Quantitative Aptitude - Number - Formula & Concept Tutorial

Formula

1. (a + b)² + (a – b)² = 2(a² + b²⁾
2. (a + b)² - (a – b)² = 4ab
3. (a² – b²) = (a – b)(a + b)
4. (a + b)² = (a² + b² + 2ab)
5. (a – b)² = (a² + b² – 2ab)
6. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
7. (a + b)³ = (a³ + b³ + 3ab(a+b))
8. (a³ + b³) = (a + b)(a² – ab + b²)
9. (a³ – b³) = (a – b)(a² + ab + b²)
10. (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
11. When a + b + c = 0, then a³ + b³ + c³ = 3abc.

Types Of number

1. Natural Numbers
   • All positive integers are called natural numbers except 0.
   • They are denoted by N. N = {1, 2, 3, 4, 5, 6……….∞}
2. Whole Numbers
   • All positive integers are called Whole numbers including 0.
   • They are also called as Non-negative integers and denoted by W. W = { 0,1,2,3,4,5,6,7,8,…………..∞}
3. Integers
   • All numbers including negative and positive are called integers. Z = {∞…….-3, -2, -1, 0, 1, 2, 3……∞}
   • Number including decimal is not integers.
4. Rational Numbers
   • A number of the form a/b where ‘a’ and ‘b’ are integers and b ≠ 0 is known as rational number.
   •  For Example  3/5, 7/9, 8/9, 13/15 etc.
5. Irrational Numbers
   •  It is a number that cannot be written as a form a/b where ‘a’ and ‘b’ are integers and b ≠ 0 is known as irrational number
   • For Example  2, 3, 7, etc..
6. Real Numbers
   • A Real numbers are the numbers which include both rational and irrational numbers.
7. Imaginary Numbers
   • A number satisfying the equation i² = −1. Because no real number satisfies this equation, i is called an imaginary number.
8. Complex Numbers
   • The numbers in the form of {a+bi}, where, a and b are real numbers and ‘i’  is the imaginary number, this format is called Complex number.
9. Even Numbers
   • A number divisible by 2 is called an even number.
   • For example: 2, 6, 8, 14, 18, 246, etc.
10. Odd Numbers
    • A number not divisible by 2 is called an odd number.
    • For example: 3, 7, 9, 15, 17, 373, etc.
11. Prime numbers
    • A number greater than 1 and has exactly two factors, namely 1 and the number itself. Then the number is called prime number.
    • For example: 2, 3, 5, 7, 11, 13, 17, etc.
12. Composite numbers
    • A numbers greater than 1 which are not prime, are known as composite numbers. For example: 4, 6, 8, 10, etc.