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How to prepare for Quantitative Aptitude Numerical Ability for exams like  IBPS Clerk, IBPS PO, SBI PO, SBI Clerk, RRB, RBI, SSC Insurance LIC AAO CSAT Railways NDA CDS & GMAT and other Competitive Exams 

Number System

What is a Natural Number?

A Counting number is called Natural Number.

What are the examples of Natural Numbers?

1, 2, 3, 4, 5, 6, 7, 8, … , ∞

What is a Whole Number?

A Natural number including zero (0) is called a whole number.

What are the examples of Whole Numbers?

0, 1, 2, 3, 4, 5, 6, 7, …, ∞

What are Integers?

Set of negative and positive whole numbers (including Zero - 0) are called Integers.

What are the examples of Integers?

-1, -2, -3, 0, 1, 2, 3, 4, 5,

What are Rational Numbers?

The numbers of the form p/q and where q β‰  0 and p and q are Integers.

What are the examples of Rational Numbers?

-1/5, -1/2, 2/4, 1/5 and others.

What are Irrational Numbers?

The numbers which are non terminating and non repeating are called Irrational Numbers.

√5, √3, √2 and others.

What are Real Numbers?

All Irrational and Rational Numbers are known as Real Numbers.

What are the examples of Real Numbers?

1, 2, 3, 4, 2/4, 4/8, 5/8, √2, √5, and others.

What is an Even Number?

A Number which is a multiple of 2 or divisible by 2 is called an Even Number.

What are the examples of Even Number?

2, 4, 6,8,10,12,14,16, and others.

What is an Odd Number?

A Number which is neither a multiple of 2 and neither divisible by 2 is called an Odd Number.

What are the examples of Odd Number?

1,3,5,7,9,11 and others.

What is a prime number?

Any number which has only two factors of 1 and itself is called a Prime Number.

What are the examples of Prime Number?

2,3,5,7, 11, 13, and others.

Which is the only Even Number which is also a Prime Number?

2 is the only Even Number which is also a Prime Number.

What are Composite Numbers?

Any Number which has more than two factors is called a Composite Number.

What are the examples of Composite Number?

2,4,6,8,9,10 and others.

Important Formulas

How to find the sum of first n natural numbers?

Sum of first n natural numbers = n (n +1) / 2

How to find the sum of first n even natural numbers?

The sum of first n even natural numbers = n ( n+1)

How to find the sum of first n odd natural numbers?

The sum of first n odd natural numbers = n 2 

How to find the sum of the squares of first n natural numbers?

The sum of the squares of first n natural numbers =

n (n+1) (2n+1)/6

How to find the sum of the cubes of first n natural numbers?

The sum of the cubes of first n natural numbers =

    {n (n+1)/2 }2

What is Decimal Fraction?

Decimal fraction is a fraction where the denominator is some power of 10.

What are the examples of Decimal Fraction?

1/10 = 0.1

1/100 = 0.01 and others

What is a Recurring Decimal?

A recurring decimal is a decimal fraction where all the figures after the decimal point are repeated.

What are the examples of Recurring Decimal?

0.3333

0.454545 and others

What is Simplification?

In an expression when more than one mathematical operators are given ( + , -, x,  Γ· ) the expression is solved by using BODMAS.

B = Bracket [ { ( - ) } ]

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

What is Simplification of Bracket?

First we simply then - (Vinculum or Bar )

() Small Bracket

{ } Curly Bracket

[ ] Square or Big Bracket

What are the Important Formulas?

( a - b)2 = a2 - 2ab + b2

( a + b)2 = a2 + 2ab + b2

 a2 – b2 = ( a + b) ( a - b)

a3 – b3 = ( a - b) ( a2 + ab + b2)

a3 + b3 = ( a + b) ( a- ab + b2)

a3 + b3+ c3 – 3abc = (a+b+c) (a2+b2+C2-ab-bc-ca)

( a - b)2 = (a + b)2 - 4ab

( a + b)2  = (a – b)2 +4ab

What is HCF – Highest Common Factor?

A common factor of two or more numbers is a number which divides each of them exactly.

What are the Methods for finding HCF?

  1. Factorization
  2. Division

What is LCM – Lowest Common Multiple?

The least number which is exactly divisible by each one of the given numbers.

What are the methods for finding LCM?

  1. Factorization method
  2. Shortcut method

What are the important formulas for HCF and LCM?

Product of two numbers = (their HCF) x (their LCM)

Please remember two numbers are coprime if their HCF is 1.

The greatest number that will divide x, y, z leaving remainders a, b and c respectively is given by HCF of (x-a) (y-b) and (z-c).

The least number which when divided by x, y and z leaves the same remainder R in each case is given by LCM of [(x, y, z) +R].

The greatest number that will divide x, y and z leaving the same remainder in each case is given by HCF of |x-y|, |y-z| and |z-x|.

Square  and Square Roots

What is Square?

When a number is multiplied by itself -  the product is called the Square of that number.

What are the examples of Square?

2x2 = 4  and 4 is called the square of 2

4x4 =16 and 16 is called the square of 4.

What is Square Root?

The square root of a given number is that number which when multiplied by itself is equal to the given number.

What is the example for Square Root?

22 = 4  and 2 is the square root of 4 and is expressed as  2=√4

What are the Important Formulas?

√ab = √a x √b

√a/b =√a/√b

What is a cube?

When a number is multiplied by itself thrice the product is called the cube of that number.

What is an example of Cube?

3x3x3 = 27 and 27 is the cube of 3

What is Cube Root?

Cube root of a number is the number which when raised to the third power will produce the given number.

What is the example of Cube Root?

43 = 64 and 64 has a cube root of 4 and is expressed as 3√

Indices and Surds

What are Indices?

If a is a real number and m is a positive integer

Then a x a x a x a x…….x m times = am and m is known as indices to the base a.

What are Surds?

If a is a rational number and m is a positive integer then if a 1/m  be an irrational number then

a1/m  is known as surds of power m.

1/am = m√a = mth root of a

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