Number System is one of the prominent topics for preparation of the quantitative aptitude for every competitive exam. Candidates should have basic knowledge of mathematical concepts, which will help the candidates in getting the good score. Safalta.com is providing some basis of Numbers followed by some sample questions to practice the concepts. Let's discuss, some basic definitions of the Number System, which are as follows:

**Number System—**The system of numeration employing the ten digits 0, 1, 2, ..... 9 is known as number system.

**Numeral— **As the name suggests, the group of digits denotes a number, which is called a numeral. As N = {1, 2, 3, 4, 5, 6,

7, 8, 9, 10, 11.......}

**Various Types of Numbers**

**(i) Natural Numbers—**Counting numbers are called as natural numbers. Also, The set of natural numbers is classified as ‘N’. Thus (N = 1, 2, 3,.....)

**(ii) Whole Numbers—**If zero (0) is included in the set of natural numbers then we get the set of whole numbers denoted as ‘W’l So, every natural number is a whole number. l 0 is the only whole number which is not a natural number.

**(iii) Integers—**All counting numbers and their negative including zero form a new set of numbers which are called as integers. The

set of integers denoted by I. Thus I = [.....– 4, –3, –2, –1, 0, 1, 2, 3, .....] is the set of integers.

**Some subset of integers**

**Positive Integers**—(1, 2, 3, .....) is the set of all positive integers.

**Negative Integers**—(–1, –2, –3, .....) is the set of all negative integers.

**Non-Positive and Non-Negative integers—**

The set (0, 1, 2, .....) is called the set of nonnegative integers. While (0, –1, –2, –3, .....)

represent the set of non-positive integers.

**(iv) Even Numbers—**The numbers which are divisible by 2 are called as even numbers.

Such as 2, 4, 6, 8, .....

**(v) Odd Numbers—**The numbers which are not divisible by 2 are called as odd numbers.

Such as 1, 3, 5, 7 .....

**(vi) Prime Numbers—**A number greater than 1 is called a Prime number if it has exactly two factors, namely 1 and itself. For example 2,

3, 5, 7, ..... are some of the prime numbers. 2 is the only even number which is prime. l If x number is not divisible by any of the

Prime number up to square root of that number then it is a Prime number.

**Sample Questions on Number System**

1. 4003–? – 1599 = 716

(A) 1598

(B) 1688

(C) 3120

(D) 1120

2. 9998 × 999 = ?

(A) 9997001

(B) 9988002

(C) 9987012

(D) 9898012

3. Two numbers are such that the ratio of their sum, difference and product is 11 : 1 : 90. Calculate the sum of the squares of the two numbers.

(A) 540

(B) 539

(C) 530

(D) 549

4. Find the largest number which divides 77, 147 and 252, leaving the same remainder is each case :

(A) 30

(B) 34

(C) 35

(D) 40

5. When a number is divided by 121, the remainder is 25. Find the remainder if the same number is

divided by 11 :

(A) 3

(B) 4

(C) 5

(D) 6

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- Location: India

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