These Number Series, Coding and Decoding – CA Foundation Logical Reasoning Questions are designed strictly as per the latest syllabus and exam pattern.
Number Series, Coding and Decoding – CA Foundation Logical Reasoning Questions
1. Number Series
Arrangement of numbers which follows a particular rule in a certain order is called Number series. In the series, some number is wrongly putted OR some number is missing. We need to observe and find the accurate number to the series of numbers.
Examples : 2, 4, 6, 8, is a series, because it follows a particular rule/pattern.
According to this rule, next number will be 10.
First of all we have to decide that what type of series are given in papers & according to that we have to use shortcut tricks as fast as we can.
Different types of Number Series
Perfect Square Series:
This type of Series are based on square of a number which is in same order and one square number is missing in that given series.
Example 1:
400, 441, 484, 529, 576 , ?
Answer:
400 = 202; 441 = 212, 484 = 222, 529 = 232, 576 = 242, 625 = 252.
Perfect Cube Series:
This type of Series are based on cube of a number which is in same order and one cube number is missing in that given series.
Example 2 :
1000, 1331, 1728, 2197, ?
Answer:
1000 = 103, 1331 = 113, 1728 = 123, 2197 = 133, 2744 = 143
Geometric Series:
This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.
Example 3:
45, 405, 3645, 32805 , ?
Answer:
45 × 9 = 405, 405 × 9 = 3645, 3645 × 9 = 32805; 32805 × 9 = 295245
Difference Series: Here difference between two consecutive terms OR difference between alternate terms are equal OR these difference make an another series.
Example 4 :
7, 12, 17, 22, ………………
Answer:
Here difference between two consecutive terms is equal i.e. 5 ;
Next term = 22 +5 = 27
Ratio Series : Here the ratio OR division of two consecutive terms are equal, ft is same pattern for altemate terms.
Example 5:
8, 24, 72, 216, ……………
Answer:
24/ 8 = 3; 72/24 = 3; 216 /72 = 3 ;
Next term = 216 × 3 = 648
Prime Number: Series of prime numbers.
Example 6 :
2, 5, 11, 19, 29, ………….
Answer:
It is a series of prime numbers. Here, between two consecutive prime numbers, there is one missing prime number. After 29 next prime number is 31. Leave it. Hence
Next term = 37
Mixed Series : It is combination of two or more different type of series.
Example 7 :
3, 4 ,7, 9, 11, 16, 15, 25, 19, …………….
Answer:
Here 1st, 3rd, 5th, 7th, 9th term are in Arithmetic progression while 4, 9, 16, are squares of consecutive numbers.
Hence Next Term = 52 = 25.
Arithmetic Progression / Series : Here arrangement of numbers makes an Arithmetic Progression.
Example 8 :
100, 95, 90, 85, …………………
Answer:
It is in AP. Here difference between two consecutive terms is equal.
Hence Next Term = 80.
Geometric Progression / Series.: Here arrangement of numbers makes a Geometric Progression.
Example 9 :
4, 12, 36, 108, ………..
Answer:
It is in GP. Here ratio between two consecutive terms is equal.
Hence Next Term = 108 × 3 = 324.
Two-Tier Arithmetic or Geometric Series : In this series, difference between two consecutive terms makes an Arithmetic or Geometric progression or series.
Example 10 :
2, 5, 10, 17, 26, ………………..
Answer:
Here (5 – 2 = 3); (10 – 5 = 5); (17 – 10 = 7); (26 – 17 = 9) i.e. difference of consecutive terms 3; 5; 7; 9; …are making Arithmetic progression.
Hence next difference = 11. & Next term = 26 + 11 = 37
Example 11 :
2, 5, 11, 23, 47, ……………….
Answer:
Here (5 – 2 = 3); (11 – 5 = 6); (23 – 11 = 12); (47 – 23 = 24) i.e. difference of consecutive terms 3; 6; 12; 24; …are making Geometric progression.
Hence next difference = 48. & Next term = 47 + 48 = 95
Alphabet Series :
Questions are also asked relating to positions of English alphabets. This topic is very important from examination point of view. So we need to memorize the positions of the alphabets so that we can handle each and every question based on this topic. If it is not memorised, then write these letters sequence as given below on blank page of the Question paper with their positions from both ends as given below :
Going forward & backward both.
On that basis we will try to understand the logic behind the series or sequence of letters, numbers or alphanumeric. There are some important assumptions given below for solving the letter series questions.
Check some points as (i) whether it is a continuous series or not (ii) Missing terms in the series (iii) Immediate next or before term of the series (iv) Squares or cubes of numbers (v) Mathematical operations like addition, subtraction, multiplication or division (vi) Arithmetic or Geometric series or Harmonic series.
Example 1:
A, E, J, O, ?
(a) T
(b) S
(c) V
(d) None
Solution:
First, we write the position of letters of given question. They are 1, 5, 10, 15, in AP
Hence next position = 20. Letter at this position is T.
So, (a) is correct.
Example 2:
C, G, K, O, ?
(a) T
(b) S
(c) U
(d) None
Solution:
First, we write the position of letters Of given question. They are 3, 7, 11, 15, inAP
Hence next position = 19. Letter at this position is S.
So, (6) is correct.
Example 3 :
A, D, H, M, S, ?
(a) X
(b) Y
(c) Z
(d) None
Solution:
First, we write the position of letters of given question. They are 1, 4, 8, 13, 19
It can be understand as (1 +3 = 4); (4 + 4 = 8); (8 + 5 = 13); (13 + 6 = 19).
So , Next term should be 19 + 7 = 26.
Hence, Letter at 26th position is Z.
So, (c) is correct.
Example 4 :
AK , FP, KU , ? , UE , ZJ
(a) PZ
(b) KT
(c) JU
(d) None
Solution:
(a) is correct.
First, we write the position of letters of given series. They are:
(1, 11), (6, 16), (11, 21) , ? , (21, 5), (26, 10).
Clearly we see that the first numbers of each pair making a definite pattern as 1, 6, 11, ?, 21, 26;
Difference between two successive terms = 5. So, 4th term = 11 + 5 = 16. Letter at this position is P.
Similarly, we see that the 2nd numbers of each pair making a definite pattern as 11, 16, 21, ?, 5, 10.
If all alphabets are put on circle to make it as cyclic order, we consider that after Z (26th position), position will start from A i.e. 1st position. Here, try to understand the sequence as (11 + 5 = 16); (16 + 5 = 21) ; (21 + 5 = 26); (0 + 5 = 5); (5 + 5 = 10). So 4th term = (21 + 5 = 26). Letter at this position = Z.
Hence ordered pair in terms of letter is (PZ).
Hence option (a) is correct.
Letter Series & Continuous Pattern Series
Letter Series type questions usually consists of a series of small letters which follow a specific pattern. However, some letters are missing from the set. The students need to identify the missing letter in the series. These missing letters are then given in proper order as one of the alternatives. Thus, the candidates can know the tips to solve the Letter Series Logical Reasoning Questions by practicing. To understand the tips of the Letter Series, first of all, the candidates must have the knowledge of the alphabetical order, its numerical position, and its opposite word. Some examples are given below:
Example 1.
QPO, NML, KJI, ______, EDC
(a) HGF
(b) CAB
(c) JKL
(d) GHI
Solution:
(a) is correct. All terms in reverse order.
Directions : In each of the following letter series, some of the letters are missing which are given in that order as one of the alternatives below it. Choose the correct alternative.
Example 2.
__ ___ aba __ ___ ba ___ ab
(a) abbba
(b) abbab
(c) baabb
(d) bbaba
Solution:
(b): The series is ab/ab/ab/ab/ab/ab. Thus, the pattern ‘ab’ is repeated.
Odd Man Out: In this type of question, all options follow a particular character except one option. That exception a option is called Odd Man Out or Odd One Out.
Example 1:
Find odd man out of the following:
2, 3, 5, 7, 11, 13, 17.
(a) 2
(b) 11
(c) 7
(d) 13
Solution:
(a) is correct.
All are odd & prime number except 2 which is even & prime number.
Example 2:
Find odd man out of the following:
1, 3, 5, 7, 11, 13, 17.
(a) 1
(b) 11
(c) 7
(d) 13
Solution:
(a) is correct.
All are prime number except 1 which is neither prime nor composite.
Example 3 :
Find odd man out of the following:
(a) 13
(b) 17
(c) 23
(d) 63
Solution:
Each of the numbers except 63, is a prime number. Hence, the answer is (d).
Example 4 :
Find odd man out of the following:
(a) 15
(b) 25
(c) 37
(d) 49
Solution:
Clearly, 37 is the only prime number in the group. Hence, the answer is (c).
Example 5 :
Find odd man out of the following:
(a) 16
(b) 36
(c) 78
(d) 256
Solution:
Each of the numbers except 78, is a perfect square. Hence, the answer is (c).
Example 6 :
Find odd man out of the following:
(a) 8
(b) 28
(c) 343
(d) 125
Solution:
Each of the numbers except 28, is a perfect cube. Hence, the answer is (b).
Example 7 :
Find odd man out of the following:
(a) 21
(b) 36
(c) 49
(d) 56
Solution:
Each of the numbers except 36, is divisible by 7. Hence, the answer is (b).
Example 8 :
Find odd man out of the following:
(a) 295
(b) 381
(c) 552
(d) 729
Solution:
Each of the numbers except 552, is an odd number. Hence, the answer is (c).
Example 9 :
Find odd man out of the following:
1, 4, 9, 16, 19, 36, 49, 64, 81
(a) 9
(b) 19
(c) 49
(d) 16
Solution:
(b) is correct.
All except 19 are perfect square. Square root of 19 does not give a whole number. Hence, the answer is (b).
2. CODING – DECODING
A CODE is a system of words, letters, figures, or symbols used to represent others, especially for the purposes of secrecy. Therefore, Coding is a method of transmitting a message between the sender and the receiver without knowing it by a third person. The Test of Coding and Decoding is set up to judge the candidate’s ability.
LETTER CODING
In this case, the letters in a word are replaced by certain other letters according to a specific rule to make its code. The candidate is required to detect the pattern or rule and answer the questions according to that rule.
Example 1.
In a certain code, TEACHER is written as VGCEJGT. How is CHILDREN written in that code ? (B.T.M. 2006)
(a) EJKNEGTP
(b) EGKNEITP
(c) EJKNFGTO
(d) EJKNFTGP
Solution:
First of all, compare 1st letter of both words i.e. compare V with T. Clearly V is 2 steps ahead with respect of T. Similarly compare remaining letters as above accordingly. We get as
Similarly, posting letters which are 2 steps ahead with respect to each letter of the word CHILDREN; we get the required result as given below.
Hence, the answer is option (d).
Example 2.
If HEALTH is written as GSKZDG, then how will NORTH be written in that code ? (M.C. A. 2005)
(a) OPSUI
(b) GSQNM
(c) FRPML
(d) IUSPO
Solution:
Analysing it, we get that : 1st reverse the order of letters of the word HEALTH as
HTLAEH then compare it with the letters of the coded word GSKZDG We get as
Similarly doing as above, we get as : Reversing the order of letters in NORTH, we get HTRON.
Hence , the required code is GSQNM . So, the answer is (b).
Previous Year Exam Questions
Question 1.
In a certain code, RIPPLE is written as 613382 and LIFE is written as 8192. How is PILLER written in that code? [1 Mark, May 2018]
(a) 318826
(b) 318286
(c) 618826
(d) 338816
Solution:
(a)
Hence code of PILLER is 318826.
Question 2.
In a certain code ‘256’ mean ‘you are good’, ‘637’ means ‘we are bad’ and ‘358’ means ‘good and bad’. Which of the following represents ‘and’ in that code? [1 Mark, May 2018]
(a) 2
(b) 5
(c) 8
(d) 3
Solution:
(c)
256 means ‘Your are good’
637 means ‘We are Bad’
358 means ‘Good and Bad’
Here, word “ good “ is common in 1 st & 3rd sentence and 5 is common in 1 st & 3rd. So, Code of good is 5 . BAD is common in 2nd & 3rd. Hence Code of‘bad ’ is 3. So, Code of “and” is 8.
Question 3.
If LOSE is coded as 1357 and GAIN is coded as 2468, what do figure 82146 for?
(a) NGLAI
(b) NGLIA
(c) GNLIA
(d) GNLA
Solution:
(a)
Code for 82146 is NGLAI
Question 4.
If PLAY is coded as 8123 and RHYME is coded as 49367. What will be code of MALE ? [1 Mark, Nov. 2018]
(a) 6217
(b) 6198
(c) 6395
(d) 6285
Solution:
(a)
Question 5.
Find out the next number in the following series 7,1 1, 13, 17, 19, 23, 25, 29? [1 Mark, Nov. 2018]
(a) 30
(b) 31
(c) 32
(d) 33
Solution:
(b) Given series
Question 6.
If HONEY is coded as JQPGA, which word is code as VCTIGVU ? [1 Mark, Nov. 2018]
(a) CARPETS
(b) TRAPETS
(c) TARGETS
(d) UMBRELU
Solution:
(c)
Question 7.
Find odd man out of the following series 15, 21, 63, 81, 69 [1 Mark, Nov. 2018]
(a) 15
(b) 21
(c) 63
(d) 81
Solution:
(d) 15, 21, 63, 81, 69
In this series only 81 is a Perfect square.
Question 8.
Find odd man out of the following series 7, 9, 13, 17, 19 [1 Mark, Nov. 2018]
(a) 1
(b) 9
(c) 19
(d) 13
Solution:
(b) 7, 9, 13, 17, 19
Since only 9 is a perfect square. So, 9 is the odd man out.
OR.
Note :- If 11 is used at the place of 9, we get a perfect series.
Question 9.
7, 23, 47, 119, 167 [1 Mark, June 2019]
(a) 211
(b) 223
(c) 287
(d) 319
Solution:
(c)
7, 23, 47, 119, 167, 287
32 – 2 = 1
52 – 2 = 23
72 – 2 = 41
112 – 2 = 119
132 – 2 = 167
172 – 2 = 287
Question 10.
Which of the following is odd one 4, 12, 44, 176, 890? [1 Mark, June 2019]
(a) 4
(b) 12
(c) 44
(d) 176
Solution:
(c)
4, 12, 44, 176, 890,
4 × 2 + 4= 12
12 × 3 + 6 = 42
42 × 4 + 8 = 176
176 × 5 + 10 = 890
Question 11.
If in a certain language, MADRAS is coded as NBESBT. How is BOMBAY coded in that language ? [1 Mark, June 2019]
(a) CPNCBX
(b) CPNCBZ
(c) CPOCBZ
(d) CQOCBZ
Solution :
(b)
Question 12.
Which of the following is odd one? [1 Mark, June 2019]
(a) CEHL
(b) KMPT
(c) OQTX
(d) NPSV
Solution:
(d)
So NPSV is odd one.