Introduction

Quantitative Analysis requires a lot of practice and hardwork since its an analytical subject. Before becoming an expert one should understand the basics of Quantitative Analysis for Government Bank Job Exams for SBI, RBI, RRB and IBPS. This section gives you all details about the basics of Quantitative Analysis. Here you can get the Free Notes and PDF downloads for Quantitative Analysis to prepare for the Bank PO and Clerical Jobs in India. Our experts are available incase you need any kind of online help to understand any topic or any kind of doubt clearing

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Our Main goal is to make Quantitative Analysis easy for every student to understand. In this section you will learn :

• Quantitative Analysis indepth Knowledge
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• Became an exeprt in limited time

1. NUMBER SYSTEM

A. TYPES OF NUMBERS

1. Natural Numbers : Counting numbers 1, 2, 3, 4, 5,..... are called natural numbers.

2. Whole Numbers : All counting numbers together with zero form the set of whole numbers. Thus,

(i) 0 is the only whole number which is not a natural number.
(ii) Every natural number is a whole number.

3. Integers : All natural numbers, 0 and negatives of counting numbers i.e.,
{…, - 3 , - 2 , - 1 , 0, 1, 2, 3,…..} together form the set of integers.

(i) Positive Integers : {1, 2, 3, 4, …..} is the set of all positive integers.
(ii) Negative Integers : {- 1, - 2, - 3,…..} is the set of all negative integers.
(iii) Non-Positive and Non-Negative Integers : 0 is neither positive nor negative.

So, {0, 1, 2, 3,….} represents the set of non-negative integers, while {0, - 1 , - 2 , - 3 , …..} represents the set of non-positive integers.

4. Even Numbers : A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8, 10, etc.

5. Odd Numbers : A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7, 9, 11, etc.

6. Prime Numbers : A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.
Prime numbers upto 100 are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Prime numbers Greater than 100 : Let be a given number greater than 100. To find out whether it is prime or not, we use the following method :
Find a whole number nearly greater than the square root of p. Let k > square root of p. Test whether p is divisible by any prime number less than k. If yes, then p is not prime. Otherwise, p is prime.

e.g,,We have to find whether 191 is a prime number or not. Now, 14 > square root of 191. Prime numbers less than 14 are 2, 3, 5, 7, 11, 13.
191 is not divisible by any of them. So, 191 is a prime number.

7. Composite Numbers : Numbers greater than 1 which are not prime, are known as composite numbers, e.g., 4, 6, 8, 9, 10, 12.

Note :
(i) 1 is neither prime nor composite.
(ii) 2 is the only even number which is prime.
(iii) There are 25 prime numbers between 1 and 100.

8. Co-primes : Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes,

B. MULTIPLICATION BY SHORT CUT METHODS

1. Multiplication By Distributive Law :
(i) a * (b + c) = a * b + a * c (ii) a * (b-c) = a * b - a * c.

Ex.
(i)567958 x 99999 = 567958 x (100000 - 1) = 567958 x 100000 - 567958 x 1 = (56795800000 - 567958) = 56795232042.
(ii)978 x 184 + 978 x 816 = 978 x (184 + 816) = 978 x 1000 = 978000.

2. Multiplication of a Number By 5ⁿ : Put n zeros to the right of the multiplicand and divide the number so formed by 2 ⁿ
Ex. 975436 x 625 = 975436 x 5⁴= 9754360000 = 609647600

C. BASIC FORMULAE

(i) (a + b)² = a² + b² + 2ab
(ii) (a - b)² = a² + b² - 2ab
(iii) (a + b)² - (a - b)² = 4ab
(iv) (a + b)² + (a - b)² = 2 (a² + b²)
(v) (a² - b²) = (a + b) (a - b)
(vi) (a + b + c)² = a² + b² + c² + 2 (ab + bc + ca)
(vii) (a³ + b³) = (a +b) (a² - ab + b²)
(viii) (a³ - b³) = (a - b) (a² + ab + b²)
(ix) (a³ + b³ + c³ -3abc) = (a + b + c) (a² + b² + c² - ab - bc - ca)
(x) If a + b + c = 0, then a³ + b³ + c³ = 3abc.

D.DIVISION ALGORITHM OR EUCLIDEAN ALGORITHM

If we divide a given number by another number, then :
Dividend = (Divisor x Quotient) + Remainder

(i) (xⁿ - aⁿ ) is divisible by (x - a) for all values of n.
(ii) (xⁿ - aⁿ) is divisible by (x + a) for all even values of n.
(iii) (xⁿ + aⁿ) is divisible by (x + a) for all odd values of n.

E. PROGRESSION - A succession of numbers formed and arranged in a definite order according to certain definite rule, is called a progression.

1. Arithmetic Progression (A.P.) : 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.

An A.P. with first term a and common difference d is given by a, (a + d), (a + 2d),(a + 3d),... The nth term of this A.P. is given by T_n =a (n - 1) d.
The sum of n terms of this A.P.

S_n = n/2 [2a + (n - 1) d] = n/2 (first term + last term).

SOME IMPORTANT RESULTS :

(i) (1 + 2 + 3 +…. + n) =n(n+1)/2
(ii) (l² + 2² + 3² + ... + n²) = n (n+1)(2n+1)/6
(iii) (1³ + 2³ + 3³ + ... + n³) =n²(n+1)²

2. Geometrical Progression (G.P.) : 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. A G.P. with first term a and common ratio r is : a, ar, ar²,

In this G.P. T_n = ar^n-1

Sum of the n terms, S_n = a(1-rⁿ) / (1-r)