Seating ArrangementsPYQ Jan 26Question 4224 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 S?

Options

AR
BP
CQ
DT
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Correct Answer

✅ Option b — P

All Options:

  • AR
  • BP
  • CQ
  • DT

Detailed Solution & Explanation

Let the six corners of the hexagonal table be numbered 1\displaystyle 1 to 6\displaystyle 6 in a clockwise direction. Since all friends face the centre:
- "Left" corresponds to the clockwise direction (increasing numbers).
- "Right" corresponds to the counter-clockwise direction (decreasing numbers).
- Opposite positions in a 6-corner hexagon are separated by 3 seats (e.g., 1\displaystyle 1 is opposite 4\displaystyle 4, 2\displaystyle 2 is opposite 5\displaystyle 5, and 3\displaystyle 3 is opposite 6\displaystyle 6).

Let us determine the positions step-by-step:
1. Place **U** at position 1\displaystyle 1.
2. "P is second to the left of U": Second to the left (clockwise) of position 1\displaystyle 1 is 1+2=3\displaystyle 1 + 2 = 3. So, **P** is at position 3\displaystyle 3.
3. "Q is neighbour of R and S": This means Q, R, and S must occupy three consecutive positions, with Q in the middle (order: R-Q-S or S-Q-R).
4. The remaining vacant positions are 2,4,5,\displaystyle 2, 4, 5, and 6\displaystyle 6. The only three consecutive vacant positions are 4,5,\displaystyle 4, 5, and 6\displaystyle 6. Therefore, Q must be at position 5\displaystyle 5, while R and S will occupy positions 4\displaystyle 4 and 6\displaystyle 6.
5. "T is second to the left of S":
- If S is at 4\displaystyle 4, second to the left of S (clockwise) is position 4+2=6\displaystyle 4 + 2 = 6, which must be occupied by T. But position 6\displaystyle 6 is already reserved for R. So S cannot be at 4\displaystyle 4.
- If S is at 6\displaystyle 6, second to the left of S (clockwise) is position 6+2=8≡2(mod6)\displaystyle 6 + 2 = 8 \equiv 2 \pmod 6, which is vacant. Thus, **T** is at position 2\displaystyle 2 and **S** is at position 6\displaystyle 6.
6. This leaves **R** at position 4\displaystyle 4.

The final arrangement (clockwise from 1 to 6) is:
1: U, 2: T, 3: P, 4: R, 5: Q, 6: S\text{1: U, \quad 2: T, \quad 3: P, \quad 4: R, \quad 5: Q, \quad 6: S}

We need to find who is sitting opposite to S (position 6\displaystyle 6):
The position opposite to 6\displaystyle 6 is 6−3=3\displaystyle 6 - 3 = 3, which is occupied by **P**.

Hence, **Option B** 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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