Question Details

Study the following information carefully and answer the questions given below.
Eight persons – P, Q, R, S, T, U, V and W sit around a circular table facing the centre, but not necessarily in the same order.
Q sits two places away from S. Two persons sit between S and P who does not sit adjacent to Q. W sits second to the right of P. T and the one who sits opposite to W are immediate neighbours. As many persons sit between Q and W as between T and V. R sits third to the left of V.

How many persons sit between Q and P when counts from the left of Q?

Options

A

One

B

Two

C

Three

D

Four

E

More than four

Show Answer

Correct Answer :

Option D

Four

Solution :

Correct Option: Four

Let us solve the seating arrangement step-by-step based on the given information.
Eight persons: P, Q, R, S, T, U, V, and W are seated around a circular table facing the centre.

Step 1: Analyzing the clues for P, S, Q, and W

1. "Two persons sit between S and P".
In an 8-person circular table, if 2 persons sit between two people, those two people are separated by 3 positions on one side and 3 on the other, or they are at positions relative to each other.
Let us fix P at position 1 (assuming positions 1 to 8 numbered clockwise).
If P is at position 1, S can be at position 4 (2 persons between them clockwise: positions 2 and 3) or position 6 (2 persons between them counter-clockwise: positions 8 and 7).

2. "W sits second to the right of P."
Since everyone faces the centre, moving "right" means moving counter-clockwise (or clockwise depending on numbering direction, let's define clockwise as right/left consistently).
Let position 1 = P.
If facing centre:
Right of position 1 is position 2, position 3, etc. (moving counter-clockwise).
So, W sits at position 3 (second to the right of P).

3. "Q sits two places away from S."
Two places away means there is 1 person between Q and S.
4. "P does not sit adjacent to Q."
Since P is at 1, Q cannot be at 2 or 8.

Let's evaluate the positions for S:
Case A: S is at position 4.
If S is at position 4, Q (2 places away from S) could be at position 2 or position 6.
Since Q cannot be adjacent to P (position 1), Q cannot be at position 2.
Thus, Q must be at position 6.

Let's check Case B: S is at position 6.
If S is at position 6, Q (2 places away from S) could be at position 4 or position 8.
Q cannot be at position 8 (adjacent to P). So Q would be at position 4.
Let's check the remaining conditions for both cases.

Step 2: Testing Case A (P = 1, W = 3, S = 4, Q = 6)

1. W is at position 3. "The one who sits opposite to W":
Opposite to position 3 in an 8-person table is position 7 (3 + 4 = 7).
2. "T and the one who sits opposite to W are immediate neighbours."
So T is an immediate neighbour of position 7. This means T can be at position 8 or position 6.
Since Q is at position 6, T must be at position 8.

3. "As many persons sit between Q and W as between T and V."
Positions of Q (6) and W (3):
Between Q(6) and W(3), there are 2 persons (positions 4 and 5 on one side, positions 7, 8, 1, 2 on the other side -> smaller count is 2 persons).
So there must be 2 persons between T(8) and V.
Counting 2 persons from T(8):
Clockwise: positions 1, 2 -> V is at position 3 (occupied by W, invalid).
Counter-clockwise: positions 7, 6 -> V is at position 5.

4. Now we have V at position 5.
5. "R sits third to the left of V."
Facing centre, left of position 5 (counter-clockwise is right, so clockwise is left):
1st left = position 6, 2nd left = position 7, 3rd left = position 8.
Position 8 is occupied by T. So this direction gives position 8.
If left of V (position 5) is clockwise: 5 -> 6 -> 7 -> 8 (occupied).
If left of V is counter-clockwise (1st left = 4, 2nd left = 3, 3rd left = 2): position 2 is vacant!
So R can sit at position 2.

Let's verify the positions clockwise from 1 to 8:
Position 1: P
Position 2: R
Position 3: W
Position 4: S
Position 5: V
Position 6: Q
Position 7: U (remaining person)
Position 8: T

Let's double check all conditions:
- Facing centre:
Right = Counter-clockwise (1 -> 2 -> 3 -> ...)
Left = Clockwise (1 -> 8 -> 7 -> ...)
- "W sits 2nd to the right of P": P=1, right is 2, 3. W=3. (Correct)
- "S and P have 2 persons between them": P=1, S=4. Between them are 2, 3 (R, W). (Correct)
- "Q sits 2 places away from S": S=4, 2 places away is 6 (Q) or 2 (R). Q=6. (Correct)
- "P does not sit adjacent to Q": P=1, Q=6. (Correct)
- "T and the one opposite W are immediate neighbours": Opposite W(3) is U(7). T is at 8, which is adjacent to 7. (Correct)
- "Persons between Q(6) and W(3) = Persons between T(8) and V(5)": Q and W have 2 persons (S, V). T and V have 2 persons (Q, U). (Correct)
- "R sits 3rd to the left of V(5)": Left of 5 is 4, 3, 2 -> 2 is R. (Correct)

Step 3: Answering the Question

"How many persons sit between Q and P when counted from the left of Q?"
Q is at position 6.
Facing centre at position 6, left is clockwise direction: position 5 (V), position 4 (S), position 3 (W), position 2 (R), until we reach P at position 1.
The persons sitting between Q and P going left from Q are: V, S, W, and R.
Count = 4 persons.

Therefore, there are Four persons between Q and P when counted from the left of Q.

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