Reasoning and aptitude part 1

                    Number system

Introduction of number system

1. Real Numbers:- Any number that can be represented on an imaginary number line from negative infinity to positive infinity is known as real number.

2. Natural number:- Set of all positive integer is known as natural number.

Ex:- 1,2,3,4,5.........

3. whole number:- set of all non negative integer known as whole number.

Ex:- 0,1,2,3,4.........

4. Even number:-Any natural number divisible by 2 is known as even number.

Ex:- 2,4,6,8............

5. odd number:- Any natural number is not divisible by 2 is known as odd number.

Ex:- 1,3,5,7............

Note:- Zero niether even nor odd.

6. Prime number:- Any natural number having exactly two distinct factor ie '1' and number itself.

Note:- 

(i)   only 2 is prime and also even number.

(ii)  except 2 and 3 all the other prime number belongs to the faimily of (6k+1) or (6k-1). Where k is natural number.

K= 1,2,3,4........Natural number.

(iii) This is the necessary condition but not sufficient.

7. Composite number:-Any natural number having exactly three distinct factor is known as composite number.

Note:- 1 is neither prime nor composite.

Ex:- 4,6,8,9,10..........

8. Rational number:- Any simplest form (reduced form) of p/q. Where both p and q are integer and q not equal to zero is known as rational number.

9. Irrational number:- Can not form p/q and both integer.

Ex:- pie, surds, log values (except 10 to the power n form), exponential.

Note:- there are two type of rational number-

(i) Terminating:-  complete divisible after decimal.

Ex:- 1/2=0.5 , 1/4=0.25 etc.

(ii) Non terminating recurring:- infinite time repeated value.

Ex:-

1/3= 0.33333333333333333.......

67/99= 0.67676767676767........

22/7 = 3.142857142857142857.........

Note:- all irrational number are non terminating and non recurring.

Ex:- √2=1.4143167918187.....

         π=3.1427165132196......

For exam point of view student have no enough time to solve question in conventional method so we describe some tricks-

Trick

(i) conversing of non terminating recurring number in to p/q form:-

(a) When bar start imidiate after decimal:-

 For example 8.676767676767......Convert in to p/q form

Solve :- first of all we take the number (867) and substrate starting number ie 8.

867-8=859 

859 will be numerator and after that we will see how much digit under the bar. So here two digit 6 and 7 under the bar. If two digit under the bar than we will write 99 in denominator. Like that for 3 digit under the bar we will write 999 and so on.

So final answer will be -

859/99.

Note:- Bar means repeated value

(b) when bar start not imidiate after decimal:-

For example 17.6289289289289289.... Convert in to p/q form
Solution:- first of all we take number and sustract the digit without bar.
176289-176=176113 this will be numerator.after that we will write in denominator.
So three digit under the bar so we write three times 9. And we will see how much digit after decimal which is not under bar so in this question 6 is without bar so we write one zero.
So final answer will be
176113/9990

This was introduction of number system.

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Reasoning and aptitude part 2

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