3 Steps to solve Linear Arrangement Logical Reasoning for CAT Exam

Linear arrangement based logical reasoning questions in CAT deal with sequentially aligning the objects by using the information given about their positions.

In most of the cases, we have to identify the unique position of each of the objects or the relative position of one object compared to the other objects.

Often, logical reasoning questions on linear arrangements are relatively easier compared to other types. However, students who are new to logical reasoning might find it difficult to comprehend the conditions, and are likely to get confused with the multiple conditions given in the logical reasoning set.

With a structured preparation and step-by-step approach will help to conquer linear arrangement logical reasoning questions.

You may also try our Online Logical Reasoning Course which contains lots of sets with moderate to a higher difficulty level for practice.

In this article, we will discuss in detail the linear arrangement type of questions, demonstrating a method of solving such questions.

Types of linear arrangement logical reasoning questions

We have categorized linear arrangement questions based on the pattern in which the objects are to be arranged into two categories:

Single row arrangement
Multiple rows arrangements

As far as approach is concerned about both these types of linear arrangement questions, there is no difference at all. However, conditions given for multiple row arrangement questions may involve higher complexity.

Steps to solve linear arrangement questions

Unlike mathematics, there is no standard pattern for the logical reasoning questions. Therefore, the steps to solve any question on linear arrangement may differ from question to question.

However, below is the list of steps which we usually take in most of these questions, to organize the data and arrive at the solution.

1. Pictorial Representation

After reading the reasoning case, prepare a pictorial linear sequence depending on the number of objects given in the reasoning set.

For example, suppose the question that we have, asks us to arrange 5 people say, Abdul, Birbal, Chaman, Druv, and Ehsan in a row according to their Heights (tallest to shortest). And it is also mentioned that no two of them have the same height. Then,

We can use the following pictorial representation about their position in which they will be standing.

2. Use symbols to represent the condition given

For Example, if the condition says that Abdul is taller than Dhruv but shorter than Ehsan, then this condition can symbolically be expressed as E>A>D.

Another condition could be that there is exactly one person who is shorter than Birbal but taller than Chaman. One of the ways to represent this condition symbolically is B _ C.

There is no limit to the number of ways such symbolic representation can be done. There are no standard approaches which are universally followed. A student must devise his own symbolic representation with which he is comfortable.

My only suggestion would be your symbolic representation should be neat and unique. Neat, because you might have to come back to that representation, and unique so that you don’t confuse one symbol with the others.

3. Combine the constraints to get the optimal solution.

After representing the conditions the final step should be to optimize the constraint such that it meets all the conditions.

This is the most critical step where the students reasoning prowess and ability to organize the data come out in the open. With adequate practice, the right approach, and determination one can overcome this challenge.

Note: At times, you may not be able to identify the positions of each of the objects uniquely, and you have to consider multiple cases. Do try to figure out all possible cases.

To help you better, I have taken a question on the linear arrangement. And with the help of video explanation, I have demonstrated how to apply the above steps.