Number Series, Coding and Decoding and Odd Man Out Chapter Notes | Quantitative Aptitude for CA Foundation PDF Download

Series

Number Series

Case 1: Missing Terms of the Series

•  In this type of question, you need to identify the missing term in the series based on a specific pattern or rule that governs the series. 
•  Your task is to detect the missing number in the series and answer the question accordingly. 

Example 1: Find the missing term of the series 2, 7, 16, ______ , 46, 67, 92 

Explanation: The pattern in the series involves increasing the numbers by progressively larger amounts: 
+5, +9, +13, +17, +21, +25, ... 
So,
2 + 5 = 7 
7 + 9 = 16 
Therefore, the missing term is: 16 + 13 = 29 

Example 2: Find the wrong term in the series 9, 29, 65, 126, 217, 344 

Explanation: The correct pattern in the series is: 
2³ + 1; 3³ + 1; 4³ + 1; 5³ + 1; 6³ + 1; 7³ + 1 
Here, 29 is the incorrect term in the series. 

Example 3: Find the missing term of the series 1, 9, 25, 49, 81, 121, ............. 

Solution: The given terms in the series are the squares of consecutive odd numbers: 
1², 3², 5², 7², ... 
So, the missing value is: 13² = 169 

Alphabet Series

In an alphabet series, letters of the alphabet are arranged in a specific pattern, often based on their position in the alphabet. For example, the series can start with the letters in order from A to Z, which corresponds to the numbers 1 to 26, and then continue in reverse order from Z to A, which corresponds to the numbers 26 to 1. 

 Example 4: In the given series, BKS, DJT, FIU, HHV, each term follows a pattern where: 

•  The first letter is moved two steps forward in the alphabet. 
•  The second letter is moved one step backward in the alphabet. 
•  The third letter is moved one step forward in the alphabet. 

Letter Series 

In these questions, you are given a series of small letters that follow a specific pattern, but some letters are missing from the series. Your task is to identify the missing letters, which are provided as options. 
Example 5: aab, ____, aaa, bba, ____
(a) baa
(b) abb
(c) bab
(d) aab 

First Blank: The first blank should be filled with 'b' to maintain the pattern of two 'a's followed by two 'b's. 
Second Blank: The second blank should be filled with 'a' to ensure there are three 'a's followed by three 'b's. 
Third Blank: The last blank must be filled with 'a'. 
Possible Answers: This leads to two possible answers: 'baa' and 'bba'. 
Correct Option: However, only 'baa' is present in the alternatives. 
Therefore, the correct answer is (a) 'baa'. 

Coding and Decoding

Before transmitting, the data is encoded and at receiver side encode data is decoded in order to obtain original data by determining common key in encoded data.
The Coding and Decoding is classified into the following types.

• Type 1: Letter Coding
• Type 2: Number Coding

Type 1: letter Coding

In these type the real alphabets in a word are replaced by certain other alphabets according to a specific rule to form its code. The candidate is required to detect the common rule and answer the questions accordingly.

Case1: To form the code for another word
Example 6: If in a certain language MYSTIFY is coded as NZTUJGZ, how is MENESIS coded in that language?

Explanation: Clearly, each letter in the word MYSTIFY is moved one step forward to obtain the corresponding letter of the code.

So, in MENESIS, N will be coded as O, E as F, M as N and so on. Thus, the code becomes NFOFTJT. 

Example 7: If TAP is coded as SZO, then how is FRIEND coded? 

Explanation: Clearly each letter in the word TAP is moved one step backward to obtain the corresponding letter of the code.

Thus, in FRIEND, F will be coded as E, R as Q , I as H, E as D, N as M and D as C. So, the code becomes EQHDMC.

Example 8: In a certain code, MENTION is written as LNEITNO. How is PRESENT written in that code?

Explanation: Clearly, to obtain the code, the first letter of the word MENTION is moved one step backward and the remaining letters are Reversed in order, taking two at a time. So, in PRESENT, P will be coded as O, and the sequence of the remaining letter in the code would be ERESTN. Thus the code becomes OERESTN. Hence, The answer is OERESTN.

Case 2: To find the word by analysing the given code (DECODING)
Example 9: If in a certain language CARROM is coded as BZQQNL, which word will be coded as HORSE?

Explanation: Each letter of the word is one step ahead of the corresponding letter of the code

So, H is coded as I, O as P, R as S, S as T and E as F. HORSE is coded a IPSTF.

Type 2: Number Coding

In these questions, either numerical code values are assigned to a word or alphabetical code letters are assigned to the numbers. The candidate is required to analyse the code as per the directions. © The Institute of Chartered Accountants of India
Case 1: When a numerical code values are assigned to words.
Example 10: If in a certain language A is coded as 1, B is coded as 2, and so on, how is AICCI is coded in that code?

Explanation: As given the letters are coded asSo in AICCI, A is coded as 1, I as 9,and C as 3. Thus, AICCI is coded as 19339.

Example 11: If PAINT is coded as 74128 and EXCEL is coded as 93596, then how would you encode ANCIENT ?

Explanation: Clearly, in the given code, the alphabets are coded as follows:So, in ANCIENT, A is coded as 4, N is coded as 2, C as 5, I is coded as 1, E as 9, and T as 8. Hence, the correct code is 4251928.

Case 2: Number to letter coding.
Example 12: In a certain code, 2 is coded as P, 3 as N, 9 as Q, 5 as R, 4 as A and 6 as B. How is 423599 coded in that code?

Explanation: Clearly as given, 4 as A, 2 as P, 3 as N and 5 is coded as R, 9 as Q. So, 423599 is coded as APNRQQ.

Odd Man Out

Classification means ‘to assort the items’ of a given group on the basis of a certain common quality they possess and then spot the stranger or ‘odd one out’.
These questions are based on words, letters and numerals. In these types of problems, we consider the defining quality of particular things. In these questions, four or five elements are given, out of which one does not belong to the group. You are required to find the ’odd one’.
Example 13: January, May, July, November
(a) January
(b) May
(c) July
(d) November
Ans: (d)

Explanation: All the months above are 31 days , whereas , November 30 days

Example 14: 14: 10, 14, 16, 18, 23, 24 and 26

(a) 26

(b) 17

(c) 23

(d) 9
Ans: (c)
Explanation: Each of the above series are even number, except 23.

Example 15: 6, 9, 15, 21, 24, 26, 30
(a) 9
(b) 26 
(c) 24
(d) 30
Ans: (b)

Explanation: All are multiples of 3, except 26, answer (b)

Example 16: 1, 5, 14, 30, 51, 55, 91
(a) 5
(b) 55
(c) 51
(d) 91
Ans: (c)

Explanation: Each pattern is 12, 12 + 22, 12 + 22 + 32, 12 + 22 + 32 + 42, 12 + 22 + 32 + 42+ 52, 12 + 22 + 32 + 42 + 52 + 62
But 51, is not of the form.

Example 17: 16, 25, 36, 62, 144, 196, 225
(a) 36 
(b) 62 
(c) 196 
(d) 144
Ans: (b)

Explanation: Each of the number except 62, is a perfect square.