RRB ALP Number System Questions With Solutions, Download PDF

RRB Number System Basics 

Topic

Concept

Examples

Natural Numbers

Counting numbers starting from 1

1, 2, 3, 4… (0 not included)

Whole Numbers

All natural numbers, including 0

0, 1, 2, 3…

Integers

Positive & negative whole numbers including 0

…-3, -2, -1, 0, 1, 2, 3…

Even Numbers

Divisible by 2

-6, -4, 0, 2, 4…

Odd Numbers

Not divisible by 2

-5, -3, 1, 3, 5…

Prime Numbers

Exactly two factors: 1 and itself

2, 3, 5, 7, 11… 

Composite Numbers

Numbers with factors other than 1 and itself

4, 6, 8, 9…

Co-Prime Numbers

Two numbers with no common factor other than 1

(2,3), (6,35)

Rational Numbers

Numbers expressed as p/q, q ≠ 0

2, 3/7, 2.5

Irrational Numbers

Cannot be expressed as p/q; non-terminating, non-repeating

√2, π

Real Numbers

All numbers on the number line

Includes rational & irrational numbers

Digits

Symbols 0–9 are used to form numbers

0,1,2…9

Place Value

Value of a digit based on its position

In 324: 3 → 300, 2 → 20, 4 → 4

Face Value

Value of the digit itself

In 324: 3 → 3

Proper Fraction

Numerator < Denominator

1/2, 3/7

Improper Fraction

Numerator ≥ Denominator

5/4, 13/2

Mixed Fraction

Whole number + proper fraction

1 ¼, 4 1/6

LCM

Smallest number divisible by given numbers

LCM of 4 & 6 = 12

HCF

The largest number that divides the given numbers exactly

HCF of 12 & 18 = 6

Divisibility Rules

Shortcuts to check divisibility

2: last digit 0,2,4…; 

3: sum of digits divisible by 3; 

5: last digit 0 or 5

Number System Tricks For Candidates

Trick 

Description

Example

Solution / Notes

Trick-1

Remainder of (x+a)n(x + a)^n when divided by xx is the same as the remainder of ana^n.

What is the remainder when 1910019^{100} is divided by 20?

Remainder in 19100mod  20=(−1)100mod  20=119^{100} \mod 20 = (-1)^{100} \mod 20 = 1

Trick-2

Remainder when A×B×CA \times B \times C is divided by nn is the same as remainder when Amod  n×Bmod  n×Cmod  nA \mod n \times B \mod n \times C \mod n is divided by nn.

What is the remainder when 56×58×9656 \times 58 \times 96 is divided by 13?

Remainder = (4×6×5)mod  13=120mod  13=3(4 \times 6 \times 5) \mod 13 = 120 \mod 13 = 3

RRB ALP Number Series Questions

SNo.

Question

Options

Solutions

1

How many whole numbers are there between 244 and 332 which are exactly divisible by 7?

(a) 15 

(b) 23

 (c) 8 

(d) 13

(d)

2

If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be?

(a) 2

 (b) 3 

(c) 4 

(d) 5

(a)

3

If x and y are two digits of the number 653xy such that this number is divisible by 80, then x + y =?

(a) 2 

(b) 3 

(c) 4

 (d) 5

(a)

4

In a division sum, the divisor is 5 times the quotient and 4 times the remainder. What is the dividend, if the remainder is 5?

(a) 80 

(b) 85 

(c) 75 

(d) 104

(b)

5

How many numbers from 1 to 100 are there? 

Which is exactly divisible by 4 but also has 4 as a digit?

(a) 21

 (b) 20

 (c) 7 

(d) 10

(c)

6

The minimum number that should be added to 2351 so that the number is divisible by 7.

(a) 1 

(b) 6 

(c) 5 

(d) 8

(a)

7

The minimum number that should be subtracted from 8774 so that the number is divisible by 13.

(a) 1 

(b) 12

 (c) 5 

(d) 8

(b)

8

On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the sum of the digits of the divisor.

(a) 12 

(b) 19 

(c) 17 

(d) 21

(c)

9

When 121012 is divided by 12, the remainder is

(a) 0

 (b) 2 

(c) 3 

(d) 4

(d)

10

The difference in the place values of 3 used at two places in the number 934530 is

(a) 29970

 (b) 30070

(c) 29570 

(d) 29990

(a)

11

Which of the following is a divisor of 53 – 33?

(a) 2 

(b) 8 

(c) 4 

(d) None of these

(a)

12

What is the common factor of (1719 + 1919) and (1717 + 1917)?

(a) (19 – 17) 

(b) (1717 + 1917) 

(c) (1719 + 1919) 

(d) (17 + 19)

(d)

13

Arrange the given ratios in descending order: (i) 7:15, (ii) 15:23, (iii) 17:25, (iv) 21:39

(a) (iii) > (i) > (ii) > (iv) 

(b) (i) > (iv) > (iii) > (ii) 

(c) (iii) > (ii) > (iv) > (i) 

(d) (iv) > (i) > (ii) > (iii)

(c)

14

What is the sum of the greatest six-digit number and the lowest 5-digit number?

(a) 199999 

(b) 109999 

(c) 1009999 

(d) 919999

(c)

15

Find the sum of the smallest and the greatest 3-digit numbers formed by using the digits 1, 2, 3, 4 without any repetition of digits.

(a) 1099 

(b) 544 

(c) 534

 (d) 555

(d)

16

The least number by which 12500 should be divided to get a perfect square is

(a) 3 

(b) 5 

(c) 15

 (d) 10

(b)

17

Which of these numbers, 6400, 125, 9261 and 4913, is not a perfect cube?

(a) 6400

 (b) 125 

(c) 9261

 (d) 4913

(a)

18

Statement I: All natural numbers are rational numbers.

 Statement-II: 1 is the smallest prime number. Choose the correct answer.

(a) Both correct 

(b) Both incorrect

 (c) Statement I correct, Statement II incorrect 

(d) Statement-I incorrect, Statement II correct

(c)

19

What is the value of the expression 1 – 2 + 3 – 4 + 5 – 6 ... up to 100 terms?

(a) –50

 (b) –55 

(c) –49

 (d) –60

(a)

20

What is the sum of all three-digit numbers which are divisible by 15?

(a) 41200

 (b) 36825

(c) 32850 

(d) 28750

(c)