Seating ArrangementsPYQ May 25Question 4054 of 145
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Six friends P, Q, R, S, T and U are sitting around the hexagonal table each at one corner and are facing the centre of the hexagonal. P is second to the left of U. Q is neighbour of R and S. T is second to the left of S. Which one is sitting opposite to P?

Options

AR
BQ
CT
DS
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Correct Answer

✅ Option d — S

All Options:

  • AR
  • BQ
  • CT
  • DS

Detailed Solution & Explanation

Let the six corners of the hexagonal table be numbered 1 to 6 in a counter-clockwise direction:
Positions: 1,2,3,4,5,6\text{Positions: } 1, 2, 3, 4, 5, 6 Since the friends are facing the centre of the table:
- Moving from x\displaystyle x to x+1(mod6)\displaystyle x+1 \pmod 6 is moving to the right (clockwise is left, counter-clockwise is right, or vice versa depending on your perspective. Let us define the left of any position x\displaystyle x as x−1(mod6)\displaystyle x-1 \pmod 6 and the right as x+1(mod6)\displaystyle x+1 \pmod 6).
Let us place U\displaystyle U at position 1:
- Position 1: U\displaystyle U

1. "P is second to the left of U."
First to the left of U\displaystyle U (at 1) is position 6. Second to the left of U\displaystyle U is position 5:
- Position 5: P\displaystyle P

2. "Q is neighbour of R and S."
This means Q\displaystyle Q must sit between R\displaystyle R and S\displaystyle S. Thus, R,Q,S\displaystyle R, Q, S must occupy three adjacent positions. Since positions 1 (U\displaystyle U) and 5 (P\displaystyle P) are already occupied, the only available block of three adjacent empty positions is 2, 3, and 4. Thus:
- Q\displaystyle Q must be at the center of this block: Position 3: Q\displaystyle Q.
- R\displaystyle R and S\displaystyle S will occupy positions 2 and 4 in some order.
- The only remaining position 6 must be occupied by T\displaystyle T: Position 6: T\displaystyle T.

3. "T is second to the left of S."
Let us check the two possible orders for R\displaystyle R and S\displaystyle S:
- **Case 1**: S\displaystyle S is at position 2 and R\displaystyle R is at position 4.
First to the left of S\displaystyle S (at 2) is position 1. Second to the left of S\displaystyle S is position 6, which is occupied by T\displaystyle T. This satisfies the condition.
- **Case 2**: S\displaystyle S is at position 4 and R\displaystyle R is at position 2.
First to the left of S\displaystyle S (at 4) is position 3. Second to the left of S\displaystyle S is position 2. But position 2 is occupied by R\displaystyle R, not T\displaystyle T. This violates the condition.

Thus, Case 1 is the correct arrangement:
- Position 1: U\displaystyle U
- Position 2: S\displaystyle S
- Position 3: Q\displaystyle Q
- Position 4: R\displaystyle R
- Position 5: P\displaystyle P
- Position 6: T\displaystyle T

4. "Which one is sitting opposite to P?"
In a hexagon, the opposite positions are:
- 1 and 4
- 2 and 5
- 3 and 6
Since P\displaystyle P is at position 5, the person sitting opposite to P\displaystyle P is at position 2, which is S\displaystyle S.

Hence, **Option D** is the correct answer.

About This Chapter: Seating Arrangements

Paper

Paper 3: Quantitative Aptitude

Weightage

5 Marks

Key Topics

Linear & Circular Seating Arrangements

A crucial part of the Logical Reasoning section. It tests spatial reasoning through linear arrangements (people sitting in a row) and circular arrangements. Students must decode right/left orientation based on the direction individuals face (North, South, or Center).

View Official ICAI Syllabus

Exam Strategy Tip

Always use abbreviations (A, B, C) and draw the diagram immediately. The key trick is to never start with a 'relative' clue; always start with a fixed, concrete clue (e.g., 'A sits at the extreme right').

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