Seating and Circular Arrangement LR Notes | EduRev

We know Seating Arrangement questions can be confusing, time-consuming, and at times brainstorming questions in the Logical Reasoning section.

• But don’t forget that around 3-4 questions are based on this topic in CAT, so answering them correctly can boost your percentile and a little mistake can cost you significantly, thanks to negative marking for that. 

• Therefore, the question arises what are the best practices or methods to solve these questions correctly inefficiently in a time-saving way? So, let’s begin and evolve a simple and straightforward way to cater to these types of arrangement problems!!!
• Firstly, we can identify that these problems can be categorized into two types:
  (a) Linear Seating Arrangement Problems
  (b) Circular Seating Arrangement Problems

Linear Seating Arrangement Problems

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, at our level, two rows questions are asked.
One row problems are those when the arrangement is made in a single line.
These problems can be divided into two types of conditions:

• In which direction of the face is not given; in these, we assume direction according to our own reference.
• In which direction of the face is given like facing north, south or towards east, west; in these, we must plan to keep in mind these directions.

In the two-row 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 in mind:

• Always note the conditions given in the short form and represent them pictorially.

• 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 re-examine 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, the given information is talking about the second person.

Example.1.
Twelve persons are sitting in two parallel rows containing six persons each, in such a way that there is an equal distance between adjacent persons. In row 1, A, B, C, D, E and F are seated (But not necessarily in the same order) and all of them are facing south. In row 2, P, Q, R, S, T, and V are seated (not necessarily in the same order) and all of them are facing north. Therefore, in the given seating arrangement, each person seated in a row faces another person of the other row.
A Sits third to the left of E. The person Facing A sits second to the left of T. Two persons are sitting between T and P. C and D are immediate neighbours. C and D do not sit at any of the extreme ends of the line. Only one person sits between B and C. the person facing D is an Immediate neighbour of Q. V is not an immediate neighbour of P. S does not face A.
Sol.

1^st paragraph gives information regarding how many persons and in which direction they face.
2^nd paragraph provides the positioning of persons.

Steps to solve the question:

Step 1: 12 persons are sitting in parallel rows, and each row contains 6 persons.

• In Row 1 – A, B, C, D, E, and F are seated and facing towards south.
• In Row 2 – P, Q, R, S, T, and V are seated and facing towards north.

From the above information, let’s make a parallel row:

Step 2: A sits third to the left of E. A sit-in Row 1 and faces south. Let’s place E at the right end of Row 1, i.e. in position 6. To the left of it, place A at the third, i.e. in position 3.

Step 3: Two persons are sitting between T and P, which means to the third left of T, P is placed, i.e. position 3 in Row 2.

Step 4: C and D are immediate neighbours. C and D do not sit at any of the extreme ends of the line.

• C and D can be placed between A and E. They cannot be placed at the left extreme end.  But the position of C and D can be decided by the next statement. i.e. Only one person sits between B and C.
• From the above statement, D is placed immediately right of E and C is placed immediate left of A and B is placed in the immediate left of A.

Step 5: The person facing D is an immediate neighbour of Q. So, Q is placed at the extreme left end of Row 2, i.e. position 1.

Step 6: V is not an immediate neighbour of P.V cannot be placed immediate left of P and immediate right of P, i.e. V cannot be placed in position 2 and position 4.
It can be placed immediately left of T., i.e. in position 5 in Row 2.

Step 7: S does not face A. So, R faces direct opposite to A, i.e. in position 4 in Row 2 and S faces direct opposite to D, i.e. position 2 in Row. The remaining One Person is F placed in Row 1 Position 1.

Henceforth now we are in a position where we can easily answer all the questions asked in the exam based on the above problem.

Note:

The above example was a problem of two ways linear seating arrangement with directions where with the use of diagrammatic approach we made it simpler and uncomplicated which would have been otherwise an obvious tedious task to solve. This is just one example, there can be numerous others with different combinations and arrangements but now we have learned how to tackle them and make them hassle-free.

Circular Seating Arrangement Problems

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 clockwise direction.
Case2: When people are facing outward of the table
(i) All their “left” refer to the anti-clockwise direction.
(ii) All their “right” refer to clockwise direction.

Example.2.
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 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 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 more 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.

• We need to map representatives to their states, respectively.
• Now first we will make a circle with 8 equidistant lines and respectively add direction in which the representatives are facing.
• Since all are facing towards the centre, everyone’s right is in the anticlockwise direction and everyone’s left is in the clockwise direction.
  

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 bottom-most 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 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. 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 case 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 9^th statement and try to reason out 2.a again.
There are 3 possible places for Z (As a representative of Madhya Pradesh, representative of Gujarat or 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.

• Thus this case 2.a is eliminated.
• On similar bases, case 2.b is also getting eliminated.
• Thus case 1 remain.
  

(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.

Direction: Each of these questions are based on the information given below :

1. 8 person E, F, G, H, I, J, K and L are seated around a square table - two on each side.
2. There are 3 ladies who are not seated next to each other.
3. J is between L and F.
4. G is between I and F.
5. H, a lady member is second to the left of J.
6. F, a male member is seated opposite to E, a lady member.
7. There is a lady member between F and I.

Solved Questions

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 labeled 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. 

Question 1: 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

Question 2: Which is the second tallest house?

a) P

b) S

c) Q

d) R

e)cannot be determined

Question 3: What is the colour of the tallest house?

a) Red

b) Blue

c) Green

d) Yellow

e)none of these

Solutions and Answers of Questions 1,2 & 3.

Before directly trying to answer the question, it is important to gather all the information given by the question.

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 colors and different heights.

T is tallest and is opposite to 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. P-U-S is one possibility and the other possibility is S-U-P.

R is yellow and is opposite to P.

Q is green and is opposite to U. We know that green house is opposite to 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 number of R is 5.

Answer of Question 1: Option (D)

Solution of Question 1: 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 heights of P, R, T, and U.

In this question, we are asked to find the house that is opposite to 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 yellow house and the colour of S is Red.

Answer of Question 2: Option (E)
Solution of Question 2:
We only know that the second tallest house is either Q or S.  Hence the answer is cannot be determined.

Answer of Question 3: Option (B)
Solution of Question 3:
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.