# Number System Previous Year Questions PDF & Study Notes

Number System Previous Year Questions PDF & Study Notes: The number system is an important topic of Quantitative Aptitude for upcoming competitive exams like SSC, Railways, Banking, UPSC, State PCS, and other competitive exams. Generally, 3 to 6 marks are covered by the Number System chapter.

In this article, we are going to provide you Number System Previous Year Questions PDF asked in SSC and Railway exams. We are also sharing basic concepts, examples, class notes, short tricks & formulae of the Number System which will help you to score better on this topic. Number System Study Materials PDF With Practice Questions Worksheet is available here in Hindi & English.

# Number System Previous Year Questions PDF: Highlights Number System Previous Year Questions PDF & Study Notes

## Introduction to Number Systems

### Numbers

Number: Arithmetical value representing a particular quantity. The various types of numbers are Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers etc.

### Natural Numbers

Natural numbers(N) are positive numbers i.e. 1, 2, 3 ..and so on.

### Whole Numbers

Whole numbers (W) are 0, 1, 2,..and so on. Whole numbers are all Natural Numbers including ‘0’. Whole numbers do not include any fractions, negative numbers, or decimals.

### Integers

Integers are the numbers that include whole numbers along with negative numbers.

### Rational Numbers

A number ‘r’ is called a rational number if it can be written in the form p/q, where p and q are integers and q ≠ 0.

### Irrational Numbers

Any number that cannot be expressed in the form of p/q, where p and q are integers and q≠0, is an irrational number. Examples: √2, 1.010024563…, e, π

### Real Numbers

Any number which can be represented on the number line is a Real Number(R). It includes both rational and irrational numbers. Every point on the number line represents a unique real number.

### Imaginary Numbers

Imaginary numbers are those numbers which we can just imagine but cannot physically perceive.

For Example √-1, √-3, etc, √-1 is represented by i, Square Root of all imaginary number is imaginary.

### Complex Number

The combination of Real and Imaginary numbers is called complex numbers. Example: (2+5i) , (1+3i) etc.

### Even number

An integer that is “evenly divisible” by two. Example 2,4,8,….. etc.

### Odd number

All the Natural numbers which are not Even numbers. Example 1, 3, 19, 21,….. etc.

### Prime number

An integer is greater than 1 which is only divisible by 1 and the number itself are called prime numbers. Example 2,3,5,7,11,13,….etc

### Co-Prime Number

If the only positive integer (factor) that divides both of them is 1. Examples:- 13 and 14 are co-prime, being commonly divisible only by 1, while 22 and 24 are not co-prime because they are both divisible by 2.

### Composite Number

All the natural numbers greater than 1 which are divisible by at least one more number other than 1 and the number itself are called composite numbers. Example: 6 can be divided exactly by 3 or 2 (as well as 1 and 6), so 6 is a composite number. But 7 cannot be divided exactly (except by 1 and 7), so is NOT a composite number (it is a prime number).

### Place value

The place or position of a digit in a number is called its place value. Example: Place value of 2 in 4289 is 200.

### Face value

The real value of any digit in a certain number is called its face value.

For example, the face value of 2 in 7246 is 2.

### Number System Short Notes

1. Number 1 is neither divisible nor prime.
2. Two consecutive odd prime numbers are called prime pair.
3. All natural numbers are whole, rational, integer and real.
4. All whole numbers are rational Integer and real.
5. All whole numbers are rational and real.
6. All rational numbers includes the integers, since every integer can be written as a fraction with denominator 1. Example (7/1) not only 7
7. All whole numbers, rational and irrational numbers are real.
8. Natural (including Prime, Composite, even or odd) numbers and whole numbers are never negative.
9. Any Prime Number can never be a Composite Number.
10. Fractions are rational.
11. All prime number except 2 are odd. Or 2 is the only even prime number.
12. Zero (0) is neither negative nor positive number.
13. If a is any number then, if a divides zero, result will be zero. If 0 divides a, then result will be infinite or not defined or undetermined i.e.
0/a =0, but a/0 =∞ (infinite)
where a is real number.
14. The sum and the product of two rational number is always a rational numbers.
15. The product or the sum of a rational number and irrational number is always an irrational number.
16. Pie (π) is an irrational number.
17. There can be infinite number of rational or irrational numbers between two rational numbers or two irrational numbers.
18. Decimal indication of an irrational number is infinite coming. as−√3,√2as−3,2The square of an even is even and the square of an odd number is odd.

## Number System Formulas

1. 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
2. (12 + 22 + 32 + ….. + n2) = n ( n + 1 ) (2n + 1) / 6
3. (13 + 23 + 33 + ….. + n3) = (n(n + 1)/ 2)2
4. Sum of first n odd numbers = n2
5. Sum of first n even numbers = n (n + 1)
6. (a + b)(a – b) = (a2 – b2)
7. (a + b)2 = (a2 + b2 + 2ab)
8. (a – b)2 = (a2 + b2 – 2ab)
9. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
10. (a3 + b3) = (a + b)(a2 – ab + b2)
11. (a3 – b3) = (a – b)(a2 + ab + b2)
12. (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac)
13. When a + b + c = 0, then a3 + b3 + c3 = 3abc
14. (a + b)n = an + (nC1)an-1b + (nC2)an-2b2 + … + (nCn-1)abn-1 + bn

## Shortcuts for number divisibility check

1. A number is divisible by 2 if its unit’s digit is any of 0, 2, 4, 6, 8.
2. A number is divisible by 3 if the sum of its digits is divisible by 3.
3. A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
4. A number is divisible by 5 if its unit’s digit is either 0 or 5.
5. A number is divisible by 6 if it is divisible by both 2 and 3.
6. A number is divisible by 8 if the number formed by the last three digits of the given number is divisible by 8.
7. A number is divisible by 9 if the sum of its digits is divisible by 9.
8. A number is divisible by 10 if it ends with 0.
9. A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a number divisible by 11.
10. A number is divisible by 12 if it is divisible by both 4 and 3.
11. A number is divisible by 14 if it is divisible by 2 as well as 7.
12. Two numbers are said to be co-prime if their H.C.F. is 1. To find if a number, say y is divisible by x, find m and n such that m * n = x and m and n are co-prime numbers. If y is divisible by both m and n then it is divisible by x.

## Number System Question And Answers PDF

Here we have shared some questions and answers of the Number System chapter. You can note down them in your notebook:

Q1. In a two-digit number, the digit at the unit’s place is 1 less than twice the digit at the ten’s place. If the digits at unit’s and ten’s place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is

(a) 23
(b) 35
(c) 47
(d) 59

Q2. The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction.

(a) 3/7
(b) 4/8
(c) 2/7
(d) 3/8

Q3. The denominator of a fraction is 3 more than its numerator. If the numerator is increased by 7 and the denominator is decreased by 2, we obtain 2. The sum of the numerator and denominator of the fraction is

(a) 5
(b) 13
(c) 17
(d) 19

Q4. 47 is added to the product of 71 and an unknown number. The new number is divisible by 7 giving the quotient 98. The unknown number is a multiple of

(a) 2
(b) 5
(c) 7
(d) 3

Q5. A fraction becomes 1/3 when 1 is subtracted from both the numerator and the denominator. The same fraction becomes 1/2 when 1 is added to both the numerator and the denominator. The sum of the numerator and denominator of the fraction is

(a) 10
(b) 18
(c) 7
(d) 16

Q6. A number whose one-fifth part increased by 4 is equal to its one-fourth part diminished by 10, is

(a) 260
(b) 280
(c) 240
(d) 270

Q7. A girl was asked to multiply a number by 7/8, instead, she divided the number by 7/8 and got the result 15 more than the correct result. The sum of the digits of the number was

(a) 4
(b) 8
(c) 6
(d) 11

Q8. The product of two numbers is 120 and the sum of their squares is 289. The sum of the two numbers is

(a) 23
(b) 7
(c) 13
(d) 169

Q9. A student was asked to multiply a number by 3/2 but he divided that number by 3/2. His result was 10 less than the correct answer. The number was

(a) 10
(b) 12
(c) 15
(d) 20

Q10. The number of three consecutive numbers is 87. The middle number is

(a) 27
(b) 29
(c) 30
(d) 28

Q11. A man ate 100 grapes in 5 days. Each day, he ate 6 more grapes than those he ate on the earlier day. How many grapes did he eat on the first day?

(a) 8
(b) 12
(c) 54
(d) 76

Q12. A farmer divides his herd of n cows among his four sons, so that the first son gets one-half that herd, the second son gets one-fourth, the third son gets one-fifth and the fourth son gets 7 cows. The value of n is

(a) 80
(b) 100
(c) 140
(d) 180

Q13. If the difference between the reciprocal of a positive proper fraction and the fraction itself be 9/20, then the fraction is

(a) 3/5
(b) 3/10
(c) 4/5
(d) 5/7

Q14. A tin of oil was 4/5 full. When 6 bottles of oil were taken out and 4 bottles of oil were poured into it, it was 3/4 full. How many bottles of oil can the tin contain?

(a) 10
(b) 20
(c) 30
(d) 40

Q15. 1/10 of a rod is colored red, 1/20 orange, 1/30 yellow, 1/40 green, 1/50 blue, 1/60 black, and the rest is violet. If the length of the violent portion of the rod is 12.08 m, then the length of the rod is

(a) 16 m
(b) 18 m
(c) 20 m
(d) 30 m

## Number System Study Materials PDF

### Download Number System Study Materials PDF

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## Frequently Asked Questions – FAQs

Q. What is number system example?
Ans. – A system for representing (that is expressing or writing) numbers of a certain type. Example: There are several systems for representing the counting numbers. … The usual “base ten” or “decimal” system: 1, 2, 3, … , 10, 11, 12, … 99, 100.

Q. What is basic number system?
Ans. – A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. A base can be any whole number greater than 0.

Q. Is the number system important for bank exams?
Ans. – Number system has a special place in the quantitative aptitude section of Banking and SSC exams.

Q. What will be the unit digit of 27?
Ans. – The unit digit of base 27 is 7, i.e l = 7.