Arrangement Problems in Logical Reasoning Section of CAT can be most ambiguous of all the problems. This topic includes variety of different subtopics with multiple variation and integration of them. One such topic in arrangements is Seating (or sitting) Arrangements, which is one of the most important and consistent in CAT. I know Seating Arrangement questions can be confusing, Time-consuming and at times brainstorming questions in 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 method to solve these questions correctly in efficient in a time-saving way?
So, let’s begin and evolve a simple and straight forward way to cater to these types of arrangement problems!!!
Firstly, we can identify that these problems can be categorized into two types
1. Linear Seating Arrangement Problems
2. Circular Seating Arrangement Problems
Now we can devise an individual approach to each of the above type. Let’s first start with 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 arrangement is made in a single line. These problems can be divided into two types of conditions.
1. In which direction of the face is not given; in these we assume direction according to our own reference.
2. 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.
And in 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 example keep in mind these important points in mind.
1. Always note the conditions given in short form and represent them pictorially.
2. If A is sitting to the immediate left of B, then it also means that B is on immediate right of A.
3. If not specified, assume that all people are facing towards the center or North (until and unless the direction is specified).
4. If you are unable to get any useful information from a sentence then better skip that line and move on to next line. Then re-examine the skipped sentence after going through other sentences.
5. The Meaning of and, who & adjacent in seating arrangement questions:
A sits third to right of P and sits fourth to 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. For example: A and B are adjacent to each other, which means they are immediate neighbour of each other.
If “who” is given in a sentence, for example: A sits third to right of P who sits fourth to 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.
Consider this example and let’s step wise solve it.
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 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 neighbors. 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 neighbor of Q. V is not an immediate neighbor of P. S does not face A.
Steps to solve the question
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 and 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.
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 the Row 1 i.e. in position 6. To left of it place A at the third i.e. in position 3.
Two persons are sitting between T and P, which mean to the third left of T, P is placed i.e. position 3 in Row 2.
C and D are immediate neighbors. 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 left extreme end. But position of C and D can be decided by next statement. i.e. Only one person sits between B and C.
From the above statement D is placed immediate right of E and C is placed immediate left of A and B is placed in immediate left of A.
The person facing D is immediate neighbour of Q. So, Q is placed at the extreme left end of Row 2 i.e. position 1.
V is not an immediate neighbor 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 immediate left of T. i.e. in position 5 in Row 2.
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. 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 exam based on the above problem .
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 learnt how to tackle them and make them hassle-free.
Now we can move on to our second type of problem i.e. Circular seating arrangement. Circular Seating arrangement is that type of seating arrangement where people are sitting or standing in circular, square or polygonal way. There can be three types of distinctive forms of questions under this:
• Circular arrangement where people face center of the table
• Circular arrangement in which people face outward of the table.
• Circular arrangement with some people facing center of the table while some people facing outward of the table.
There can be two cases depending upon the facing of people
When people are facing inwards or center of table then
1. All their “rights” refer to anticlockwise direction.
2. All their “left” refer to clockwise direction.
When people are facing outward of the table
1. All their “left” refer to anti clockwise direction.
2. All their “right” refer to clockwise direction.
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 center 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 right of the representative from Kerala. Representative from Madhya Pradesh is to the immediate right of the representative from Kerala. N is third to 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 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 left of the representative from Punjab. Representative from Delhi sits second to 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.
1) Read the question carefully and note down the name or the characters that have to be arranged carefully.
2) Check and write down whether all the character is facing towards the center or outwards or haphazardly some facing towards while others outward.
3) 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.
4) After this start reading the information and allot the places to the characters according to the information given in question
5) Make cases for more multiple possibilities and then rule out those cases that doesn’t fit the given information in the question
6) Similarly go on deducing the cases and reach out to one possible case which is the solution and eliminate all others.
Now we will use 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 center everyone’s right is in anticlockwise direction and everyone’s left is in clockwise direction.
Now we will read the main problems and try to get the direct information. According to the problem:
1) V sits second to the right of the representative from Kerala.
2) Representative from Madhya Pradesh is to the immediate right of the representative from Kerala.
3) N is third to right of the representative from Madhya Pradesh.
Here, we will first place V at 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 representative from Kerala. Then we place the representative from Madhya Pradesh and N as given in 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 next statements.
4) T is to the immediate left of P.
5) Neither P nor T is an immediate neighbor of either N or the representative from Gujarat. So, we get three possible cases.
6) Representative from Gujarat sits second to 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 total 4 cases.
9) Z sits third to left of the representative from Punjab.
10) Representative from Delhi sits second to 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.
1. i) If we place the representative of Delhi as R there is no place for 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 representative of Karnataka.
iv) If we place the representative of Delhi as T, there is no place for representative of Karnataka.
So placing representative of Delhi as N is possible as shown below.
The diagram looks like this.
Now we take 9th statement and try to reason out 2.a again.
There are 3 possible places for Z (As representative of Madhya Pradesh, representative of Gujarat or representative of Karnataka)
2. i) Madhya Pradesh is not possible as there is no place for representative 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 remains.
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.