smallest six digits number = 100000
Difference between greatest and smallest = 999999 - 100000 = 899999

19. The largest number of four digits which, when divided by 6, 12 and 18 leaves the same remainder 5 in each case is: [RRB NTPC 27/01/2021 (Morning)]

Correct Answer: (a) 9977
Solution:

The smallest number divisible by 6, 12 and 18 → LCM(6,12,18) = 36
when largest 4-digit number is divided by 36 it gives quotient 277 and Remainder 27
So, the number is 9999 - 27 = 9972
ATQ,
The required number is 9972 + 5 = 9977

20. How many numbers lie between the largest three digit number and the largest four digit number which are divisible by 5? [RRB NTPC 27/01/2021 (Evening)]

Correct Answer: (c) 1800
Solution:

Largest 3-digit number = 999
Largest 4-digit number = 9999
Difference = 9999-999 = 9000
Numbers divisible by 5 = 9000/5 = 1800