M, N, O, P, Q and R are sitting around a circular table facing the centre. O is an immediate neighbour of M. Only two people sit between O and Q. P sits second to the left of R. N is an immediate neighbour of P. Who is sitting second to the right of M?
Correct Answer :
N
Solution :
The correct option is N.
Let's step through the logical reasoning step-by-step to find the seating arrangement around the circular table.
1. Understand the Setup:
There are 6 people: M, N, O, P, Q, and R sitting around a circular table facing the centre. Facing the centre means:
- "Left" moves in the clockwise direction.
- "Right" moves in the counter-clockwise direction.
2. Analyze the Given Clues:
Clue 1: "Only two people sit between O and Q."
In a circle of 6 people, having 2 people between O and Q means O and Q are directly opposite each other.
Clue 2: "P sits second to the left of R."
If we place R at a position, P will be 2 positions clockwise from R.
Clue 3: "N is an immediate neighbour of P."
This means N is adjacent to P.
Clue 4: "O is an immediate neighbour of M."
This means M is adjacent to O.
3. Determining the Positions:
Let's number the positions around the circle clockwise as 1, 2, 3, 4, 5, 6.
Place R at position 1.
Since P sits second to the left (clockwise) of R, P is at position 3.
Now, P is at position 3. Its neighbors are positions 2 and 4. N must be next to P, so N is either at position 2 or position 4.
Also, O and Q are opposite each other. The pairs of opposite positions are (1, 4), (2, 5), and (3, 6).
Since R is at 1 and P is at 3, the only available opposite positions for O and Q are (2, 5).
Since positions 2 and 5 are occupied by O and Q, and N is adjacent to P (positions 2 or 4), N must be at position 4.
Now, the remaining position for M is position 6.
Since M is at position 6 and O is an immediate neighbour of M, O must be at position 5 (adjacent to 6), which places Q at position 2.
Let's verify the complete clockwise order from position 1 to 6:
1: R
2: Q
3: P
4: N
5: O
6: M
Verification of Conditions:
- Facing centre: Left is clockwise, Right is counter-clockwise.
- O (5) is adjacent to M (6): Satisfied.
- 2 people between O (5) and Q (2) [positions 3, 4 or 6, 1]: Satisfied.
- P (3) is 2nd to the left (clockwise) of R (1): Satisfied.
- N (4) is an immediate neighbour of P (3): Satisfied.
4. Answer the Question:
Who is sitting second to the right of M?
- M is at position 6.
- Facing the centre, "right" moves in the counter-clockwise direction (towards position 5, then position 4).
- 1st to the right of M is position 5 (O).
- 2nd to the right of M is position 4 (N).
Therefore, N is sitting second to the right of M.
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