There are eight persons – A, B, C, D, P, Q, R and S. All of them are sitting in a straight row and are facing in the south direction but not necessarily in the same order. D sits to the immediate right of A. There are only two persons between B and S. A is second to the left of B, who is fourth from the right corner. The number of persons between A and P is the same as the number of persons between S and C. P sits at one corner of the row. R is not a neighbour of C, who is to the immediate left of Q. How many persons are seated to the left of Q?
- ASix
- BThree
- CTwo
- DFour
Solution & Step-by-step Explanation
Let's create the line configuration. Since all individuals face South:
Left side is towards our Right.
Right side is towards our Left.
Let's number the 8 positions from Left to Right relative to our perspective (Pos 1 to 8, where 1 is the westernmost/leftmost end from our view and 8 is the easternmost/rightmost end from our view).
Facing South:
Left-hand side of a person points to Pos 8 (Right corner of our view).
Right-hand side of a person points to Pos 1 (Left corner of our view).
Let's process the clues step by step:
"B is fourth from the right corner":
The right corner from a South-facing perspective is Pos 1 (left of our view). So fourth from the right corner means position 4.
Let's check: right corner is Pos 1, second from right is 2, third is 3, fourth is 4. So B is at Pos 4.
"A is second to the left of B":
Left means towards Pos 8. Second to the left of B (Pos 4) is Pos 6. So, A = Pos 6.
"D sits to the immediate right of A":
Right means towards Pos 1. Immediate right of A (Pos 6) is Pos 5. So, D = Pos 5.
"There are only two persons between B and S":
B is at Pos 4. S could be at Pos 1 or Pos 7. If S is at Pos 7, let's see. Let's test both.
"P sits at one corner of the row":
P can be at Pos 1 or Pos 8.
If S is at Pos 7: Then P could be at Pos 1 or 8.
"The number of persons between A and P is same as between S and C."
If P is at Pos 8: persons between A (6) and P (8) is 1. Then persons between S (7) and C must be 1 → C would be at Pos 5 (occupied by D) or 9 (out of bounds). So P cannot be at Pos 8 if S is at Pos 7.
If P is at Pos 1: persons between A (6) and P (1) is 4. Then persons between S (7) and C must be 4 → C would be at Pos 2.
Let's check if C is at Pos 2: "C is to the immediate left of Q". Left means towards Pos 8, so Q must be at Pos 1. But Pos 1 is occupied by P. Contradiction!
Therefore, S must be at Pos 1.
Since S is at Pos 1, P must be at the other corner, which is Pos 8.
Now let's calculate the spacing:
Number of persons between A (6) and P (8) is 1 (which is position 7).
Therefore, the number of persons between S (1) and C must be 1. This means C is at Pos 3.
"C is to the immediate left of Q":
Left means towards Pos 8. If C (Pos 3) is to the immediate left of Q, then Q must be at Pos 2.
Now we have positions 1 to 8:
Pos 1: S
Pos 2: Q
Pos 3: C
Pos 4: B
Pos 5: D
Pos 6: A
Pos 7: R (since R is the only one remaining)
Pos 8: P
Let's double-check: "R is not a neighbour of C". R is at 7, C is at 3. Correct.
Question asks: "How many persons are seated to the left of Q?"
Q is at Pos 2.
Left for a South-facing person means towards Pos 8.
The positions to the left of Q are Pos 3, 4, 5, 6, 7, 8.
Counting these positions: there are exactly 6 persons (C, B, D, A, R, P).
Left side is towards our Right.
Right side is towards our Left.
Let's number the 8 positions from Left to Right relative to our perspective (Pos 1 to 8, where 1 is the westernmost/leftmost end from our view and 8 is the easternmost/rightmost end from our view).
Facing South:
Left-hand side of a person points to Pos 8 (Right corner of our view).
Right-hand side of a person points to Pos 1 (Left corner of our view).
Let's process the clues step by step:
"B is fourth from the right corner":
The right corner from a South-facing perspective is Pos 1 (left of our view). So fourth from the right corner means position 4.
Let's check: right corner is Pos 1, second from right is 2, third is 3, fourth is 4. So B is at Pos 4.
"A is second to the left of B":
Left means towards Pos 8. Second to the left of B (Pos 4) is Pos 6. So, A = Pos 6.
"D sits to the immediate right of A":
Right means towards Pos 1. Immediate right of A (Pos 6) is Pos 5. So, D = Pos 5.
"There are only two persons between B and S":
B is at Pos 4. S could be at Pos 1 or Pos 7. If S is at Pos 7, let's see. Let's test both.
"P sits at one corner of the row":
P can be at Pos 1 or Pos 8.
If S is at Pos 7: Then P could be at Pos 1 or 8.
"The number of persons between A and P is same as between S and C."
If P is at Pos 8: persons between A (6) and P (8) is 1. Then persons between S (7) and C must be 1 → C would be at Pos 5 (occupied by D) or 9 (out of bounds). So P cannot be at Pos 8 if S is at Pos 7.
If P is at Pos 1: persons between A (6) and P (1) is 4. Then persons between S (7) and C must be 4 → C would be at Pos 2.
Let's check if C is at Pos 2: "C is to the immediate left of Q". Left means towards Pos 8, so Q must be at Pos 1. But Pos 1 is occupied by P. Contradiction!
Therefore, S must be at Pos 1.
Since S is at Pos 1, P must be at the other corner, which is Pos 8.
Now let's calculate the spacing:
Number of persons between A (6) and P (8) is 1 (which is position 7).
Therefore, the number of persons between S (1) and C must be 1. This means C is at Pos 3.
"C is to the immediate left of Q":
Left means towards Pos 8. If C (Pos 3) is to the immediate left of Q, then Q must be at Pos 2.
Now we have positions 1 to 8:
Pos 1: S
Pos 2: Q
Pos 3: C
Pos 4: B
Pos 5: D
Pos 6: A
Pos 7: R (since R is the only one remaining)
Pos 8: P
Let's double-check: "R is not a neighbour of C". R is at 7, C is at 3. Correct.
Question asks: "How many persons are seated to the left of Q?"
Q is at Pos 2.
Left for a South-facing person means towards Pos 8.
The positions to the left of Q are Pos 3, 4, 5, 6, 7, 8.
Counting these positions: there are exactly 6 persons (C, B, D, A, R, P).