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