Number Series

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            Series is very important chapter of verbal reasoning tests. Few reasoning questions in your exam will surely come from this chapter. Here in this page we will discuss series reasoning with solution which will help you to solve series questions very quickly and easily. Reasoning tricks are nothing but to solve reasoning questions very fast and accurately. Here we will show you the method of "How to solve reasoning using shortcut tricks".

            Time is very important thing in every exam. You need to finish your examination within time but in every examination they also test your calculation ability within a given time frame. They tests now fast you can solve a paper. That's why so many students won't complete their exam within time. But if you use tricks of reasoning and series then it will help you to solve SSC, Bank, Railway, Government or any other exam paper much faster. We provide so many short tricks here in www.wifistudy.com and online tests.

            Now let's starts the detail discussion of series and few important reasoning question answer.

Type of series :

            Number series

            Mixed series

            Alphabetical series

Number Series :

            In this topic, we deal with the questions in which series of numbers, which are generally called the terms of the series. These terms follow a certain pattern throughout the series. Candidates are asks either to insert a missing number or to find the one that does not follow the pattern of the series. A number series can be formed by using various characteristics of number and by using various type of calculations.

Type of questions :

            There are mainly three types of questions which are asked in various competitive exams.

            Type 1. To find a missing terms (Number)

            Here we are given a sequence of numbers including one missing number. This series follows a pattern, keeping this pattern in mind, we will/have to find the missing term :

            Example : (1) Look at this series : 22, 21, 23, 22, 24, 23 .......... what number should come next.

            (A) 22                    (B) 25                       (C) 24                    (D) 26

           Solution : (C)    

           In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and soon.

            Example : (2) Look at this series :

                2, 1, 1 half comma space 1 fourth ...... what number should come next ?

            (A) 1/3                   (B) 1/8                      (C) 2/8                   (D) 1/16

            Solution : (B) This is a simple division series; each number is one - half of the previous number.

            In other terms to say, the number is divided by 2 successively to get the next result.

            4/2 = 2

            2/2 = 1

            1/2 = 1/2

            (1/2)/2 = 1/4

            (1/4)/2 = box enclose 1 divided by 8 end enclose  and so on.

            Example : (3) 32, 87, 332, 1635, ?

            (A) 9675                (B) 6649                   (C) 8875                (D) 9774

             Solution : (D) This pattern is :

             Hence, missing term = (1635 – 6) × 6 = 9774

            Type - 2 Find the number that does not follow the pattern :

            Here we are given a sequence of number. Whole sequence except one number follow a certain rule. You have to find that number which does not follow the rule -

            Example : (1) 53, 53, 48, 40, 27, 27 ...... which term does not follow the rule -

            (A) 53                    (B) 48                       (C) 40                    (D) 27

             Solution : (B)

           

           In this series, each number is repeated, then 13 is subtracted to arrive at the next number.

            Example : (2) 840, 168, 44, 14, 7, 7

            Find the wrong element in above number series.

            (A) 168                  (B) 44                       (C) 14                    (D) 840

            Solution : (B)

          

          Example : (3) 258, 130, 66, 34, 18, 8, 6

            Which term does not follow the rule in above series ?

            (A) 258                  (B) 8                         (C) 66                    (D) 18

          Solution : (B)

          Hence, number 8 is wrong and should be replaced by 10.

            Example : (4) 78, 162, 489, 1972, 9885, 59346

            (A) 162                  (B) 489                     (C) 1972                (D) 59346

             Solution : (A)

Miscellaneous Pattern

            Using the same methods, you can practice with some important questions.

            (1) Based on addition : These questions have a certain pattern of addition -

            Example : (1) 73, 78, ?, 103, 123, 148

            (A) 80                    (B) 82                       (C) 86                    (D) 88

            Solution : (D)

           

            Example : (2) 93, 96, 109, 132, ?, 208

            (A) 142                  (B) 165                     (C) 158                  (D) 196

            Solution : (B)

            

            (2) Based on subtraction : These questions have a pattern of subtraction -

            Example : (1) 58, ?, 49, 40, 28, 13

            (A) 52                    (B) 53                       (C) 55                    (D) 50

            Solution : (C)

            

            Example : (2) 782, 759, ?, 719, 702, 687

            (A) 740                  (B) 723                     (C) 728                  (D) 738

            Solution : (D)

            

            (3) Based on addition /subtraction of prime numbers -

            These questions have a pattern of addition/subtraction of prime number.

            Example : 13, 15, 18, 23, 30, ?

            (A) 37                    (B) 35                       (C) 48                    (D) 41

            Solution : (D)

           

            Example : 48, 31, 18, 7, ?

            (A) 3                      (B) 4                         (C) 7                      (D) 0

            Solution : (D)

            

            (4) Based on multiplication and division :

            These questions have a pattern based on multiplication and division.

            Example : 17, 51, 204, 1020, 6120, ?

            (A) 42840              (B) 36720                 (C) 36600              (D) 30600

            Solution : (A)

           

            Example : ?, 2916, 972, 324, 108, 36, 12

            (A) 2916                (B) 5832                   (C) 8748                (D) 11664

            Solution : (C)

           

            (5) Alternate Series : These types of questions have a pattern of alternate series.

            Example : 9, 6, 16, 10, 30, 18, 58, ?

            (A) 18                    (B) 32                       (C) 34                    (D) 28

            Solution : (C)

          

            (6) Based on addition/subtraction of squares of natural numbers :

            These questions consist of a pattern based on addition/subtraction of squares of natural numbers :

            Example : 69, ?, 82, 98, 123, 159

            (A) 70                    (B) 80                       (C) 73                    (D) 68

            Solution : (C)

           

            Example : 260, ?, 219, 210, 206, 205

            (A) 250                  (B) 255                     (C) 235                  (D) 240

            Solution : (C)

           

            (7) Based on addition/subtraction of cube of natural numbers :

            These questions consist of a sequence based on addition subtraction of cubes of natural numbers.

            Example : 7, ?, 16, 43, 107, 232

            (A) 8                      (B) 10                       (C) 12                    (D) 14

            Solution : (A)

           

          There are given few square root & cube root which will be helpful for students for solve the questions which related to series.

          * 1 to 60 square and square root :

          * 1 to 30 cube and cube root :

'7 stars' you will never go wrong

            We will be doing revision worthy quick study on syllogisms today, starting with 7 stars.

7 Stars of syllogism :

            (1) I hope all of you prefer to solve syllox with the help of Venn - diagrams.

            (2) Direct relations which are given in the question, will always hold true. Thus if in the statement you are given 'All cats are rats'. And in the conclusion too you are given 'All cats are rats'. It is true.

            (3) Thus, any contradiction to a direct relation, will always be wrong.

            If statement is 'Some scooters fly', and in conclusion you have 'Some scooters do not fly', the conclusion is wrong. Contradiction of direct relation.

            (4) But, if the contradiction to a direct relation is coupled with the word 'Possibility', then the conclusion will be correct.

            'There is a possibility that some scooters do not fly.' is correct.

            (Standard rule : Where with any conclusion which is directly coming from the statements, the word 'possibility' is added many a times the conclusion, which otherwise is wrong, will become correct.)

            (5) If in a statement given, relation is not made between such elements will be wrong.

            Cats are rats. Bats are dogs - is the statements.

            Some rats are dog - is the conclusion, and it is wrong.

            Is there any connection between rats/cats with bats/dogs, that we can understand from the statement ?

            No ! Hence, the direct relation in the conclusion is wrong.

            But if the word possibility is added, then, 'some rats being dogs is a possibility', Becomes correct !

            (6) And where direct relation exists, then adding the word 'possibility' is wrong.

            Statements - All apples are bad.

            Conclusion - All apples being bad is a possibility, - is wrong, as in the direct relation it is given that all apples are bad !

            (7) Either/Or conditions :

            When all the under mentioned 3 conditions follow cumulatively, only then will either/or follow option.

            (i) One conclusion is +ve and one is –ve.

            (ii) The elements are same in both the options.

            (iii) Individually both conclusions must be wrong.

Check this out :

            Statements : (i) No truck is rover. (ii) All rovers are land.

            Conclusion : (i) No land is truck. (ii) Some land is truck.

          Conclusion I is wrong and conclusion II is wrong too.

          (Please note readers, if in both the conclusions of the word 'possibility' was added then they would have become correct!)

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