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Number Systems For CAT

Number Systems For CAT



Basic Formula
  1. (a+b)² = a² + b² + 2ab
  2. (a−b)² = a² + b²− 2ab
  3. (a+b)² − (a−b)² = 4ab
  4. (a+b)² + (a−b)² = 2(a²+b²)
  5. (a²−b²) = (a+b)(a−b)
  6. (a+b+c)² = a² + b² +c² + 2(ab+bc+ca)
  7. (a³+b³) = (a+b)(a²−ab+b²)
  8. (a³−b³) = (a−b)(a²+ab+b²)
  9. (a³+b³+c³−3abc) = (a+b+c)(a²+b²+c²−ab−bc−ca)
  10. If a+b+c=0, then a³+b³+c³ = 3abc

Type of Number

  1. Natural Number:
  2. Whole Number
  3. Integer Number
  4. Even Number
  5. Odd Number
  6. Prime Number
  7. Composite Number
  8. Co Prime Number
  9. Real Number

Remainder and Quotient

The remainder is r when number p is divided by k" means p=kq+r the integer q is called the quotient. For Example: remainder is 1 when 5 is divided by 2 means 5 = 2 x 2 + 1

Even, Odd Number 

A number n is even if the remainder is zero when n is divided by 2:n=2z+0, or n=2z.
A number n is odd if the remainder is one when n is divided by 2:n=2z+1.

The following properties for odd and even numbers are very useful - you should memorize them:
  1. even x even = even
  2. odd x odd = odd
  3. even x odd = even
  4. even + even = even
  5. odd + odd = even
  6. even + odd = odd

Divisibility of Number

Divisibility By 2
Divisibility By 3
Divisibility By 4
Divisibility By 5
Divisibility By 6
Divisibility By 7
Divisibility By 8
Divisibility By 9
Divisibility By 10

Arithmetic Progression 

If each term of a progression differs from its preceding term by a constant, then such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P.
  1. (1+2+3+....+n) = n(n+1)⁄2
  2. (l2+22+32+...+n2)=n(n+1)(2n+1)6
  3. (13+23+33+...+n3)=n2(n+1)24

Geometrical Progression

A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression. The constant ratio is called the common ratio of the G.P.

Point to Remember





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