Greetings !

Welcome to the Quant Section. You have come to the right place to learn Quants. Our Quants lessons will cover everything from basic numbers to complex mind boggling problems. So let us get started.!

Quants cannot exist without numbers. So let us begin by learning all about numbers. This section will cover the following topics:

## TYPES OF NUMBERS

Numbers are basically classified into two types:

• Rational numbers
• Irrational numbers

### RATIONAL NUMBERS

Rational numbers have a finite decimal value (the value could even be 0) or infinite values with a finite repeating pattern.

## Examples

• The value of the fraction ½ is 0.5 which is a finite decimal value. So, ½ is a rational number.

### IRRATIONAL NUMBERS

If the decimal part of the fractional number goes like a never ending stream of random digits without a repeating pattern, it is called an irrational number.

## Examples

• pi (22/7). The value of the fractional number 22/7 is 3.1415926535

This neither has an end nor has a repeating pattern. The exact value of this number can never be found. So, it is approximated by considering the first two decimal digits to 3.14.

## CLASSIFICATION OF RATIONAL NUMBERS

Non-fractional numbers are classified into five basic types:

1. Integers: Integers include all the non- fractional numbers (numbers that don’t have a decimal point). An integer can either be positive or negative.

Example: 2, -34, -75, 0, 5.

1. Natural Numbers: All the positive integers from 1 to infinity are natural numbers.

Example: 1, 2, 3, 4, 5……

1. Whole Numbers: All the positive integers from 0 to infinity are whole numbers.

Example: 0, 1, 2, 3, 4….

1. Even Numbers: All the integers that end with one of these: 0, 2, 4, 6, 8.

Example: -2, 40, -68, 274.

1. Odd numbers: All the integers that end with one of these: 1, 3, 5, 7, 9.

Example: 1, -3, 39, -47, 393.

1. Prime number: any integer that cannot produce a non-fractional quotient when divided by any number other than 1 or the number itself

Example: -2, 5,-7, 11.

1. Composite numbers: All integers except prime numbers are composite numbers

Example: 6, 8, 9, 12.

Shakuntala Devi

## PROCEDURES AND WORKED EXAMPLES

How to check if a number is a prime number?

Procedure:

Suppose A is the given number.

• Step 1: Find the perfect square number that is nearest to and greater than A. Let this number be K.
• Step 2: Check if A divisibleby any prime number less than the square root of K.

If yes A is not a prime number. If not, A is prime number.

Worked Examples:

1. Find if 337 is a prime number or not?

Step 1: The nearest perfect square number of 337 is 361.

Step 2: the square root of 361 is 19. The Prime numbers less than 19 are 2, 3, 5, 7, 11, 13, and 17. 337 is not divisible by any of them.

Therefore 337 is a prime number.

1. Find if 48 is a prime number or not?

Step 1: The nearest perfect square number of 48 is 49.

Step 2: the square root of 49 is 7. The Prime numbers less than 19 are 2, 3, and 5. 48 is divisible by 2 and 3.

Therefore 48 is not a prime number.

## DIVISIBILITY TESTS

Divisibility tests are one of the most important topics in quantitative aptitude. Fortunately, this topic is simple. These tests become a piece of cake for any big number if you get to know the divisibility rules of a few particular numbers. Let us start with the simplest ones first.

A Number is divisible byDivisibleNot Divisible
2 - if the last digit is even (0,2,4,6,8)188191
3 - if the sum of the digits is divisible by 3111431
4 - if the last two digits form a number divisible by 4123481234
5 - if the last digit is 0 or 519801588
6 - if the number is divisible by both 2 and 32462
8 - if the number formed by the last three digits will be divisible by 820643111
9 - if the sum of the digits of the number is divisible by 9810521
10 - if the last digit is 014503828
11 - if the difference between the sum of the alternate digits of the number should be 0 or 1123654594
12 - If the number is divisible by both 3 and 4, it is also divisible by 12.76829658

#### EXAMPLE

• Find out whether 54766987758726635 is divisible by 11.

Sol:

4   7   6   6   9   8   7   7   5   8   7     6   6   3   5

Adding all the indicated marks we will get a sum of  54 and sum of all the other alternative places is 47

So the now the difference will  be 54 – 47 = 7 so when you divide 54766987758726635 by 11 then the remainder would 7. So to make 54766987758726635 to be divisible by 11 we should either subtract it with 7 or add 4.

Thus, in this section we have studied the concepts regarding number systems and performing operations using it. In the next section, we will study about the concepts regarding L.C.M and H.C.F and solve some examples.