CAT Logical Sequence : Basic Concepts and Notes PDF

What is Logical Sequence

Logical sequence questions, often found in aptitude tests or IQ assessments, require individuals to identify a pattern or rule governing a series of numbers, letters, or symbols. Students are then asked to apply this pattern to predict the next item in the sequence or fill in a missing element.

Example:
In the series you provided (2, 5, 10, 17, ---, 37), let's try to identify the pattern:
5 - 2 = 3
10 - 5 = 5
17 - 10 = 7
It seems that the differences between consecutive terms are increasing by 2 each time. Therefore, if we continue this pattern:
17 + 9 = 26
So, the missing number in the series is 26. The complete series would be 2, 5, 10, 17, 26, 37.

Types of Logical Sequence Questions

 Logical sequences can be broadly categorized into two types: alphabet-based sequences and number-based sequences.

1. Alphabet-based Sequences:

In alphabet-based sequences, the pattern or rule governing the sequence is based on the order of letters in the alphabet. This can involve skipping letters, following a specific pattern, or applying transformations to the letters.
Example:
Consider the sequence - A, C, E, G, ---, K
In this case, the pattern is an alphabetical order with a step of two letters. The missing letter is "I," and the complete sequence is A, C, E, G, I, K.

2. Number-based Sequences:

Number-based sequences involve a pattern or rule applied to a series of numbers. The pattern can be based on addition, subtraction, multiplication, division, or any other mathematical operation.
Example:

Take the sequence - 2, 4, 8, 16, ---, 64
Here, the pattern is a doubling of the previous number. So, the missing number is obtained by doubling 16, resulting in 32. The complete sequence is 2, 4, 8, 16, 32, 64.

Understanding the distinction between these two types of sequences is crucial when solving logical sequence questions. It requires keen observation and an analytical mindset to identify the underlying pattern correctly. Whether it's identifying letter patterns or numerical relationships, these types of questions assess one's ability to recognize and apply logical rules in a systematic manner.

Tips and Tricks

1. Practice Regularly: Familiarize yourself with different types of patterns and sequences by practising a variety of problems regularly. This builds your pattern recognition skills.

2. Identify the Type: Quickly categorize the sequence as number-based or alphabet-based. This initial classification can guide your approach in solving the problem.

3. Start Simple: Begin by looking for straightforward patterns like arithmetic progressions, geometric progressions, or alphabetical order. Sometimes, the solution is apparent with a basic analysis.

4. Check for Alternate Patterns: Be open to the possibility of multiple patterns in the same sequence. There might be more than one logical rule governing the series.

5. Use Options Strategically: If the question provides answer choices, plug them into the sequence to see if they follow the identified pattern. This can help you confirm your solution.

6. Check Endpoints: Examine the endpoints of the sequence. The rules might apply differently to the first and last elements.

7. Elimination Technique: Eliminate answer choices that clearly do not follow any logical pattern. This increases your chances of selecting the correct answer even if you're uncertain.

Remember, with regular practice and exposure to different types of sequences, you'll develop a sharper intuition for recognizing patterns, making it easier to tackle these questions efficiently in competitive exams.

Solved Examples

Question 1: Find the missing letters in the pattern:

E_G_EFF_E_FG_FG_EF
(a) GFGEEE
(b) FGGGEF
(c) FGGEEG
(d) EGFEFG

Correct Answer is Option (c)
The series follows, +1,+1,+0 addition pattern.
So going by options, we get Option C to be correct.

Question 2: Find the missing letters in the pattern:

_CAM_AMC_M_A_CAM
(a) CMAMC
(b) MACAM
(c) MCAMC
(d) MCACM

Correct Answer is Option (d)

This is a Series with MCA blocks repreated.
So, Our series must be
MCA MCA MCA MCA MCA M
Going by Options, We see Option D is correct

Question 3:  2, 3, 8, 27, 112, ? 
(a) 156
(b) 224
(c) 375
(d) 565

Correct Answer is Option (a)
This series follows the rule of *2 and *2+ last term.
15*2 =30
30*2 +15= 75
75*2 = 150.
Thus, 150 is the wrong term.

Question 4: What will be the next term in? 
ZAM, YBL, ----, WDJ, VEI
(a) XCK
(b) UFH
(c) ZAC
(b) PFD

Correct Answer is Option (a)
Look at the middle term.
We see the following Series.
A B C D E
Thus C is missing.
Going by options, We get A to be correct.

Question 5:  What will be the next term in? 
G, T, I, R, K, P, ___,___
(a) M,N
(b) O,P
(c) Q,R
(d) S,T

Correct Answer is Option (a)
In the number System of the digits, we see the series relates to an alternating +2,-2 series.
Number the letters, we get the following : 7,20,9,18,11,16. So the next two terms will be 13th and 14th term. Which are : M and N
Thus, Option A.

Question 6: Find the wrong number in the given series?
3, 6, 11, 18, 29, 38, 51, 66
(a) 18
(b) 29
(c) 38
(d) 51

Correct Answer is Option (b)
The next term of the series is denoted by adding consecutive odd terms starting from 3
3+3=6
6+5 =11
11+7=18
18+9=27
27+11 =38
Since we have 29 in place of 27. It is the wrong term

Question 7: Find the wrong number in the given series?
9, 28, 65, 126, 217, 344, 213
(a) 65
(b) 126
(c) 217
(d) 213

Correct Answer is Option (d)
The series is an increasing series.
213 the last term is a smaller term that the previous one.
Thus it is Wrong.

Question 8: Arrange the words given below in a meaningful sequence.

1. Rainbow   2. Rain   3. Sun   4. Happy   5. Child     

(a)    4, 2, 3, 5, 1

(b)    2, 3, 1, 5, 4

(c)    4, 5, 1, 2, 3

(d)    2, 1, 4, 5, 3

Correct Answer is Option (b)

The correct order is :

Rain(2)  →  Sun(3)  →  Rainbow(1)  →  Child(5)  →  Happy(4)

Question 9: Arrange the words given below in a meaningful sequence.

1. Probation    2. Interview    3. Selection

4. Appointment    5. Advertisement    6. Application

(a)   5, 6, 3, 2, 4, 1

(b)   5, 6, 4, 2, 3, 1

(c)   5, 6, 2, 3, 4, 1

(d)   6, 5, 4, 2, 3, 1

Correct Answer is Option (c)

The correct order is :

Advertisement(5)  →  Application(6) →  Interview(2) →  Selection(3)  →  Appointment(4) →  Probation(1)

Question 10: Find the missing series.

G2X, J4V, M8T, ?, S32P

(a) N64S
(b) P16R  
(c) Q16R
(d) P8S

Correct Answer is Option (b)

Explanation:

G + 3 = J + 3 = M + 3 = P + 3 = S

2 * 2 = 4 * 2 = 8 * 2 = 16 * 2 = 32

X - 2 = V - 2 = T - 2 = R - 2 = P