Number System-Railway Maths Part II

Total Questions: 50

1. If 4 + 4ⁿ ⁺ ⁵ = 260 , then find the value of 5ⁿ ⁺ ³ [Group D 26/08/2022 (Afternoon)]

Correct Answer: (a) 25
Solution:

4 + 4ⁿ⁺⁵ = 260
4ⁿ⁺⁵ = 256 = 4⁴
On comparing powers, we get: n+5 = 4
⇒ n = -1 ⇒ 5⁻¹ ⁺ ³ = 5² = 25

2. The prime factorisation of the number 266805 is: [Group D 29/08/2022 (Morning)]

Correct Answer: (b) 3² × 5 × 7² × 11²
Solution:

3. When a number is divided by a divisor, the remainder is 16. When twice the original number is divided by the same divisor, the remainder is 3. Find the value of that divisor. [Group D 30/08/2022 (Afternoon)]

Correct Answer: (a) 29
Solution:

Number (N) = DQ + R , where D is the divisor, Q is quotient and R is the remainder
So, N = DQ + 16
2N = 2DQ + 32 or 29 +3
Now, the divisor is either 29 itself or the factor of 29 which is more than 3.
On checking the options we get the least possible value of D = 29

4. The sum of two numbers is 27. Five times one number is equal to 4 times the other. The smaller of the two numbers is: [Group D 30/08/2022 (Afternoon)]

Correct Answer: (b) 12
Solution:

Let the first number be x then second number = (27 - x)
5x = 4(27 - x)
⇒ 5x + 4x =108 ⇒ 9x=108 ⇒ x=12
Smaller number = 12

5. The sum of a two-digit number and the number obtained by reversing the digits is 99. If the digits of the number differ by 5, then the two-digit number can be: [Group D 01/09/2022 (Morning)]

Correct Answer: (a) 27
Solution:

Let the unit digit number be x, and the digit at ten's place be y.
10y + x + 10x + y = 99
⇒ 11x + 11y = 99  ⇒ x + y = 9.........(1)
x - y =5.........(2 )
By solving eq, (1) and (2),
we get x = 7 and y = 2
Hence, the required number = 27

6. The sum of a number, its half, its 1/3 and 27, is 71. Find the number. [Group D 01/09/2022 (Afternoon)]

Correct Answer: (b) 24
Solution:

7. Three numbers x ≤ y ≤ z which are co-prime to each other are such that the product of the first two numbers is 143 and that of the last two numbers is 195. The sum of the three numbers is______. [Group D 01/09/2022 (Afternoon)]

Correct Answer: (b) 39
Solution:

A × B = 143 ⇒ 11 × 13
Let A = 11 So , B = 13 ,
B × C = 195 So , C = 15
11, 13 and 15 are co- prime to each other
The sum = 11 + 13 + 15 = 39

8. Find the smallest number that can be added to 467851 to make the sum a perfect square. [Group D 01/09/2022 (Afternoon)]

Correct Answer: (a) 5
Solution:

By taking option A 467851+5 = 467856
Which is square of 684

9. The sum of two positive numbers is 45 and their difference is 19. What are the numbers? [Group D 01/09/2022 (Evening)]

Correct Answer: (a) 32, 13
Solution:

Let the numbers are a and b.
a + b =45........(1) and a - b = 19........(2)
on solving eq,(1) and (2), we get a = 32 and b = 13

10. Find the greatest number by which when the numbers 158 and 215 are divided, it leaves remainders 4 and 5, respectively. [Group D 02/09/2022 (Morning)]

Correct Answer: (d) 14
Solution:

158 - 4 = 154 and 215 - 5 = 210
H.C.F of 154 and 210 = 14