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**Introduction**

- Arrangement Problems in the Logical Reasoning Section of CAT can be the
**most ambiguous of all the problems**. - This topic includes a variety of different subtopics with multiple variations 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.
- 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.**

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 Arrangement

**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:__

**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.

- 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 :

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

Try yourself:**Who among the following is to the immediate left of F?**

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Try yourself:**What is true about J and K?**

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Try yourself:**How many persons are seated between K and F?**

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Try yourself:**Who among the following are three lady members?**

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Try yourself:**Who among the following is seated between E and H?**

View Solution

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