Number Series, Letter Series, Codes and Relationships

It is an important topic in reasoning, especially for UGC NET Paper 1. In series completion, the term follows a certain pattern throughout. The candidate is required to identify the pattern either to complete the given series with the most suitable option or to find the wrong or missing term in the series.

Series Completion

There are three types of series completion:

UNIT V – Reasoning (including Mathematical) (Click on the topic to read)

Types of reasoning
Number series, Letter series, Codes and Relationships. (You are reading this topic)
Mathematical Aptitude (Fraction, Time & Distance, Ratio, Proportion and Percentage, Profit and Loss, Interest and Discounting, Averages etc.).

UGC NET Study Materials for Paper 1 (eBook with MCQs) Download Now

1. NUMBER SERIES

In this of series completion, you have to find out the next or the wrong or the missing number in the series, which follows a particular pattern.

E.g., Which number would replace the question mark (?) in series 2, 7, 14, 23, ?, 47
(a) 28 (b) 34 (c) 31 (d) 38

Ans.: The given sequence is +5, +7, +9, and so on.
i.e. 2+5 =7, 7 +7 =14, 14 +9 = 23

The missing number would be, 23+11 = 34.
Q. Which is the number that should come next in the following series? 4, 6, 12, 14, 28, 30, ——
(a) 32 (b) 64 (c) 62 (d) 60

Ans.: The given sequence is a combination of two series 4, 12, 28, …. and 6, 14, 30, ….
Clearly the number to be found belongs to the first series. Now the pattern followed is +8, +16, +32.
So, the missing number = (28 + 32) = 60, Hence, the answer is (d)

Q. Find the wrong number in the series. 7, 28, 63, 124, 215, 342
(a) 7 (b) 28 (c) 124 (d) 215

Ans.: The right sequence is 2³ – 1, 3³ – 1, 4³ – 1, …etc.
Here 28 is wrong; so the answer is (b)

2. ALPHABET SERIES

Alphabet series consists of alphabets placed in a specific pattern. If you keep in your mind the order of the alphabet with their respective position (number), it will help you answer the questions quickly. We all know that the total alphabets are 26.
We can arrange in ascending and descending order, like

E.g.: What will be the next term in BKS, DJT, FIU, HHV,?
(a) IJX (b) IGX (c) JGW (d) IGU

Ans: (c). In each term, the first letter is moved two steps forward, the second letter one step backward, and the third letter one step forward to obtain the corresponding letter of the next term. So, the missing term is JGW.

3. LETTER SERIES

This type of question usually consists of a series of small letters that follow a certain pattern. However, some letters are missing from the series. The candidate is required to choose this alternative as the answer.

Eg: aab – aaa – bba –

(a) baa (b) abb (c) bab (d) aab

The first blank space should be filled in by ‘b’ so that we have two a’s followed by two bs.
The second blank space should be fiiled in either by ‘a’. So that we have four as followed by two b or by ‘b’. So that we have three as followed by three b.
The last space must be filled in by ‘a’.
Thus we have two possible answers – ‘baa’ and ‘bba’. But only ‘baa’ appears in the alternatives. So the answer is (a).
In case we had both the possible answers in the alternatives, we should choose the one that forms a more prominent pattern, which is aabb/aaabbb/aa. and our answer would have been ‘bba’.

CODING-DECODING

A code is a system of signals. Therefore, coding is a method of transmitting messages between the sender and receiver without any knowledge of a third party. The Coding-Decoding test is set up to judge the candidate’s ability to decipher the law that codes a particular message and break the code to reveal the message.

TYPES OF CODING-DECODING

LETTER CODING
In this type of reasoning, the letters are coded in another letters and we have to find out the pattern. After finding the pattern, we have to ask to identify the code for the given letters.

E.g: If COURSE is coded as FRXUVH, how is RACE coded in that code?
(a) HFDU (b) UCFH (c) UDFH (d) UDHF

In the given code, each letter is moved three steps forward than the corresponding letter in the word. So R is coded as U, A as D, C as F, E as H. Hence (c) is the answer.

NUMBER CODING

In this type of questions, either numerical code values are assigned to a word or alphabetical code values are assigned to numbers. The candidate is required to analyse the code as per directions.

E.g.: If in a certain code ROPE is coded as 6821, CHAIR is coded as 73456. What will be the code for CRAPE?
(a) 73456 (b) 76421 (c) 77246 (5) 77123

Clearly, in the given code, the alphabets are coded as follows.
R O P E C H A I
6 8 2 1 7 3 4 5

So, CRAPE is coded as 76421. Then, the answer is (b)

DECODING

In these questions, artificial or code values are assigned to a word or a group of words and the candidate is required to find out the original words.

E.g: If in a certain language FLOWER is written as EKNVDQ, what will be written as GNTRD?

(a) HEOUS (b) HOUES (c) HUOSE (d) HOUSE

Each letter of the word is one step ahead of the corresponding letter of the code.

Thus, HOUSE is written as GNTRD, So the answer is (d)

Blood Relation

A person who is related to another by birth rather than by marriage.

Blood relations of a group of persons are given in jumbled form. In this type of reasoning, the success of a candidate depends upon knowledge of the Blood Relations, some of which are summarised below. The questions which are asked in this section depend upon Relation.

To remember easily the relations may be divided into two sides as given below:

Relations of Paternal side:

Father’s father → Grandfather
Father’s mother → Grandmother
Father’s brother → Uncle
Father’s sister → Aunt
Children of uncle → Cousin
Wife of uncle → Aunt
Children of aunt or uncle → Cousin
Husband of aunt → Uncle

Relations of Maternal side:

Mother’s father → Maternal grandfather
Mother’s mother → Maternal grandmother
Mother’s brother Maternal uncle
Mother’s sister → Aunt
Children of maternal uncle → Cousin
Wife of maternal uncle → Maternal aunt

Other Relation

Grandfather’s son » Father or Uncle
Grandmother’s son » Father or Uncle
Grandfather’s only son » Father
Grandmother’s only son » Father
Mother’s or father’s mother » Grandmother
Son’s wife » Daughter-in-Law
Daughter’s husband » Son-in-Law
Husband’s or wife’s sister » Sister-in-Law
Brother’s son » Nephew
Brother’s daughter » Niece
Uncle or aunt’s son or daughter » Cousin
Sister’s husband » Brother-in-Law
Brother’s wife » Sister-in-Law
Granson’s or grand daughter’s daughter » Great grand daughter

Relations from one generation to next:

Examples: Pointing to a photograph of a boy Suresh said, “He is the son of the only son of my mother.” How is Suresh related to that boy?

a) Brother b) Cousin c) Uncle d)Father
Answer: D
Explanation: The boy in the photograph is the only son of the son of Suresh’s mother i.e., the son of Suresh. Hence, Suresh is the father of boy.

Example: Pointing to a photograph Lata says, “He is the son of the only son of my grandfather.” How is the man in the photograph related to Lata?
a) Brother b) Uncle c) Cousin d) Data is inadequate
Answer: Option A
Explanation: The man in the photograph is the son of the only son of Lata’s grandfather i.e., the man is the son of Lata’s father. Hence, the man is the brother of Lata.

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