Number System-Railway Maths

Total Questions: 50

1. A number, when divided by the sum of 335 and 265, gives three times the difference between 335 and 265 as the quotient and 35 as the remainder. What is that number? [Group D 22/08/2022 (Morning)]

Correct Answer: (a) 126035
Solution:

Difference = 335 - 265 = 70
According to the question,
Quotient = 70 × 3 = 210,
Divisor = 335 + 265 = 600,
remainder = 35 We know that,
Dividend = quotient × divisor + remainder Therefore,
Number = 210 × 600 + 35 = 126035

2. If the 8 digit number 3x5479y4 is divisible by 88 and the 8-digit number 425139z2 is divisible by 9, then what is the greatest possible value of (3x + 2y - z)? [Group D 09/09/2022 (Evening)]

Correct Answer: (b) 33
Solution:

If 3x5479y4 is divisible by 88 it must be divisible 11 and 8
Divisibility rule for 8 → if last three digit number of any number divisible by 8 it will be divisible by 8
For 3×5479y 4 ⇒ Y=0,4,8  (for greatest value we take Y = 8 )

Divisibility rule for 11 → difference between sum of digit of odd place and sum of digit of even place should be 0 or multiple of 11
3+5+7+y(x+4+9+4) = o or 11
15+y-(x+17) = 0 ⇒ Y= 0,4,8

Divisibility rule for 9 → sum of all digit is divisible by 9,
425139z2 →4+2+5+1+3+9+z+2 = 26+z
=Z=1=(3x+2y-z) = (3×6+2×8-1) = 33

3. By adding 2 to the numerator and 5 to the denominator of a fraction, the fraction obtained is equal to 1/2 Also, the fraction obtained by subtracting 2 from both the numerator and the denominator is equal to 1/3. Find the Fraction. [Group D 24/08/2022 (Afternoon)]

Correct Answer: (d) 3/5
Solution:

Let the numerator be x and denominator be y

Subtracting eq, (2) from (1)
x = 3 and y = 5 , Required fraction = x/y = 3/5

4. Four prime numbers are taken in ascending order. The product of the first three prime numbers is 1771 and the sum of the last two prime numbers is 82. What is the product of the last two prime numbers? [Group D 25/08/2022 (Afternoon)]

Correct Answer: (d) 1357
Solution:

1771 = 7 × 11 × 23
Sum of last two prime numbers= 82
Fourth prime number = 82 - 23 = 59

5. Find the sum of the prime factors of 9⁶ × 12⁴ × 7⁷? [Group D 26/08/2022 (Evening)]

Correct Answer: (b) 12
Solution:

9⁶ × 12⁴ × 7⁷ = (3 × 3)⁶ × (2 × 2 × 3)⁴ × 7⁷
Hence, sum of the prime factors = 2 + 3 + 7 = 12

6. If the 5-digit number 688xy is divisible by 11 and 21, then what is the value of (8x - 3y + xy)? [Group D 12/09/2022 (Morning)]

Correct Answer: (b) 24
Solution:

7. From the numbers 367, 489, 514, 632 and 728, if 2 is added to the first digit of each of the numbers, how many new numbers will be thus formed whose sum of all digits will be divisible by three? [Group D 17/09/2022 (Morning)]

(Example-697 First digit-6, second digit-9 and third digit-7)

Correct Answer: (d) Two
Solution:

Divisibility of 3 = Sum of digits should be divisible by 3.
3 + 2 = 5, then new number = 567 (divisible by 3)
4 + 2 = 6, then new number = 689 (not divisible by 3)
5 + 2 = 7, then new number = 714 (divisible by 3)
6 + 2 = 8, then new number = 832 (not divisible by 3)
7 + 2 = 9, then new number = 928 (not divisible by 3)
So, there are two numbers which will be divisible by 3.

8. The product of two consecutive positive integers is 552. If the smaller of these two integers is represented by x, which of the options below will correspond to the equation for finding out the value of x ? [Group D 20/09/2022 (Afternoon)]

Correct Answer: (c) x² + x − 552 = 0
Solution:

Smaller positive integers is x and the larger positive integer = x+1
⇒ x( x + 1) = 552 ⇒ x² + x - 552 = 0

9. If 600 = p³× q²× r²× s¹ where p, q, r and s are consecutive prime numbers in ascending order, then what is the value of (3p + 2q - r + s) ? [Group D 11/10/2022 (Afternoon)]

Correct Answer: (c) 14
Solution:

12600 = p³ × q² × r² × s¹
12600 = 7¹ × 3² × 2³ × 5²
P = 2, Q = 3, R = 5, S = 7
(3p + 2q - r + s) = 3(2) + 2(3) - 5 + 7 = 14

10. Arushi was to multiply a number by 2.4, but instead multiplied by 4.2. If the product she obtained was 65.1, then what is the correct product that she should have got? [NTPC CBT II Level 5 (12/06/2022) Shift 1]

Correct Answer: (c) 37.20
Solution:

Let the number = x
Actual result = 2.4x
Mistaken result = 4.2x
As per question,
4.2x = 65.1 ⇒ x = 15.5
So, Actual number
= 2.4x = 2.4 x 15.5 = 37.2