March 21, 2019

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# REASONING AND APTITUDE

## MADE EASY GATE HANDWRITTEN CLASSROOM NOTES

Reasoning and Aptitude Made Easy GATE Handwritten Notes PDF free download from CivilEnggForAll. Also download all Civil Engineering original GATE Handwritten Notes of ACE and Made Easy institutes only at CivilEnggForAll.

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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.

## PASSWORD : CivilEnggForAll

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