Seating ArrangementsPYQ Jan 26Question 4523 of 145
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Eight persons P, Q, R, S, T, U, V, and W are sitting around a circular table facing the centre. Two persons sit between Q & W. V sits immediate left of W. Three persons sit between S & T. R sits immediate left of T. U is not the neighbour of P. One person sits between P & Q. Which of the following statement is correct?

Options

AQ sits to the immediate right of U
BOne person sits between P & S
COne person sits between S & U
DThree persons sit between Q & R
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Correct Answer

✅ Option c — One person sits between S & U

All Options:

  • AQ sits to the immediate right of U
  • BOne person sits between P & S
  • COne person sits between S & U
  • DThree persons sit between Q & R

Detailed Solution & Explanation

Let us place the eight persons (P, Q, R, S, T, U, V, W) in positions numbered 1\displaystyle 1 to 8\displaystyle 8 around the circular table in a clockwise direction.
Facing the centre means:
- "Immediate left" of a position x\displaystyle x is the next position in the clockwise direction, i.e., x+1\displaystyle x + 1 (modulo 8).
- "Immediate right" of a position x\displaystyle x is the previous position in the clockwise direction, i.e., x−1\displaystyle x - 1 (modulo 8).

Let us construct the arrangement step-by-step:
1. Place **Q** at position 1\displaystyle 1.
2. "Two persons sit between Q & W": This means W must be at position 4\displaystyle 4 or 6\displaystyle 6. Let us place **W** at position 4\displaystyle 4.
3. "V sits immediate left of W": Left of position 4\displaystyle 4 (clockwise) is position 5\displaystyle 5. So, **V** is at position 5\displaystyle 5.
4. "One person sits between P & Q": Since Q is at 1\displaystyle 1, P can be at position 3\displaystyle 3 or 7\displaystyle 7. Let us place **P** at position 3\displaystyle 3.
5. "Three persons sit between S & T": In an 8-person circular table, this means S and T must be diametrically opposite to each other. The available opposite pairs of seats are (2,6)\displaystyle (2, 6) since positions 1,3,4,5\displaystyle 1, 3, 4, 5 are already occupied. Thus, {S,T}={2,6}\displaystyle \{S, T\} = \{2, 6\}.
6. "R sits immediate left of T": Left of T must be R. If T were at position 2\displaystyle 2, then R would have to be at position 3\displaystyle 3, which is already occupied by P. Therefore, **T** must be at position 6\displaystyle 6, and **R** is at position 7\displaystyle 7 (immediate left/clockwise of 6\displaystyle 6).
7. Since T is at 6\displaystyle 6, **S** must be at position 2\displaystyle 2.
8. Now, the only remaining position is 8\displaystyle 8, which must be occupied by **U**. So, **U** is at position 8\displaystyle 8.

Let us verify the remaining condition: "U is not the neighbour of P".
- P is at position 3\displaystyle 3 (its neighbours are S at 2\displaystyle 2 and W at 4\displaystyle 4).
- U is at position 8\displaystyle 8.
Since U is not adjacent to P, this arrangement is fully consistent.

The final circular order (clockwise from 1 to 8) is:
1: Q, 2: S, 3: P, 4: W, 5: V, 6: T, 7: R, 8: U\text{1: Q, \quad 2: S, \quad 3: P, \quad 4: W, \quad 5: V, \quad 6: T, \quad 7: R, \quad 8: U}

Now let us evaluate the options:
- **Option a:** "Q sits to the immediate right of U". Right of U (8) is R (7). Incorrect.
- **Option b:** "One person sits between P & S". P (3) and S (2) are adjacent. Incorrect.
- **Option c:** "One person sits between S & U". S is at 2\displaystyle 2 and U is at 8\displaystyle 8. Position 1\displaystyle 1 (occupied by Q) lies between them. Correct!
- **Option d:** "Three persons sit between Q & R". Q is at 1\displaystyle 1 and R is at 7\displaystyle 7. Only U (8) is between them on one side. Incorrect.

Hence, **Option C** 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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