Topics

Series - Questions and Answers

In this topic, Continuous literals will be given, and we have to find out missing or next literal of given problem.

Note: Literals can be numbers, symbols and alphabet.

Importance of topic

Questions from this topic are appeared in almost all the examinations like Bank PO, SSC CGL, Clerical, CAT, IBPS, UPSC, MAT, CMAT, CET etc.

Pre-Requisites

Squares, cubes up to 30 will be required for easy and quick solution of problem.
Numeric position of alphabet is required for alphabet based series.
It is necessary to have knowledge about prime and composite numbers, Fibonacci series and factorial of a number. It is mandatory, because problems can be based on any of the above concepts.

Suggestions

i) Draw basic chart of alphabet having letters and their numerical position.

Note: Write reverse numbers also i.e. a-26, b-25, c-24 …up to a-1 or use another approach of writing letters and their numerical position by multiplication of 5.

ii) Addition of a letter’s numerical position from ascending and descending order is 27.
E.g.: A-1-26 (1+26=27),
B-2-25 (2+25=27)
.....
Y-25-2 (25+2=27)
Z-26-1 (26+1=27)

iii) Use pyramid approach if you are not getting any series even after single iteration.
E.g.:
Diagram of Pyramid based problem.

Types of questions

There are basically 3 major types of problems asked.

A) Numerical

In this type of problems series of numeric are given and in series, there must be some sort of relation or logic exists. We have to find out the relation as well as logic amongst given series.

Logic might be of:

i) Addition or Subtraction - In addition or Subtraction, difference between two numbers is small. This logic comes under Arithmetic Progression(AP)

ii) Multiplication or Division - If the relation between two numeric is of Multiplication or Division, then difference is High. This logic comes under Geometric Progression(GP)

iii) Squares or Cubes - If it is Squares or Cubes, then difference is too High

iv) Prime or Composite numbers - Series are provided with prime numbers or composite numbers also. i.e. 2, 3, 5, 7, 11, 13 are prime number while 4, 6, 8, 9, 10, 12 are composite numbers

v) Factorial or Fibonacci - Problems are asked based on factorial of a number or from a Fibonacci series

vi) Other miscellaneous types - In this type of problems, it can have some observation type of logic. We can’t apply some addition, subtraction or any arithmetic operation directly. We have to observe the given problem and then we can get some solution like, breaking down each number or reversing each number from series

Examples:

i) 8, 10, 12, 14, ?

a) 18
b) 15
c) 26
d) 16

View solution

Correct Option: (d)

Arithmetic progression type of question. +2 difference


ii) 19, 25, 32, 40, ?, 59

a) 46
b) 49
c) 55
d) 51

View solution

Correct Option: (b)

Observe difference between two terms. It is not randomly incrementing. So it might be arithmetic progression type of question. Let’s try to solve it. Difference is in increasing order. Difference is +6, +7, +8, +9 .. So, 40+9=49


iii) 9, 18, 54, 216, ?, 6480

a) 432
b) 864
c) 1080
d) 1512

View solution

Correct Option: (c)

As we can see that difference between two terms is high. So it there is possibilities that this is geometric progression type of question. Let’s try to solve it. *2, *3, *4, *5 … So 216*5=1080


iv) 216, 72, 36, 12, ?, 2

a) 8
b) 6
c) 4
d) 3

View solution

Correct Option: (b)

As we can see from series that difference is random. So might be geometric progression type of series and more on terms are in decreasing order, so it must be division operation applied. Difference is /3, /2, /3, /2 … So, 12/2=6


v) 8, 27, 64, 125, ?, 343

a) 312
b) 216
c) 189
d) 225

View solution

Correct Option: (b)

We can clearly see that 8, 27, 64 are the cubes of 2, 3, 4 respectively. So after 125 there must be 63 = 216. So answer is 216


vi) 1, 4, 27, 16, 125, ?, 343

a) 216
b) 25
c) 36
d) 225

View solution

Correct Option: (c)

Problem has fluctuated terms and they are in random order. As we can see, all the terms are combination of squares and cubes. Let’s find out pattern between terms 4=22, 27=33, 16=42, 125=53 and 343=73. So missing term will be 62=36. Pattern is like 22, 33, 42, 53, 62


vii) 2, 5, 10, 17, 28, ?

a) 37
b) 35
c) 41
d) 40

View solution

Correct Option: (c)

Let’s find out difference between two terms. We are getting difference like +3, +5, +7, +11 all differences are prime numbers, next prime number after 11 is 13. So answer is 28+13=41


viii) 21, 34, 55, 89, 144, ?, 377

a) 199
b) 233
c) 220
d) 241

View solution

Correct Option: (b)

First we have to find out difference between two terms because numbers are not randomly increasing. We got differences are +13, +21, +34, +55. Differences clearly show the Fibonacci series (i.e. Addition of previous 2 numbers). So answer is 144+89=233


ix) 41, 93, 165, 257, 369, ?

a) 4861
b) 4211
c) 4911
d) 4411

View solution

Correct Option: (c)

Let’s find out differences, But from differences we are not getting any kind of relations. This is miscellaneous type of question in which, we can break down numbers. Let’s break down each and every numbers. So we got proper logic for this series i.e. first half is the squares of some continuous numbers like 2, 3, 4, 5, 6 and second half is continuous odd numbers


B) Alphabetical Series

Examples:

i) CEH, ?, OQT, UWZ

a) ACG
b) IKN
c) FGJ
d) KLM

View solution

Correct Option: (b)

2nd letter is obtained by skipping 1 letter in alphabet from 1st letter and 3rd letter is obtained by skipping 2 letters from 2nd letter


ii) BDA, FHE, ?, NPM

a) JKI
b) IMJ
c) JLI
d) INJ

View solution

Correct Option: (c)

Series starts from 3rd letter. i.e. I
1st letter (J)- next letter in the alphabet of the 3rd letter.
2nd letter (L)- skip 1 letter in the alphabet from 1st letter(J)


iii) HFD, NLJ, ??O, XVT

a) PQ
b) SQ
c) QP
d) QS

View solution

Correct Option: (b)

Series is in reverse order. i.e. series starts from the last letter of the word. Then keep on skipping 1 lette


iv) AEFG, BHIJ, ?, DNOP

a) CIJK
b) CFGH
c) CKLM
d) CKMN

View solution

Correct Option: (c)

There are two series in this question. 1st series is with the first letter only- ABCD. The second series involve the remaining letters- EFG, HIJ, KLM and NOP


C) Alphanumeric

In this type of series, problems asked with combination of alphabet, symbols and numbers.

i) 2E2, 1H9, 1K6, 1N3, ?

a) 1P4
b) 1J9
c) 1Q0
d) 1R8

View solution

Correct Option: (c)

This is alphanumeric type of question. In first term 2E2, E is 22nd letter from Z – So, 2E2.
Similarly, K is 16th letter from Z – So, 1K6.
So, Answer is 1Q0 – M is 10th letter from Z


ii) H8, L12, O15, S19, ?

a) U21
b) W23
c) V22
d) Y25

View solution

Correct Option: (c)

Alphabet letter of first term is H and number in it is 8 i.e. numerical position of H in alphabet. Same way in second term 12 is the numerical position of L in alphabet. Let’s find out difference between two terms. So, we got differences are +3, +2, +3, +2… So next term will be S + 2 letters from S = V. Thus answer is V22