Six persons, A, B, C, D, E and F, are sitting in a straight line, all facing the same direction. E is sitting between B and F. A is third to the right of F. E is fourth to the left of A. C is not sitting next to A. Who is sitting between F and D?
C
Solving the Linear Seating Arrangement Puzzle
This question requires us to determine the sitting arrangement of six persons (A, B, C, D, E, and F) in a straight line based on the given conditions. All individuals are facing the same direction, which simplifies the relative positioning (right is always to one side, left to the other).
Understanding the Conditions
Let's list the given conditions:
- Six persons: A, B, C, D, E, F.
- Sitting in a straight line, facing the same direction.
- E is sitting between B and F. (Possibilities: B-E-F or F-E-B)
- A is third to the right of F.
- E is fourth to the left of A.
- C is not sitting next to A.
Step-by-Step Deduction of the Arrangement
We need to combine the given conditions to find the unique linear arrangement.
Let's use the conditions involving A and F/E to establish a base structure:
- A is third to the right of F: This means there are two persons between F and A, with A being to the right of F. If we denote positions with dashes (_), this looks like:
F _ _ A(Assuming right is towards A) - E is fourth to the left of A: This means there are three persons between E and A, with E being to the left of A.
E _ _ _ A(Assuming left is towards E)
Now, let's combine these two relative positions. Notice that A is the rightmost point in both structures. This implies E must be to the left of F.
Aligning them based on A:
E _ _ _ A
F _ _ A
Combining these, we get a sequence relative to each other:
E _ F _ _ A
This combined structure accounts for 6 positions, which is the total number of persons. So, this is the full arrangement structure, with the underscores representing positions occupied by the remaining persons.
The arrangement is: Position 1, Position 2, F, Position 4, Position 5, A.
Now, let's use the condition: E is sitting between B and F.
In our structure E _ F _ _ A, E and F are already placed. For E to be between B and F, B must be next to E. Since F is to the right of E, B must be to the left of E.
Placing B to the left of E in the structure E _ F _ _ A gives us:
B E F _ _ A
Let's verify the conditions with this new partial arrangement B E F _ _ A:
- E is between B and F? Yes.
- A is third to the right of F? From F, the positions to the right are _, _, A. Yes, A is in the 3rd spot to the right.
- E is fourth to the left of A? From A, the positions to the left are _, _, F, E. Yes, E is in the 4th spot to the left.
The arrangement is currently B E F _ _ A. The persons placed are B, E, F, and A. The total number of persons is 6. The remaining persons are C and D. The two empty spots are between F and A.
So the arrangement is B E F (P1) (P2) A, where (P1) and (P2) are the positions occupied by C and D.
The possible ways to place C and D in these two spots are:
- P1 = C, P2 = D → B E F C D A
- P1 = D, P2 = C → B E F D C A
Now, let's use the final condition: C is not sitting next to A.
- Consider arrangement 1: B E F C D A. Is C next to A? No, D is between C and A. This arrangement is Valid.
- Consider arrangement 2: B E F D C A. Is C next to A? Yes, C is immediately to the left of A. This arrangement is Invalid.
Therefore, the only valid arrangement is B E F C D A.
Answering the Question
The question asks: Who is sitting between F and D?
Looking at the final confirmed arrangement: B E F C D A
The persons are arranged from left to right. F is at the 3rd position and D is at the 5th position. The person sitting between F and D is C, who is at the 4th position.
The person sitting between F and D is C.
Based on the options provided:
1. C
2. E
3. A
4. B
The correct option is C.
| Position | Person |
|---|---|
| 1 | B |
| 2 | E |
| 3 | F |
| 4 | C |
| 5 | D |
| 6 | A |
Final Answer Derivation
By carefully applying all the given conditions one by one, we deduced the unique linear arrangement of the six persons. This arrangement is B E F C D A. Inspecting this arrangement, the person located between F and D is C.
Revision Table: Linear Seating Arrangement
| Condition | Inference / Structure |
|---|---|
| Six persons in a line | _ _ _ _ _ _ (6 positions) |
| A is 3rd right of F | F _ _ A |
| E is 4th left of A | E _ _ _ A |
| Combined F-A & E-A | E _ F _ _ A (6 positions) |
| E is between B and F | B must be next to E; since F is right of E, B is left of E. |
| Placing B | B E F _ _ A |
| Remaining persons (C, D) fill gaps | B E F (C/D) (D/C) A |
| C is not next to A | Eliminates B E F D C A. Confirms B E F C D A. |
| Final Arrangement | B E F C D A |
Additional Information: Seating Arrangement Concepts
Seating arrangement questions are common in logical reasoning sections of competitive exams. They test your ability to understand and combine multiple pieces of information to deduce a final arrangement.
Key concepts include:
- Linear Arrangement: Persons are in a single line. Direction (facing North, South, etc.) is crucial for left/right relations. If facing the same direction, left and right are consistent. If facing opposite directions, left/right is relative to each person.
- Circular Arrangement: Persons are in a circle, often facing towards or away from the center. Left and right are relative to the person and the direction they are facing.
- Relative Positioning: Phrases like "to the right of", "to the left of", "between", "immediate neighbor", "second to the left/right" define positions relative to others.
- Absolute Positioning: Sometimes, a person's position from an end (e.g., "third from the left end") might be given.
- Negative Information: Conditions like "C is not sitting next to A" are used to eliminate possibilities after a partial arrangement is formed.
Solving these puzzles often involves:
- Reading all conditions carefully.
- Starting with the most concrete or restrictive conditions.
- Combining conditions to build a partial or full structure.
- Using remaining conditions (especially negative ones) to eliminate invalid arrangements.
- Drawing diagrams or using notations like underscores to visualize the positions.
Important Questions from Linear Arrangement
Eight friends, A, B, C, D, E, F, G and H, are sitting in two lines of four persons each. Both the lines are facing each other. A is facing D. E is to the immediate left of G. H is to the immediate right of B. C is facing G. F is facing H. B is to the immediate right of the person who is facing G. D is to the immediate left of F. Which four persons are sitting in the same line?
Nine employees, K, L, M, N, O, P, Q, R and S, are sitting in the office in a straight line, all facing the east. O is third to the right of M. K is third to the left of P. Q is between P and S. N is fourth to the right of M. P is to the immediate right of N. R is fourth to the left of O. Which of the following statements is NOT correct?
Eight north-facing restaurants named P, Q, R, S, T, U, V and W are located in a straight line. S is second to the left of T. W is third to the left of P. T is between P and V. S is third to the left of V. W is to the immediate right of U. R is third to the right of P. Who is sitting fourth to the right of S?
Anamika, Gopal, Nischal, Vanmayi, Shresta and Sripad are sitting in a straight line facing the north. Nischal is to the immediate left of Gopal. Shresta is between Anamika and Sripad. Sripad is at the second place from the right end. Four persons are sitting between Nischal and Vanmayi. If Gopal and Sripad interchange their positions, then who will be sitting between Vanmayi and Shresta?
A question is given, followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and select the appropriate answer.
Question: How many people are standing in the row where all people are facing north?
Statements:
(I) A is fourth from the left end; M is second to the right of A; and R is second from the left end.
(II) M is fourth from the right end; only two people Stand between M and B.
