Linear Arrangements – Explained in Detail

Linear Arrangements 

Hello Readers

Today we will discuss Topic – Linear Arrangements. 

In linear arrangements, we have to arrange a group of persons in linear way i.e. in straight line or rows.


There are two types of Linear Arrangements:


  • Simple Arrangements – in this we have to arrange the persons only.
  • Complex Arrangements – In this we have to arrange the persons as well as the associated variables given in the questions.


Before discussing the examples, let’s understand some important points related to this topic.

As we have already discussed, that we have arrange the persons in these types of questions, we must know how to take the directions of the persons i.e. which is the direction (North/South) they are facing


Directions –


Generally, the directions given in these types of questions are North and South.


a) Persons facing North


linear arrangement Facing North


b) Persons facing South


linear arrangement Facing South


linear arrangement LA table

Statements –


Now, we will discuss about the different statements that are generally used in questions to give directions of the persons or associated variables. These statements are similar to the statements that we have discussed in Circular Arrangements.


a) Whenever sentences are combined with Conjunction like and, but, while, whereas, etc. than it is in the reference of the first person given in the statement.


linear arrangement 1


b) Whenever sentences are combined with Pronouns like who, which etc. than it is in the reference to the person preceding pronoun.


linear arrangement 2

In both Linear and Circular Arrangements, we have to arrange the persons. But there is difference between the two arrangements while we start arranging the persons or associated variables.


a) Circular Arrangements – No fixed starting point

linear arrangement 1


b) Linear Arrangements –


linear arrangement LA 2


Let’s discuss some examples –


Example – Simple Arrangement

Seven students A, B, C, D, E, F and G are standing in a line facing North. G is to the right of D and to eh left of B. A is on the right of C, A, and D have one child between them. E and B have two children between them.D and F two children between them.


1) Who is on the extreme right ?

a) B

b) E

c) F

d) G

e) None of these


2) Who is exactly in the middle?

a) A

b) C

c) D

d) E

e) None of these


8) Who is on the extreme left?

a) A

b) B

c) C

d) D

e) None of these


Solution –

linear arrangement LA 3


Example –Complex Arrangement


Read the following information carefully to answer these questions –


a) Six flats on a floor in two rows facing North and South are allotted to P, Q, R, S, T and U.

b) Q gets North facing flat and is not next to S.

c) S and U get diagonally opposite flats.

d) R, next to U, gets South facing flat and T gets North facing flat.


1) Flats of which of the other pairs than SU, are diagonally opposite?

a) QP

b) PT

c) QR

d) TS


2 Which of the following combination gets South facing flats?

a) UPT

b) URP

c) QTS

d) Data Inadequate


Solution – 

linear arrangement LA 4


linear arrangement LA 5


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