Series CLAT Notes | EduRev

Logical Reasoning for CLAT

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Chapter 3

Series

A series or sequence consists of several terms. In other words, the unit of a sequence are called TERMS. Each term in the series has its own importance as there exists certain relationship between the two consecutive / alternating terms. This relationship is repeated in the series and based on this relationship; we are required to find out the missing term. We come across several types of questions based on any given series. (Base on whether the series consist of the alphabets or the numerals (numbers) or the words, the series can be classified into the following types).

TYPE OF SERIES

1)    NUMBER SERIES                      
 2)    ALPHABET SERIES                              
 3)    MIXED SERIES         

It is quite easy to decipher an alphabetic series as it is easy to remember the place of alphabet in the series. In case of number series also the pattern can be found out but in case of mixed series or jumbled series, it is very difficult to remember the position of each term.

 A mixed series comprises letters, numbers and symbols and unlike the English alphabet series, the number of terms is not fixed in such series. A mixed series may contain any number of terms viz. 23, 24, 26, 28, 30, 31 or 32. Such questions require sufficient practice as there are no definite SHORT CUTS for these questions. The questions on mixed series can be divided into two major heads:

i.  Series of letters and numbers.

ii. Series of letters, numbers and symbols.

 

In questions based on mixed series one is required to judge and find out the relationship between the given terms and find out the answer. To begin with, count the terms and find out the relationship between the required terms

SOME IMPORTANT TIPS

  • First of all, count the terms in the given series.
  • Break up the series into groups of threes / fours depending on the requirements of the question.
  • Pin-point the middle term, if the number of countable terms is odd.
  • Write down the total number of letters, numbers and symbols respectively.
  • Form the groups of five terms, counting from either end so that you can recognize the position of the required term quickly.

NUMERICAL SERIES

ANALYSIS OF NUMERICAL SERIES: A close analysis of the above examples show that the number series can be of the following types.

  • Pure Series: In this type the number follow a pattern which can be easily understood. The number itself may be:
  1. Perfect square                                                ii. Perfect cube
  2. Prime number                                                iv. Combination

Difference Series: The difference series in of the first number with the next number makes a series.

Ex: i) 1, 3, 5, 7, 9, 11, ……. The difference between two consecutive numbers is 2. So it makes a series.

Ex: ii)  1, 2, 4, 7, 11, 16……. The difference between the consecutive number is 1, 2, 3, 4, 5 and so on it also makes a perfect series.

COMPLETING THE GIVEN SERIES 

Ex. 1. Which is the number that comes next in the sequence?

1,  5,  13,  29, __ , 125

 1) 32    2) 62      3) 61   4) 31                                      

Sol.  In this case, the series is increasing by +4, +8, +16, +32, +64. So our answer is 61, as by adding the number 32 to 29 we get the required number i.e. 61. 

Ex.2.  1,    4,    9,    16,    25,      ? 

1) 35  2) 36  3) 48   4) 49                                      

Sol. : The number are 12,   22,  33,  42,   52,

Hence 62 = 36   

Ex.3. Which is the number that comes next in the sequence?

6, 11, 21, 36, 56, __

1) 42   2) 51   3) 81  4) 91                                      

The answer here is (3) 81 because the series is progressing by factor of 5,10 ,15, 20, 25.

Ex. 4.  Which is the number that comes next in the sequence?

 0,    6,    24,    60,    120,   210     ?

1) 240  2) 290  3) 336  4) 504                    

Sol.  Clearly, the given series is : 13 – 1,   23 – 2,    33 – 3,    43 – 4,    53 – 5,    63 – 6.

Next number = 73 – 7 = 343 – 7 = 336                                          
Hence the answer is (3)

Ex. 5.  Which is the number that comes next in the sequence?

3,      7,    15,    31,    63,   ?

1) 92   2) 115   3) 127    4) 131                              

Sol. Each number in the series is the preceding number multiplied by 2 and then increased by 1. Thus, (3 x 2) + 1 = 7, (7 x 2) + 1 = 15, (15 x 2) + 1 = 31 and so on

Missing number = (63 x 2) + 1 = 127

Hence the answer is (3) 

Ex. 6.        3,     6,     18,   72,     ?

1) 144        2) 216    3) 288    4) 360   

Sol.  The pattern is x 2, x 3, x 4, ____         

Missing number =  72  x 5 = 360, i.e. answer is 360. 

ALPHABET SERIES 

In problems based on alphabet series, the pattern of alphabet in the series is to be deducted and the next term is to be found out. There are no set rules, yet the problems can easily be solved if the place number of each alphabet is memorized. Like for K’s place value in the alphabet sequence is 11 and that of V is 22 , that of Q is 17 and X is 24. If these places are known, the questions become easy to solve.

 

There can be omission of alphabets one each time. Alphabets may be omitted in an increasing order or decreasing order;  for example one each time or two each time or three each time and so on. There can also be alternate order such as first one alphabet is skipped, then two may be skipped and then three may be omitted. The skipping pattern may be

Regular Order: In this case the number of alphabets skipped remain the same through the series.

Increasing Order: Each time the number of alphabets skipped increase in a given pattern.

 

The theory can only be understood with the help of practical examples only.

Ex. 1.  What terms will fill the blank spaces?

 A,  B,  C ,  D,   E,    (……),   (……)                                                                                                         1) O, K   2)  N, M   3)  K, S  4) F, G          

Sol. : The given series consist of alphabets in their original order. So, the missing terms would be F and G. Ans. (4)

Ex. 2.  What terms will fill the blank spaces?

Z,   X,   V,   T,   R,    (……),   (……)                                                                                             

1) O, K   2) N, M  3) K, S  4) P, N            

Sol. : Clearly, the given series consist of alternate letters in a reverse order. The alphabets are skipped one at a time. So, the missing terms would be P and N. Ans. (4)

Ex. 3  Find the missing alphabet: B, D, G, K, P, (……),   (……)

Sol. : Each time the number of letters skipped increases by one.  So the answer here is V.

B

D

G

K

P

V

2

4

7

11

16

22

  

B is second alphabet in the series, D is fourth in the series, G is seventh, K is eleventh, P is sixteenth and so the next will be twenty second i.e. V of the series.

Ex.4   
OTE,    PUF,   QVG,   RWH, (……….)                                                                         

1) SYJ    2) TXI    3) SXJ     4) SXI

Sol.  The first letters of the terms are in alphabetical order, and so are second and third letters. 

OPQRS,    TUVWX,    EFGHI                                                                               

Ans. SXI (4)

Ex. 5         FLP, INS, LPV, (……)  

(a) ORY    (b) UXZ   (c) VXY   (d) SVW

The first and third letters of each term are moved three steps forward and the second letter is moved two steps forward to obtain the corresponding letters of the next term.

We pick one letter from one group at a time. Like F from FLP, I from INS, L from LPV.

                           

F6          I9        L12       O15  

L12       N14        P16         R18

P16        S19        V22       Y25

MIXED SERIES 

Series Consisting of Letters & Numbers

Directions (1 – 3):  Study the following arrangement carefully and answer the questions given below:

W 1 5 E J R 2 M A 9 T K U N 4 B I 8 D H 3 F 6 P Z 7 Q

Ex. 1. How many such consonants are there, each of which is immediately preceded by a number and immediately followed by a vowel?

(1) None    
(2) One  
(3) Two    
(4) Three               

Ex. 2.  Which of the following is the seventh to the left of 4?

(1) M
(2) A
(3) F
(4) 3                         

Ex. 3. How many such vowels are there, each of which is immediately preceded and also immediately followed by a consonant?

(1) None
(2) One
(3) Two
(4) Three           

ANSWER WITH EXPLANATION

1.  (3)

Series CLAT Notes | EduRev

2.  (1)

Series CLAT Notes | EduRev

3.  (2)

Series CLAT Notes | EduRev

SERIES CONSISTING OF LETTERS, NUMBERS & SYMBOLS

In order to make series more complicated, letters and numbers are combined with different symbols. Consider the following examples:

Directions (4 –6): Study the following arrangement carefully and answer the questions given below :

K P 5 # 7 M N E 2 D A ¶ 4 F H I T 9 1 $ U 6% W 3

Ex. 4: How many such vowels are there in the above arrangement, each of which is either immediately preceded by a number or immediately followed by a symbol?

(1) None
(2) One
(3) Two
(4) Three          

Ex. 5: Which of the following is the sixth to the right of the fifteenth element from right end in the above arrangement?

(1) T
(2) 7
(3) 2
(4) U                

Ex. 6:  Which of the following is in exactly middle between seventh from the left and ninth from the right end?

(1) A
(2) H
(3) 4
(4) None of these

ANSWER WITH EXPLANATION

4.  (2)

Series CLAT Notes | EduRev

5.  (1) 

15th element from right Þ A

 6th to right of A Þ T

Trick    Required element

 =15 – 6 = 9th term from right.

6.  (4)  None of these

MISCELLANEOUS TYPE

Ex. 12. How may such digits are there in the number 82134967 each of which is as far away from the beginning of the number as when they are arranged in descending order?

(1) None
(2) One
(3) Two
(4) Three                

Answer: (2) 

Series CLAT Notes | EduRev

4 is such number in the series which is at the same position in the original and also when arranged in a descending order.

 

Ex. 13. How may such digits are there in the number 57394162 each of which is as far away from the beginning of the number as when they are arranged in descending order?

(1) None
(2) One
(3) Two
(4) Three                

Answer:  (3) Two. The figure 7 & 4 are at second and fifth position from left. When we place these figures in descending order these will again appear at second and fifth position from left. So our answer is ( 3 ) i.e. there is one such digit in the series which is at same position after arrangement in descending order as when it was in the original series.

 

Series CLAT Notes | EduRev

7 and 4 are such numbers in the series which is at the same position in the original and also when arranged in a descending order.

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