REASONING AND APTITUDE

MADE EASY GATE HANDWRITTEN CLASSROOM NOTES

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Reasoning and Aptitude Made Easy GATE Handwritten Notes PDF

NUMBERS IMPORTANT FORMULAE :

1. Numeral : In Hindu Arabic System, we use ten symbols 0,1,2,3,4,5,6,7,8,9 called digits to represent any number. A group of digits denoting a number is called a numeral.
2. Place value or Local Value of a Digit in a Numeral :
For example, consider a numeral 689745132.
Place value of 2 is 2×1=2
Place value of 3 is 3×10 = 30
Place value of 1 is 1×100 = 100
Place value of 5 is 5×1000 = 5000 and so on
Place value of 6 is 6×10^8 = 600000000
3. Face Value : The face value of a digit in a numeral is the value of the digit itself at whatever place it may be. In the above numerical example, the face value of 2 is 2, the face value of 3 is 3 and so on.

TYPES OF NUMBERS :

1. Natural Numbers : Counting the numbers 1,2,3,4,5,…. are called Natural Numbers.

2. Whole Numbers : All counting numbers together with Zero form the set of Whole Numbers. Thus 0 is the only whole number which is not a natural number and every natural number is a whole number

3. Integers : All natural numbers, 0 and negatives of counting numbers together for the set of integers.
Positive Integers : {1,2,3,4,….} 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 : 0 is neither positive nor negative. So {0,1,2,3,… } represents the set of non negative integers, while {0,-1,-2,-3… } represents the set of non negative integers.

4. Even Numbers : A number divisible by 2 is called an even number. Example : 2,4,6,8,10,etc

5. Odd Numbers : A number not divisible by 2 is called an odd number. Example : 1,3,5,7,9,etc

6. Prime Numbers : A number greater than 1 is called a prime number if it has exactly two factors, namely 1 and the number itself.
Prime Numbers upto 100 : 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

7. Composite Numbers : Numbers greater than 1 which are not prime, are known as Composite Numbers. Example : 4,6,8,9,10,12,etc

8. Co-Primes : Two numbers a and b are said to be co-primes if their HCF is 1. Example : (2,3), (4,5), (7,9), (8,9), etc are co-primes.