Seating ArrangementsPYQ May 25Question 4050 of 145
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Seven persons namely H, I, J, K, M, N, O are sitting in a straight line facing North direction. Total three number of persons are sitting between H and N. Both N and H sits at extreme sides. Total two number of persons sit between H and O. M is not an immediate neighbour of H or N. I sits third to the right of M. I and H both are not an immediate neighbours. M is also not an immediate neighbour of J. Who is sitting between H and M?

Options

AJ
BO
CI
DK
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Correct Answer

✅ Option d — K

All Options:

  • AJ
  • BO
  • CI
  • DK

Detailed Solution & Explanation

To find the seating arrangement, let us analyze the given conditions step-by-step:
1. There are 7 positions in a straight line facing North, which we can number 1 to 7 from left to right:
Line: _______\text{Line: } \_ \quad \_ \quad \_ \quad \_ \quad \_ \quad \_ \quad \_ 12345671 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7
2. "Both N and H sit at extreme sides."
This means one of them is at position 1 and the other is at position 7. Let us consider the two cases:
- **Case 1**: H\displaystyle H is at position 1 and N\displaystyle N is at position 7.
- **Case 2**: N\displaystyle N is at position 1 and H\displaystyle H is at position 7.

3. "Total two number of persons sit between H and O."
- In **Case 1** (H\displaystyle H is at 1), the two persons between H\displaystyle H and O\displaystyle O are at positions 2 and 3. Thus, O\displaystyle O must be at position 4.
- In **Case 2** (H\displaystyle H is at 7), the two persons between H\displaystyle H and O\displaystyle O are at positions 5 and 6. Thus, O\displaystyle O must be at position 4.
In both cases, O\displaystyle O is at position 4.

4. "M is not an immediate neighbour of H or N."
Since the extreme positions 1 and 7 are occupied by H\displaystyle H and N\displaystyle N, their immediate neighbours are at positions 2 and 6. Therefore, M\displaystyle M cannot be at position 2 or 6. Since O\displaystyle O is at position 4, the possible positions for M\displaystyle M are 3 or 5.

5. "I sits third to the right of M."
This means if M\displaystyle M is at position x\displaystyle x, then I\displaystyle I must be at position x+3\displaystyle x + 3.
- If M\displaystyle M is at position 5, then I\displaystyle I would be at 5+3=8\displaystyle 5 + 3 = 8, which is outside the line of 7 people. Thus, M\displaystyle M cannot be at position 5.
- Therefore, M\displaystyle M must be at position 3, which placing I\displaystyle I at position 3+3=6\displaystyle 3 + 3 = 6.

6. "I and H both are not immediate neighbours."
Let us evaluate our two cases with I\displaystyle I at position 6:
- In **Case 2** (H\displaystyle H is at 7), I\displaystyle I (at 6) and H\displaystyle H (at 7) would be immediate neighbours, which violates this condition. Thus, Case 2 is ruled out.
- In **Case 1** (H\displaystyle H is at 1), I\displaystyle I (at 6) is not an immediate neighbour of H\displaystyle H (at 1). This is a valid configuration.
So, the positions so far are:
- Position 1: H\displaystyle H
- Position 3: M\displaystyle M
- Position 4: O\displaystyle O
- Position 6: I\displaystyle I
- Position 7: N\displaystyle N

7. "M is also not an immediate neighbour of J."
The remaining unoccupied positions are 2 and 5. Since M\displaystyle M is at position 3, J\displaystyle J cannot be at position 2 (which is adjacent to 3). Therefore, J\displaystyle J must be at position 5.

8. The only remaining position 2 must be occupied by K\displaystyle K.
The final seating arrangement from left to right (1 to 7) is:
Arrangement: HKMOJIN\text{Arrangement: } H \quad K \quad M \quad O \quad J \quad I \quad N
We need to find who is sitting between H\displaystyle H and M\displaystyle M. Looking at the arrangement, K\displaystyle K is sitting at position 2, which is between H\displaystyle H (at 1) and M\displaystyle M (at 3).

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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