NUMBERS
Now days most of the students are studying for IBPS. IBPS Conducts over 400 examination each year. Every year more than one crore candidates apply for these examination.
There are Three important topics for IBPS preliminary examinations-
i) Reasoning Ability
ii) Quantitative Aptitude
iii) English Language
iv) General Awareness
Now in this article, let us look at the numbers related problems and solutions.
I) Numbers :-
In Hindu-Arabic system, there are ten digits, namely 0,1 ,2. 3, 4 , 5.........,9.
A number is denoted by a group of digit is called as numeral.
II) Place value and Face value of digit in a Numeral:-
Face value = The face value of a digit is its own value, at whatever place it .
Example:- In the number 62987 , the face value of 2 is 2, the face value of 6 is 6.
Place Value = The place value of a digit in a numeral is its digit value of its place.
Examples:- In the number 62987 , the place value of 2 is 2000, the face value of 6 is 60000.
Place value of ones digit = ( one digit ) * 1
Place value of tens digit = (tens digit ) * 10
Place value of hundreds digit = ( hundreds digit ) * 100 and so on.
III) Various Types of numbers :-
1. Natural numbers :-
The numbers is used to counting is called as natural numbers.
1, 2, 3, 4........etc.\
2. Whole Numbers :-
All counting numbers, together with 0, form the set of whole numbers.
Ex. 0, 1, 2, 3, 4....................etc.
3. Even Numbers:-
A number divisible by 2 called an even number.
Ex. 0, 2, 4, 6, 8,10,12,14,16,18,20............etc.
4. Integers :-
All natural numbers , zero and negative of natural numbers , from the set of integers.
Ex. ......., -3, -2, -1, 0, 1, 2, 3...........etc.
Set of positive integer = { 1, 2, 3, 4, 5...........}
Set of negative integer = { -1, -2, -3, -4, -5............}
Set of all non-negative integer = { 0, 1, 2, 3, 4, 5...........}
5. Odd Numbers :-
A number not divisible by 2 is called an Odd numbers.
Ex. 1, 3, 5, 7, 9...................etc.
6. Prime Numbers :-
A numbers is called prime numbers if it has exactly two factors , namely itself and 1.
Ex. 2, 3, 5, 7, 11, 13................etc.
7. Composite Number :-
All numbers, which are not prime are called composite numbers. or The number who has more than two factors is called Composite numbers.
Ex. 4, 6, 8, 9, 10...............etc.
8. Perfect Number :-
Perfect number = sum of its factors.
Ex. 6, 28..............etc.
6 = factors of 6 is 1, 2, 3
sum of factors= 1+2+3=6
9. Co-Primes :-
Two numbers whose H.C.F is 1 is called co-prime numbers.
Ex. (2,3) is pairs of co-prime numbers.
10. Twin Primes :-
Two prime numbers whose difference is 2 are called is twin primes numbers.
Ex. (3, 5) , (5, 7) are twin primes numbers.
11. Rational Numbers :-
Number which can be expressed in the form p/q , where p and q are integer and q is not equal to 0, are called rational number.
Ex. 1/8, -8/11. etc.
12. Irrational Numbers :-
Number which when expressed in decimal would be in non-terminating and non-repeating form, are called irrational numbers.
Ex. √2, √3, √5 √7, π , e, 0.231764735.......
II) Important Facts :-
1. All natural numbers are whole numbers.
2. All whole numbers are note natural numbers.
3. Even number+ Even number = Even number
Odd number + Odd number = Even number
Even number + Odd number = Odd number
Even number - Even number = Even number
Odd number -Odd number = Even number
Even number - Odd number = Odd number
Odd number - Even number = Odd number
Even number * Even number = Even number
Even number * Odd number = Even number
Odd number * Odd number = Odd number.
4. The smallest prime number is 2.
5. The only even prime number is 2.
6. The first odd prime number is 3.
7. 1 is neither prime nor composite number.
8. The least composite number is 4.
9. The least odd composite number is 9.
Now days most of the students are studying for IBPS. IBPS Conducts over 400 examination each year. Every year more than one crore candidates apply for these examination.
There are Three important topics for IBPS preliminary examinations-
i) Reasoning Ability
ii) Quantitative Aptitude
iii) English Language
iv) General Awareness
Now in this article, let us look at the numbers related problems and solutions.
I) Numbers :-
In Hindu-Arabic system, there are ten digits, namely 0,1 ,2. 3, 4 , 5.........,9.
A number is denoted by a group of digit is called as numeral.
II) Place value and Face value of digit in a Numeral:-
Face value = The face value of a digit is its own value, at whatever place it .
Example:- In the number 62987 , the face value of 2 is 2, the face value of 6 is 6.
Place Value = The place value of a digit in a numeral is its digit value of its place.
Examples:- In the number 62987 , the place value of 2 is 2000, the face value of 6 is 60000.
Place value of ones digit = ( one digit ) * 1
Place value of tens digit = (tens digit ) * 10
Place value of hundreds digit = ( hundreds digit ) * 100 and so on.
III) Various Types of numbers :-
1. Natural numbers :-
The numbers is used to counting is called as natural numbers.
1, 2, 3, 4........etc.\
2. Whole Numbers :-
All counting numbers, together with 0, form the set of whole numbers.
Ex. 0, 1, 2, 3, 4....................etc.
3. Even Numbers:-
A number divisible by 2 called an even number.
Ex. 0, 2, 4, 6, 8,10,12,14,16,18,20............etc.
4. Integers :-
All natural numbers , zero and negative of natural numbers , from the set of integers.
Ex. ......., -3, -2, -1, 0, 1, 2, 3...........etc.
Set of positive integer = { 1, 2, 3, 4, 5...........}
Set of negative integer = { -1, -2, -3, -4, -5............}
Set of all non-negative integer = { 0, 1, 2, 3, 4, 5...........}
5. Odd Numbers :-
A number not divisible by 2 is called an Odd numbers.
Ex. 1, 3, 5, 7, 9...................etc.
6. Prime Numbers :-
A numbers is called prime numbers if it has exactly two factors , namely itself and 1.
Ex. 2, 3, 5, 7, 11, 13................etc.
7. Composite Number :-
All numbers, which are not prime are called composite numbers. or The number who has more than two factors is called Composite numbers.
Ex. 4, 6, 8, 9, 10...............etc.
8. Perfect Number :-
Perfect number = sum of its factors.
Ex. 6, 28..............etc.
6 = factors of 6 is 1, 2, 3
sum of factors= 1+2+3=6
9. Co-Primes :-
Two numbers whose H.C.F is 1 is called co-prime numbers.
Ex. (2,3) is pairs of co-prime numbers.
10. Twin Primes :-
Two prime numbers whose difference is 2 are called is twin primes numbers.
Ex. (3, 5) , (5, 7) are twin primes numbers.
11. Rational Numbers :-
Number which can be expressed in the form p/q , where p and q are integer and q is not equal to 0, are called rational number.
Ex. 1/8, -8/11. etc.
12. Irrational Numbers :-
Number which when expressed in decimal would be in non-terminating and non-repeating form, are called irrational numbers.
Ex. √2, √3, √5 √7, π , e, 0.231764735.......
II) Important Facts :-
1. All natural numbers are whole numbers.
2. All whole numbers are note natural numbers.
3. Even number+ Even number = Even number
Odd number + Odd number = Even number
Even number + Odd number = Odd number
Even number - Even number = Even number
Odd number -Odd number = Even number
Even number - Odd number = Odd number
Odd number - Even number = Odd number
Even number * Even number = Even number
Even number * Odd number = Even number
Odd number * Odd number = Odd number.
4. The smallest prime number is 2.
5. The only even prime number is 2.
6. The first odd prime number is 3.
7. 1 is neither prime nor composite number.
8. The least composite number is 4.
9. The least odd composite number is 9.
