Number System And Codes PDF Free Download

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Number System And Codes PDF Free Download, Number System (Definition, Types, Conversion & Examples), Chapter 1 :number Systems And Codes.

Number System And Codes PDF Free Download

Number Series Is A Sequential Arrangement Of Numbers Following A Certain Defined Pattern.

In This Section, We Deal With Questions In Which A Series Of Numbers, (Which Are Generally Called The Terms Of The Series) Is Given. These Numbers/terms Follow A Certain Pattern Throughout The Series. Candidates Are Asked Either To Find A Missing Term Or To Find The Wrong Term Of The Series.

Different Series Based On Some Particular Patterns Are Discussed Below

I. Based On Addition/subtraction Of Numbers

1. Addition/subtraction Of Consecutive Odd/even Numbers These Series Follow The Pattern Of Addition Or Subtraction Of Even Or Odd Numbers.

Example 1: 5, 6, 9, 14, 21, ?

                A. 26   B. 28   C. 30   D. 34

Solution: (C) Pattern Of The Series Is As Shown Below

The Series Consists Of A Pattern Of Addition Of Consecutive Odd Numbers.

Example 2: 40, 30, 22, 16, ?

               A. 10          B. 12   

                C. 15         D. 17

Solution: (B) Pattern Of The Series Is As Shown Below

The Series Consists Of A Pattern Of Subtraction Of Consecutive Even Numbers.

2. Addition/subtraction Of Prime Numbers These Series Follow The Pattern Of Addition/subtraction Of Prime Numbers.

Example 3: 1, 3, 6, 11, 18, ?

                   A. 25       B. 29   

                   C. 32       D. 35

Solution: (B) Pattern Of The Series Is As Shown Below

The Series Consists Of A Pattern Of Addition Of Prime Numbers.

Example 4: 32, 19, 8, ?

               A. 12         B. 3   

               C. 1           D. 5

Solution: (C) Pattern Of The Series Is As Shown Below

The Series Consists Of A Pattern Of Subtraction Of Prime Numbers.

Ii. Based On Multiplication Or Division Of Numbers

These Series Follow The Pattern Based On Multiplication And Division Of Numbers.

Example 5: 1, 3, 9, 27, 81, ?

               A. 216      B. 220   

               C. 243      D. 250

Solution: (C) Pattern Of The Series Is As Shown Below

Here, Next Number Of This Series Is Multiplication Of 3 With Previous One.

Example 6: 1296, 648, 216, ?, 36, 18, 6, 3

                 A.112           B. 108

                 C. 106          D. 110

Solution: (B) Pattern Of The Series Is As Shown Below

Here, The Terms Are Divided By 2 And 3 Alternately.

So, Missing Term Is Obtained As 216/2 = 108

Iii. Based On Addition/subtraction Of Squares/ Cubes Of Natural Numbers

1. Additional/subtraction Of Squares Of Natural Numbers These Series Follow The Pattern Based On Addition/subtraction Of Squares Of Natural Numbers.

Example 7: 1, 2, 6, 15, 31, ?

                A. 56        B. 64   

                C. 60        D. 58

Solution: (A) Pattern Of The Series Is As Shown Below

The Series Is Based On Addition Of Squares Of Consecutive Natural Numbers.

Example 8: 71, 55, 46, 42, ?

                    A. 40       B. 41   

                    C. 39       D. 38

Solution: (B) Pattern Of The Series Is As Shown Below

The Series Is Based On Subtraction Of Squares Of Consecutive Natural Numbers.

2. Addition/subtraction Of Cube Of Natural Numbers These Series Questions, Follow The Pattern Based On Addition/ Subtraction Of Cubes Of Natural Numbers.

Example 9: 1, 2, 10, 37, 101, ?

                  A. 402       B. 206   

                  C. 226       D. 320

Solution: (C) Pattern Of The Series Is As Shown Below

The Series Is Based On Addition Of Cubes Of Consecutive Natural Numbers.

Example 10: 225, 100, 36, 9, 1, ?

                   A. 7             B. 6   

                   C. 0             D. 1

Solution: (C) Pattern Of The Series Is As Shown Below

The Series Is Based On Subtraction Of Cubes Of Consecutive Natural Numbers.

Iv. Based On Multiple Operation

These Series Follow The Pattern Based On More Than One Mathematical Operations. The Multiple Operations Can Be Multiplication And Addition, Multiplication And Subtraction, Division And Subtraction Etc.

Example 11: 13, 25, 51, 101, 203, ?

                   A. 405             B. 406   

                   C. 407             D. 411

Solution: (A) Pattern Of The Series Is As Shown Below

The Series Is Based On Multiplication Of 2 And Then Subtraction And Addition Of 1 Alternately.

Example 12: 5, 11, 23, 47, 95, ?

                   A. 198             B. 194   

                   C. 191             D. 185

Solution: (C) Pattern Of The Series Is As Shown Below

All Most In All The Entrance Tests, As Well As Interviews Number Series Questions, Are Asked To Evaluate Iq. Solve These Number Series Problems And Practice For Competitive Exams. People Who Love Mathematics Definitely Enjoy Solving Number Series Questions And Answers. This Section Is Devoted To All Such Enthusiast Brain Buddies.

Let’s Have Some Important Number Series Questions And Answers To Solve Yourself For Better Practice Of Competitive Exams. As Well As Of These Questions, You Should Know Number Series Problems With Solutions For Saving Time In The Competitive Exams.

In Number Series Reasoning, Series Is A Sequential Order Of Letters, Numbers, Or Both Arranged In Such A Way That Each Term In The Series Is Obtained According To Some Specific Rules. These Rules Can Be Based On Mathematical Operations, Place Of Letters In Alphabetical Order, And So On. In Questions Related To The Number Series Logical Reasoning Section, A Specified Sequence Or Order Of Letters, Numbers Or A Combination Of Both Will Be Given In Which One Of Terms Such As Letter/number/letter And Number Of The Series Will Be Missing Either At The End Of The Series Or In Between The Series. Candidates Need To Identify The Pattern Involved In The Formation Of Series And Accordingly Find The Missing Term To Complete The Series.

Number Series Refers To A Sequence Of Numbers Following Some Pattern. Candidates Need To Find The Missing Or Wrong Number In The Provided Series. There May Be Some Questions Where One Of The Terms In The Given Series Will Be Incorrect, And Candidates Need To Find Out The Term Of The Series By Identifying The Pattern Involved In The Formation Of The Series.

There Is No Set Pattern And Each Question May Follow A Different Type Of Pattern Or Sequential Arrangement Of Letters Or Digits, Which Candidates Need To Detect Using Their Common Sense And Reasoning Ability. On The Basis Of Various Types Of Questions That Are Asked In Various Competitive Examinations, We Have Classified The Number Series Reasoning Section Into Several Types, Which Are Given Below.

Types of Number Series 

Let us see the various types of questions that may come one by one from below. 

1. Addition Series: In this type of number series reasoning, specific numbers based on some pattern are added to get the next number. 

2. Subtraction Series: In this type of number series reasoning, specific numbers based on some pattern are subtracted to get the next number. 

3. Multiplication Series: In this type of number series reasoning, a particular type of number pattern is multiplied to get the next number. 

4. Division Series: In this type of number series reasoning, a particular type of number pattern is divided to get the next number. 

5. Square Series: In this type of number series reasoning, each number is a perfect square of a particular number pattern. 

6. Cube Series: In this type of number series reasoning, each number is a perfect cube of a particular number pattern. 

7. Fibonacci Series: In this type of number series reasoning, the next number is the addition of two previous numbers.

8. Alternating Series: In this type of number series reasoning, multiple number patterns are used alternatively to form a series. 

9. Mixed Operator Series: In this type of number series reasoning, multiple operators are applied to get the next number in the series. 

10. Arranging Number: In this type of number series reasoning, candidates need to rearrange numbers, as specified, and then answer the given questions. 

Tips and Tricks on Number Series Reasoning

Candidates can find various tips and tricks below for solving the questions related to the Number Series reasoning section. 

Tip 1:  Candidates need to find the process involved in the given series such as addition, subtraction, multiplication, division, and so on to find out the correct answer. 

Tip 2: For arranging type number series, candidates need to rearrange the given series by using various processes to find out the correct answer.