# CAT Logical Reasoning: Solving Seating Arrangement Problems

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Seating arrangement problems are constant in the logical reasoning section of MBA entrance exams. One can expect up to 3-4 sets of seating arrangement problems in the CAT Logical Reasoning section. A lot of students struggle to make sense of these questions. Here are some easy steps to solve seating arrangement problems.

## Establishing a sense of direction

The first step to solving seating arrangement problems for MBA entrance exams is establishing the direction in which people are facing. Consider the following situations and their representation. Notice how the direction of facing affects the sense of left and right in each case.

1. 5 people A, B, C, D & E are standing (not necessarily in the same order) in a line facing south
2. 8 people are seated across 2 parallel rows. Each row is occupied by 4 people. A, B, C, D (not necessarily in the same order) are in row 1 facing south. S, T, U, V (not necessarily in the same order) are in row 2 facing north
3. 5 people are sitting across a circular table. Their faces are towards the centre of the table
4. 5 people are sitting across a circular table. Their faces are away from the centre of the table

## Linear Arrangement:

Here the people are positioned in a line. They could form a single row or a double row.

• Establish which direction the people are facing (East, West, North or South). If the question does not mention the direction, assume that everyone is facing the North.
• In the case of double rows, you can assume that the 2 rows are facing each other. (Unless otherwise specified)
• When you assume everyone facing north, their left and right become your left and right. This simplifies a lot of things.
• Make a note of all the direct information provided in the question. Once you have a list of direct information, draw a pictorial representation of the problem. Remember, there can be more than one way to represent the problem.
• Write the clue statements in shortcuts. For eg: B is sitting third to the right of C can be written as C | | B.
• Pay special attention to indicative words like beside, adjacent, towards the end etc. These provide key information regarding the placement.
• If there are two people possible for a particular position, break the diagram into two taking each possibility one by one. Once every clue is taken into account, one possibility will automatically get rejected due to contradictions.
• Mark the finalised places with a square around the letter or the name of the person.
• While solving questions, you can also start by eliminating incorrect options. The correct answer would be consistent with the overall logic of the question.

### Example:

P, Q, R, S, T, U and V are sitting in a row facing North

• The person who is third to the left of S is at one of the ends.
• T is 4th to the right of V.
• R is the neighbour of Q and S
• U is to the immediate right of T.

Let’s begin by creating a pictorial representation of the problem

U is to the immediate right of T. This means U and T are adjacent to each other.

Since T is 4th to the right of V, the position of V can either be 1 or 2 (if we place V in any other position we won’t have a place for both U and T)

R is a neighbour of both Q and S, which means it lies between Q and S. Thus, their relative position can be Q, R, S or S, R, Q.

The person third to the left of S is at one end. Since this could only mean the left end, we can fix the position of S at 4.

We have 2 possibilities

1. Placing R and Q in positions 5 & 6 respectively
2. Placing Q & R in positions 2 & 3 respectively

If we go with the first option, we won’t be able to place T & U according to the given conditions. Thus, option 2 is right as it is consistent with the logic of the question.

This leaves us with V at position 1. T being 4th to the right of V is placed at position 5. U is to the immediate right of T at position 6. P can be placed at the remaining position 7.

What is the position of P?

A. Extreme left
B. Between T and S
C. Extreme right
D. Centre

Who are the neighbours of Q?

A. V and U
B. R and T
C. R and S
D. R and V

Which of the following statements is not true?

A. P is at one of the ends
B. T is to the immediate left of S
C. U is second to the right of S
D. V is to the immediate left of Q

Who all are to the left of R?

A. V and Q
B. V, Q and S
C. Only Q
D. S, T, U and P

## Circular Arrangement:

Here the people are sitting around a circular table. The seating can be facing the centre or away from it. Another variation of this problem which sometimes appears in CAT is where people are sitting across a rectangular table.

• Draw a circle, mark the seating places (4/6/8/10) and then read the clues one by one.
• Understand whether people are facing towards the centre of the table or away from it. Mark them with inwards/ outwards arrows.
• Unless specified otherwise, all people must face the centre. Place the first person at the bottom chair of the arrangement so that your left & right become his left & right.
• Make a list of all the direct information provided regarding each person.
• Pay attention to words like diagonally opposite, besides, to the right of etc.
• Now do a pictorial representation of the problem. Make sure to cover all the cases that are possible. We can eliminate the incorrect ones when we get new information at a later stage.

### Example:

A, B, C, D, E, F, G and H are sitting around a circular table. All of them are facing the centre of the table. A sits third to the right of H and third to the left of B. D sits second to the right of E. G sits second to the left of C. E is not the neighbour of B while F is neither a neighbour of E nor of H.

Let’s make a pictorial representation of this problem.

A sits third to the right of H and third, to the left of B. Placing A at position 1, we can place H and B at 4th and 6th positions respectively. Now E is not a neighbour of B, thus it cannot occupy positions 5 or 7. We have 3 other open positions (8,2,3) for E.

1. Let’s try placing E at position 8. D sits second to the right of E but this position is already occupied by B. Hence, E cannot be at 8th position.
2. Let’s try placing E at position 2. Then D can be placed in position 8. Now F is not a neighbour of H nor E. Thus the only open position for F is 7. Also, G sits second to the left of C. This places C at 3rd position and G at 5th position. Now all the spots are occupied and the logic is consistent with the question.

Who sits between F and A?

1. B
2. E
3. G
4. D
5. None of these

Who sits second to the left of G?

1. A
2. D
3. E
4. F
5. None of these

Four of the following pairs form a pattern based on their placement in the arrangement. Which one of these pairs is the odd one out?

1. A, B
2. A, F
3. C, A
4. D, B
5. H, E

If we look closely in a clockwise direction, each of these pairs has exactly one element between them in the arrangement. A & F have D in between them, C & A have E in between them, D & B have F in between them and H & E have C in between them. Only A & B have 2 elements in between them thus (1) is the answer.

Keeping A’s position fixed, if we re-arranged the remaining letters in alphabetical order in the clockwise direction, then the seating position of how many members (excluding A) remains the same?

1. One
2. None
3. Three
4. Two