Linear Arrangements

Linear Arrangements

Linear Arrangements

Last Updated on Nov 11, 2019

The question of seating arrangement is a regular feature of almost every competitive examination. In these questions, you have to arrange a group of persons fulfilling certain conditions. This is also written as sitting arrangement or sitting arrangement reasoning at some places. Here we can classify these problems into 4 types:

1) Linear Arrangement: Here the arrangement of the persons is linear i.e. you have to arrange them in a line. Here generally a single row of arrangement is formed.

2) Double row arrangement: In these questions, there will be two groups of persons. You have to arrange one group in one row and the other group in other row. The persons in these rows normally face each other.

3) Circular arrangement: In the circular seating arrangement questions, you have to arrange the persons around a circular table etc. fulfilling certain conditions.

4) Rectangular arrangement: These arrangements are almost similar to the circular arrangements; the only difference is that the persons are sitting around a rectangular table.

Types of Information
  • Direct information: This is the information that is clearly mentioned in the statement of the question. This is the information that you will use when you start solving the questions
  • Indirect information: After filling the direct information you will look for the connection between different parts of the information. These connections form the indirect information.
    While arranging the persons, the direction to which the persons are facing is very important

In the case of circular arrangements questions, or rectangular arrangements, the persons may be facing the center of the circle or they may be looking away from the center.

If they are looking towards the center, then the right-hand side will be in the anti-clockwise direction and left-hand side will be in the clockwise direction.

If the persons are looking away from the center then the right-hand side will be in the clockwise direction and left-hand side will be in the anti-clockwise direction.

Next, while solving the questions related to linear arrangements or double row arrangements, the information regarding the position of the persons is very important. If it is written that A is sitting next to B, then it means that A and B are sitting together.

B may be to the right or left of A. Further if it is given that B is sitting to the right/left of A, then it does not mean that B is sitting immediate right/left of A. There may be some other persons sitting between A and B. If B is sitting immediate right/left of A then it will be mentioned in the statement of the question.

Example: Study the following information carefully and answer the questions given below:
D, E, F, G, H, P, Q and R are seated in a straight line but not necessarily in the same order. Some of them are facing south while some are facing North. G faces to south direction. D sits fourth to the left of P. P sits at one of the extreme ends of the line. Both the immediate neighbors of D face North. E sits second to left of R. R is not an immediate neighbor Of D. Neither R nor F sits at the extreme end of the line. F faces Opposite direction to G.

Both the immediate neighbors of F face North. H sits to the immediate left of Q. Immediate neighbors of G face opposite directions (i.e. if one neighbor of G faces North then the other faces South and vice-versa). Immediate neighbors of E face opposite directions (i.e., if one neighbor of E faces North then the other faces South and vice-versa). People sitting at the extreme ends face opposite directions (i.e., if one person faces north then the other faces South and vice-versa).

Who amongst the following sits second to the left of G?

  1. P
  2. E
  3. D
  4. R
  5. None of the Above

Answer: D

Reference: 

1. D sits fourth to left of P. P sits at one of the extreme ends of the line.
2. Both the immediate neighbors of D face North.
3. People sitting at the extreme ends face the opposite directions.
4. E sits second to left of R. R is not an immediate neighbor Of D. Neither R nor F sits at the extreme end of the line.
5. G faces to south direction. Immediate neighbors of G face opposite directions. Here, case 2 is eliminated.
6. H sits to the immediate left of Q. Both the immediate neighbors of F face North. We know that F will not sit at extreme end.
7. Immediate neighbors of E face opposite directions. Both the immediate neighbors of F face North.
Hence, D sits second to the left of G.

This video lays out the basics of Linear Arrangements. Understanding this topic well is necessary to solve questions that are asked in various competitive exams in the Logical Reasoning section - applicable to CAT, XAT, MAT, SNAP, IIFT, CLAT, AILET, DU LLB, any other entrance exam as well. For more such content, visit our website - examvictor.com

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