MBA Quantitative Aptitude Basic Concepts – Number System

In order to prepare for the Quantitative aptitude section of MBA entrance, you must learn the basic concepts of Number system chapter at jagranjosh.com. These concepts would aid you in your preparation for CAT, CMAT, MAT, XAT, IIFT, SNAP etc.

Oct 30, 2020, 16:22 IST

Number System covers various types of numbers viz. natural numbers, whole numbers, integers, rational and irrational numbers which constitutes the Real number system.

VARIOUS TYPES OF NUMBERS

1. Natural Numbers: All the positive numbers 1, 2, 3 ,.., etc. that are used in counting are called Natural numbers. Types of Natural Numbers based on divisibility:

Prime Number: A natural number larger than unity is a prime number, if it does not have other divisors except for itself and unity.

Examples for Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, etc.

Note: Unity, i.e. 1 is not prime number.

Composite Numbers: Any number other than 1, which is not a prime number, is called a composite number.

Examples for composite numbers are 4, 6, 8, 9, 10, 14, 15, etc.

2. Whole Numbers: All counting numbers and 0, form the set of whole numbers.

For example: 0, 1, 2, 3…, etc. are whole numbers.

3. Integers: All counting numbers, Zero and negative of counting numbers, form the set of integers.

Therefore,…-3, -2, -1, 0, 1, 2, 3,.. are all integers.

4. Rational Numbers

A number which can be expressed in the form p/q, where p and q are integers and q≠0, is called a rational number.

For example 2 can be written as 2/1, therefore 2 is also a rational number.

5. Irrational Numbers

Numbers which are not rational but can be represented by points on the number line called irrational numbers.

6. Even and Odd Numbers

Numbers divisible by 2 are called even numbers whereas numbers that are not divisible by 2 are called odd numbers.

For example 2, 4, 6, etc are even numbers and 3, 5, 7, etc are odd numbers.

The following rules related to Even and Odd numbers are important:

Read & Understand Practical Application of Number System

Factors and Co-Primes

Factorization Method for LCM and HCF

LCM: Here we can write all the given numbers in their prime factorization format.

For example: 15 = 3 X 5

18 = 3² X 2

24 = 2³ X 3

Now take all primes number the given numbers and write their maximum powers. So LCM of 15, 18, 24 =2³ X 3²X 5 = 360

HCF: 12 = 2² X 3

18 = 3² X 2

Now, HCF of 12 and 18 = 3 X 2 = 6

Take Practice Test for Number System – Factors

TESTS OF DIVISIBILITY OF NUMBERS

Divisible by 2: if its unit digit of any of 0, 2, 4, 6, 8.
Divisibility by 3: When the sum of its digits is divisible by 3.
Divisibility by 9: When the sum of its digits is divisible by 9.
Divisibility by 4: if the sum of its last two digits is divisible by 4.
Divisibility by 8: If the number formed by hundred’s ten’s and unit’s digit of the given number is divisible by 8.
Divisibility by 10: When its unit digit is Zero.
Divisibility by 5: When its unit digit is Zero or five.
Divisibility by 11: if the difference between the sum of its digits at odd places and the sum of its digits at even places is either o0 or a number divisible by 11.

Take Practice Test for Remainders Concept in Number System

ALGEBRAIC FORMULAE

(a + b)² = a² + 2ab+ b²
(a - b)² = a² - 2ab+ b²
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)
(a + b + c)² = a² + b2 + c² +2ab+2bc +2ca
(a + b + c)³ = a³ + b³ + c³+ 3a² b + 3a² c + 3b² c + 3b² a + 3c² a + 3c² b + 6abc
a² - b² = (a + b)(a – b)
a³ – b³ = (a – b) (a² + ab + b²)
a³ + b³ = (a + b) (a² - ab + b²)
(a + b)² + (a - b)² = 4ab
(a + b)² - (a - b)² = 2(a² + b²)
If a + b +c =0, then a³ + b³ + c³ = 3abc