27 September, 2015

Quantitative Aptitude Preparation Tips for SSC- Number System-Page1

Welcome Job Aspirants,
  Quantitative Amplitude is one of the most important chapters for all SSC exam syllabus. It is also important for all other competitive exams like  UPSC or RRB and all other  Banking Examinations. There are almost 25% of SSC exam paper  questions are covered with Quantitative Aptitude Questions. Since Quantitative Aptitude for SSC is a very vast chapter which includes many small chapters like Number system, Time/Speed, Time/Work, Average, Number series, Profit/Loss and Many More. In this Post Series We will be discussing Various Tips and Tricks to solve Quantitative Aptitude questions. In this post we are discussing about Quantitative Aptitude Preparation tips and tricks for Number system problems.

Quantitaive Aptitude Preparation Tips for SSC : Number System

Understanding of Number systems:
Numbers systems of our daily life is Classified in Various sub-field as Follows:

i. Real Number: Real Number are Composition (super set or mix) of all the Rational and irrational Numbers. Now this common question for many students what is Rational Number and Irrational Number? Well let's define rational and irrational Numbers as follow:
Rational Number:  The easiest answer is any Number that can be expressed in terms of P/Q where, Q!=0(Not equal to zero ) P, Q are only Integer Number(…-3, -2, -1, 0,1,2,3…) .So we can say that Rational Number pure fraction form like 4/5, 5/1, 7/1, 8/9 etc. It is denoted as Q.
Irrational No: So the opposite of rational No i.e. those No which cannot be expressed in terms of P/Q form. e.g.,  3,5,7 or any square root of Prime Number. Many of us think that has a value of 22/7 (P/Q form) then why it is irrational Number. The Polite answer is actually ∏ don’t have actually 22/7 Value, It is just an Approximated value for solving geometrical question. The actual Value of ∏ is 3.1425……up to ∞ (Never ending). So we have an idea that Those Numbers whose value after decimal point is never ending is called irrational Number.       
Tips & Tricks 1: 

a). Addition or Subtractions Of Rational And Irrational Number Results in Irrational Number. e.g. say rational Number 9/2 and Irrational Number 3.1425…. .
So,  9/2 + 3.1425…..= 7.6425……∞ is irrational No.
b). Multiplication Of Rational And Irrational No Results in Irrational No. e.g. say rational No 1  and Irrational No 3.1425…. .
So, 1 X 3.1425…..= 3.1425……∞ is irrational No.

>Rational ± Irrational= Irrational
>Rational x Irrational= Irrational

ii. Natural Numbers: Natural Number are the Numbers which are used in our day to day life for counting or calculating. E.g 1,2,3,4…(All positive Numbers except 0, i.e. 0 is not a natural Number). Natural Number is denoted as 'N'. Natural Number is sub divided into two set Even Number and Odd Number 

Even Number: All the numbers that have 2 as a common factor. i.e. All even number must be divisible by 2 without any remainder part. E.g 2,4,6,8,10…..

Odd Number: All the Natural numbers except even. i.e.  All Odd Numbers are not be divisible by 2 . E.g 1,3,5,7….. 

So, Natural NO= Even No + Odd No  

iii. Whole Numbers: Whole Numbers are defined as Natural including 0. i.e. Whole Number are all positive Number Starts From 0. Whole Number is Denoted with W ={0,1,2,3,4…..}

iv. Integer Numbers: Integer Numbers are whole with their Negative part i.e. if we include negative set of all whole no to the Set of Whole number then it is called Set of  Integer Number. Denoted with I. So, I ={-…..-3,-2, -1,0,1,2,3,4….+∞}.( Negative Number of any Positive Number is also Called Additive Inverse of the Number. And Additive inverse of any Number is defined as the Number by which addition to any number results in zero. e.g. additive Inverse of X is –X because X+(-X)=0 ). Integer Number is Further Divided into two subsets.  

Positive Integer: All whole Numbers Except Zero,  can be called Natural Numbers= {1,2,3,4…} 

Negative Integer: All negative integer Numbers except Zero.{…-3,-2.-1,}Note: Zero is not included either in positive of negative integer set 

 Prime Numbers: Prime Numbers are those which are divisible by 1 and the Number itself (Except 1, i.e. 1 Is not included in Prime Number). I.e. All the prime Number have only two factors namely 1 and the number itself. e.g. 7 is a prime Number because it can be divided by 1 and 7 only thus it has only two factors 1, 7.Other Examples of Prime Numbers are: 2, 3, 5,  7, 11, 13, 17, 19, 23,29,31…… 

Tips & Tricks 2:
a)Checking Any Number whether Prime or not- All the prime Number except 3 can be expressed in terms of  (6X-1) or (6X+1) where X is an positive Integer number (1,2,3,4, 5…..). So for checking primeness of any number is Just equal both 6X+1=Number and 6X-1=Number and find X. If X is an integer in any one case then the number is prime. If X is not integer in both the cases i.e. a fractional Number then the Number is not prime Number.(Note: This Rule is applicable for all Number greater then 3)  
b)There are 25 Prime Numbers between 1 to 100. By heart all off them 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
c)All the Prime Number are Odd Number except 2. 
d)2 is the Smallest Prime Number. 1 is neither Prime nor Composite Number
Vi. Composite Numbers: All the Numbers that are not prime number and greater than 1 are composite Numbers. E.g. 4,6,8,9,10,12,14,15…………….etc. 

Vii. Co-prime Numbers: Co-primeness is defined for two nos. i.e. any two number is said to be Co-Prime number it the have a common factor 1. i.e. Both Numbers are divisible only a common number 1. E.g. 4,5 are co-prime. Simily,  (13,14) are co-prime,( 8,9) are co-prime.

Viii. Imaginary Numbers: All the Numbers that are not real number are called Imaginary Number. All the square root of any negative Number is Imaginary Number. e.g.√-1,√-2,√-3…. . Imaginary Number are denoted with ‘i’ (iota). So, i=√-1. 
√-2 = √-1*√2 = √2i since  I = √-1; 

Tips & Tricks 3:
  •  i*i= i^2= -1
  •  i*i*i = i^3 = i^2*i = -i
  •  i^4 = 1
  •  i^4n = 1 where n is any positive integer no(1,2,3,4…)

IX. Complex Numbers: Composition of Real Number and Imaginary Number is a called Complex Number. Complex Number is the super-set of both real and Imaginary Number. It is the generalized form of any Number. Complex Numbers is defined as Z=X+iY, Where X is the Real Part and Y is the Imaginary Part. Any Number can be expressed in term of Complex Number.
e.g.  2= 2+i.o that is real Part is 2 and imaginary part is zero. 
Similarly, imaginary Number 3i can be expressed in term of complex :
e.g  3i = 0 + 3.i, here real part is zero. 
A full complex Number is combination of both Real and Imaginary Numbers: e.g.  Z= 2 +3i  where real part is 2 and Imaginary part is 3.

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