Seating ArrangementsPYQ Sept 25Question 4452 of 145
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Six people, A, B, C, D, E and F are sitting in a hexagonal shape. All the sides of the hexagon so formed are of same length. A is not adjacent to B or C; D is not adjacent to C or E; B and C are adjacent; F is in the middle of D and C. Which of the following is not a correct neighbour pair?

Options

AA and F
BD and F
CB and E
DC and F
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Correct Answer

✅ Option a — A and F

All Options:

  • AA and F
  • BD and F
  • CB and E
  • DC and F

Detailed Solution & Explanation

Let the six vertices of the hexagon in order be represented by positions 1, 2, 3, 4, 5, and 6.
1. **F is in the middle of D and C**: This means F is adjacent to both D and C. Thus, the three vertices must be adjacent in the sequence D−F−C\displaystyle D - F - C.
2. **B and C are adjacent**: Since B is adjacent to C, B must be next to C on the other side of F. This expands the sequence to D−F−C−B\displaystyle D - F - C - B. Let us assign these to positions: D\displaystyle D at 1, F\displaystyle F at 2, C\displaystyle C at 3, and B\displaystyle B at 4.
3. **Determining positions for A and E**: The remaining positions are 5 and 6. We must place A and E at these positions.
- **D is not adjacent to C or E**: Since D is at 1, its adjacent positions are 2 (occupied by F) and 6. Since D cannot be adjacent to E, E cannot be at position 6. Thus, E must be at position 5.
- This leaves position 6 for A. Let us check if this arrangement is consistent with the remaining conditions:
- Arrangement: D(1),F(2),C(3),B(4),E(5),A(6)\displaystyle D(1), F(2), C(3), B(4), E(5), A(6).
- **A is not adjacent to B or C**: A is at 6, adjacent to D(1) and E(5). A is not adjacent to B(4) or C(3). This condition is satisfied.
- **D is not adjacent to C or E**: D is at 1, adjacent to F(2) and A(6). D is not adjacent to C(3) or E(5). This condition is satisfied.
- **B and E are adjacent**: B is at 4 and E is at 5. They are adjacent. This matches the arrangement.
Let us evaluate the neighbour pairs in the options:
- **Option a: A and F**: A is at position 6 and F is at position 2. They are not adjacent. Thus, they are not a correct neighbour pair.
- **Option b: D and F**: D is at 1 and F is at 2. They are adjacent. This is a correct neighbour pair.
- **Option c: B and E**: B is at 4 and E is at 5. They are adjacent. This is a correct neighbour pair.
- **Option d: C and F**: C is at 3 and F is at 2. They are adjacent. This is a correct neighbour pair.
Hence, **Option A** 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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