As the name suggests, linear seating arrangement problems are those where arrangements are made in rows or lines. The arrangement can be in a single row, or there can be multiple rows, but generally, tworow questions are asked.
Onerow problems are those when the arrangement is made in a single line.
These problems can be divided into two types of conditions:
In the tworow arrangement, objects are arranged in two different rows facing each other. Now we can move on to solve an example of linear arrangement so that we have a better understanding of these types of questions.
But before moving forward with an example, keep in mind these important points:
If A is sitting to the immediate left of B, then it also means that B is on the immediate right of A.
If not specified, assume that all people are facing towards the centre or North (until and unless the direction is specified).
If you are unable to get any useful information from a sentence then better skip that line and move on to the next line. Then reexamine the skipped sentence after going through other sentences.
The meaning of and, who & adjacent in seating arrangement questions:
Example: A sits third to the right of P and sits fourth to the right of T. It denotes A sits third right of P, A sits fourth right of T i.e. the given information is talking about the first person.
Adjacent means next to each other, not opposite to each other.
Example: A and B are adjacent to each other, which means they are immediate neighbours of each other.
If “who” is given in a sentence, for example, A sits third to the right of P who sits fourth to the right of T. It denotes A sits right of P, P sits fourth right of T, and the given information is talking about the second person.
Example.1.
Direction: Study the following information and answer the given questions.
Pawan, Qaseem, Rajan, Suresh, Tariq, Uzma, Waseem, and Zainab are sitting in a line facing north. Zainab sits third to the left of Suresh. Zainab sits at the extreme end of the row. Only one person sat between Suresh and Qaseem. Only two people sit between Qaseem and Waseem, who is an immediate neighbour of Pawan. Uzma sits third to the left of Rajan.
Q: Who is an immediate neighbour of Tariq?
Sol:
People: Pawan, Qaseem, Rajan, Suresh, Tariq, Uzma, Waseem, and Zainab.
Zainab sits third to the left of Suresh.
Zainab sits at the extreme end of the row.
Only one person sat between Suresh and Qaseem.
Only two people sit between Qaseem and Waseem, who is an immediate neighbour of Pawan.
Uzma sits third to the left of Rajan
Hence, Qaseem and Rajan an immediate neighbours of Tariq.
Example 2
Eight persons A, B, C, D, E, F, G and H are sitting in a line and an equal number of persons are facing north and south direction. Not more than two consecutive adjacent persons face in the same direction. Persons at extreme ends face in the same direction.
A sits third to the right of D, who sits immediately right of H. H faces north direction. Two people sit between A and E. D does not sit at the extreme end. B sits immediately right of C and both face south direction. B and A are not adjacent to each other. G does not face south.
Q: If row1 people sit in alphabetical order starting from the left end then who will face S?
Sol:
D is facing the person who is sitting 2nd to the right of the person who faces C.
B is sitting to the left of D.
P is sitting 2nd to the right of S.
Neither P nor S sits at any of the extreme ends of the row.
R sits second to the left of T.
E is not an immediate neighbour of D.
Using statement 7, Case 1. B will be eliminated.
A sits to the left of E.
D will face S if persons of Row 1 are arranged according to alphabetical order.
So the correct answer is D.
The circular seating arrangement is that type of seating arrangement where people are sitting or standing in a circular, square, or polygonal way.
There can be three types of distinctive forms of questions under this:
• Circular arrangement where people face the centre of the table.
• Circular arrangement in which people face outward of the table.
• Circular arrangement with some people facing the centre of the table while some people facing outward of the table.
Circular ArrangementThere can be two cases depending upon the facing of people:
Case1: When people are facing inwards or centre of the table then
(i) All their “rights” refer to the anticlockwise direction.
(ii) All their “left” refer to the clockwise direction.
Case2: When people are facing outward of the table
(i) All their “left” refer to the anticlockwise direction.
(ii) All their “rights” refer to a clockwise direction.
Candidates can find various tips and circular arrangement reasoning tricks below for solving the questions related to the Circular Arrangement Reasoning section.
Tip 1: Circular Arrangement can be of clockwise and anticlockwise directions.
Tip 2: Practice mock tests and quizzes as much as possible to get wellversed with all the topics and their question patterns to score well in the circular arrangement reasoning section.
Example.3.
Consider an example now, representatives from eight different states viz. L, N, P, R, T, V, X and Z are sitting around a circular table facing the centre but not necessarily in the same order. Each of them is from a different state namely, Maharashtra, Assam, Gujarat, Kerala, Karnataka, Delhi, Madhya Pradesh and Punjab.
V sits second to the right of the representative from Kerala. A representative from Madhya Pradesh is to the immediate right of the representative from Kerala. N is third to the right of the representative from Madhya Pradesh. T is to the immediate left of P. Neither P nor T is an immediate neighbour of either N or the representative from Gujarat who sits second to the right of R. R is neither the representative of Kerala nor Madhya Pradesh. X and the representative from Maharashtra are immediate neighbours of each other. N is not the representative of Maharashtra. Only one person sits between P and a representative from Assam. Z sits third to the left of the representative from Punjab. A representative from Delhi sits second to the left of the representative of Karnataka. L is not the representative of Assam.
Now before moving forth to the solution, understand these basic steps that will help us solve this problem:
(i) Read the question carefully and note down the name or the characters that have to be arranged carefully.
(ii) Check and write down whether all the character is facing towards the centre or outwards or haphazardly some facing towards while others outward.
(iii) Now we will use diagrammatic representation to solve the question. Draw a circle with equidistant points and with the help of arrows signify the direction in which the characters are facing.
(iv) After this start reading the information and allot the places to the characters according to the information given in the question.
(v) Make cases for multiple possibilities and then rule out those cases that don’t fit the given information in the question.
(vi) Similarly go on deducing the cases and reach out to one possible case, which is the solution and eliminate all others.
Sol.
Now we will use the above steps and formulate the solution above problem:
In the above example, we are given 8 alphabets each corresponding to 8 states.
Representatives: L, N, P, R, T, V, X and Z
States: Maharashtra, Assam, Gujarat, Kerala, Karnataka, Delhi, Madhya Pradesh and Punjab.
Now we will read the main problems and try to get direct information. According to the problem:
1. V sits second to the right of the representative from Kerala.
2. A representative from Madhya Pradesh is to the immediate right of the representative from Kerala.
3. N is third to the right of the representative from Madhya Pradesh.
Here, we will first place V at the bottommost place. We then place the representative from Kerala second to the left of V. This is because V sits second to the right of the representative from Kerala. Then we place the representative from Madhya Pradesh and N as given in the problem. So, we get the following figure.
Now no other direct information is given with which we can plot the diagram. So, we move on to the next statements.
4. T is to the immediate left of P.
5. Neither P nor T is an immediate neighbour of either N or the representative from Gujarat. So, we get three possible cases.
6. Representative from Gujarat sits second to the right of R.
7. R is neither the representative of Kerala nor Madhya Pradesh.
So the third case gets eliminated as there is no place left for Gujarat.
Thus, cases 1 and 2 get amended, as shown below:
8. Only one person sits between P and the representative from Assam.
We know the possible positions of P so we can place a representative from Assam accordingly.
Here for each case, we get 2 cases, so now we have a total of 4 cases.
9. Z sits third to the left of the representative from Punjab.
10. A representative from Delhi sits second to the left of the representative of Karnataka.
Plotting information given in these statements, possibilities 2. a and 2. b get eliminated. We can see this as below:
When we see in cases 2. a and 2. b we have 4 places for these two representatives (Delhi & Karnataka).
Now, in case 2:
(A)
(i) If we place the representative of Delhi as R, there is no place for a representative of Karnataka.
(ii) If we place the representative of Delhi as N, it is possible.
(iii) If we place the representative of Delhi to the left of T, there is no place for a representative of Karnataka.
(iv) If we place the representative of Delhi as T, there is no place for the representative of Karnataka.
So placing a representative of Delhi as N is possible as shown below.
The diagram looks like this.
Now we take the 9^{th} statement and try to reason out 2. a again.
There are 3 possible places for Z (As a representative of Madhya Pradesh, a representative of Gujarat or a representative of Karnataka)
(B)
(i) Madhya Pradesh is not possible as there is no place for representatives of Punjab.
(ii) Similarly, Gujarat and Karnataka are also not possible.
(11) X and the representative from Maharashtra are immediate neighbours of each other.
(12) N is not the representative of Maharashtra.
(13) L is not the representative of Assam.
From this statement, we get that only case 1. a is valid all else gets eliminated.
Hence, we get the final seating arrangement diagram of the circular arrangement as follows.
Directions for the following three questions: Answer the following questions based on the statements given below:
(i) There are three houses on each side of the road.
(ii) These six houses are labelled as P, Q, R, S, T, and U.
(iii) The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White.
(iv) The houses are of different heights.
(v) T, the tallest house, is exactly opposite to the Red coloured house.
(vi) The shortest house is exactly opposite to the Green coloured house.
(vii) U, the Orange coloured house, is located between P and S.
(viii) R, the Yellow coloured house, is exactly opposite to P.
(ix) Q, the Green coloured house, is exactly opposite to U.
(x) P, the White coloured house, is taller than R, but shorter than S and Q.
Q1: What is the colour of the house diagonally opposite to the Yellow coloured house?
a) White
b) Blue
c) Green
d) Red
e)none of these
Ans: Option (D)
Sol:
There are three houses on each side of the road => Draw 6 lines, 3 in each row, to accommodate P, Q, R, S, T, and U.
The houses are of different colours and different heights.
T is the tallest and is opposite to the red house => Let’s number T as 1.
The shortest house is opposite to greenhouse.
U is orange and is between P and S => Two cases arise here. PUS is one possibility and the other possibility is SUP.
R is yellow and is opposite to P.
Q is green and is opposite U. We know that the greenhouse is opposite the shortest house. This implies that U is the shortest house => Number of U is 6.
P is white and is taller than R but shorter than S and Q => Apart from T, S and Q are also taller than P => S and Q can be 2 and 3 in any order => Number of P is 4 and the number of R is 5.
We know that P is opposite to R and Q is opposite to U => S is opposite to T
It is given that T is opposite to red house => S is the red house and hence T is the blue house.
So, we know the colours of all houses and the heights of P, R, T, and U.
In this question, we are asked to find the house that is opposite the yellow house. R is the yellow house, P is opposite to R and S is on the other corner in P’s row. Hence S is the house that is diagonally opposite to the yellow house and the colour of S is Red.
Q2: Which is the second tallest house?
a) P
b) S
c) Q
d) R
e)cannot be determined
Ans: Option (E)
Sol:
We only know that the second tallest house is either Q or S. Hence the answer cannot be determined.
Q3: What is the colour of the tallest house?
a) Red
b) Blue
c) Green
d) Yellow
e)none of these
Ans: Option (B)
Sol:
We know that P is opposite to R and Q is opposite to U => S is opposite to T
It is given that T is opposite to red house => S is the red house and hence T is the blue house.
T is the tallest house and hence the colour of the tallest house is blue.
Direction: Each of these questions is based on the information given below :
129 videos124 docs121 tests

CAT based Questions: Seating Arrangement Doc  19 pages 
Practice Test: Seating Arrangement  1 Test  10 ques 
Introduction to Circular & Linear Arrangement Video  20:11 min 
1. What is the importance of linear and circular arrangement in bank exams? 
2. What are the steps to solve linear arrangement questions? 
3. Can you provide an example of a linear seating arrangement question? 
4. What are the tips and tricks to solve circular arrangement reasoning questions? 
5. Can you provide an example of a circular seating arrangement question? 
CAT based Questions: Seating Arrangement Doc  19 pages 
Practice Test: Seating Arrangement  1 Test  10 ques 
Introduction to Circular & Linear Arrangement Video  20:11 min 

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