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: Four people, A, B, C and D, are sitting in a straight line, facing south. Who is sitting at the right end? Statements: (I) Only two people sit between B and D; A sits to the immediate left of B. (II) Only one person sits between B and C; A sits to the immediate right of C.
Data in statement I alone is sufficient to answer the question while data in statement II is not
Understanding the Seating Arrangement Problem
The question asks us to determine who is sitting at the right end of a straight line of four people (A, B, C, D) who are all facing south. We are given two statements and need to evaluate if either statement alone, or both together, are sufficient to answer the question.
When people are facing south, their left is towards our right perspective, and their right is towards our left perspective. Let's denote the positions in the line from their left end to their right end:
Their Left End → Position 1 → Position 2 → Position 3 → Position 4 ← Their Right End
From our perspective (looking at them), the order would be:
Our Left End → Position 4 → Position 3 → Position 2 → Position 1 ← Our Right End
The question asks who is at their right end, which corresponds to Position 4 in their perspective or Position 1 from our perspective.
Analyzing Statement I
Statement I provides two conditions:
- Only two people sit between B and D.
- A sits to the immediate left of B.
Let's analyze these conditions in the context of the four positions (1, 2, 3, 4) from their left end to right end:
- Condition 1: If there are exactly two people between B and D, they must be at the ends of the line. So, either B is at Position 1 and D is at Position 4, or D is at Position 1 and B is at Position 4.
- Condition 2: A sits to the immediate left of B (from their perspective). This means if B is at a certain position, A is at the position immediately to its left (one position lower in our numbering 1-4).
Let's test the possibilities from Condition 1 with Condition 2:
- Case 1: B is at Position 1 (Their Left End), D is at Position 4 (Their Right End).
Arrangement: B _ _ D
According to Condition 2, A must sit to the immediate left of B. But B is at Position 1, which is their leftmost position. There is no position to the left of Position 1. So, this case is impossible. - Case 2: D is at Position 1 (Their Left End), B is at Position 4 (Their Right End).
Arrangement: D _ _ B
According to Condition 2, A must sit to the immediate left of B. B is at Position 4. The position immediately to the left of Position 4 is Position 3. So, A must be at Position 3.
Arrangement becomes: D _ A B
With the arrangement D _ A B, positions 1, 3, and 4 are occupied by D, A, and B respectively. There are four people in total (A, B, C, D). The remaining person is C, and the remaining position is Position 2.
So, the complete arrangement from their left end to their right end is:
Position 1 (D) → Position 2 (C) → Position 3 (A) → Position 4 (B)
This unique arrangement derived from Statement I shows that B is at Position 4, which is their right end.
Since Statement I alone provides a definite answer to the question "Who is sitting at the right end?" (the answer is B), Statement I is sufficient.
Analyzing Statement II
Statement II provides two conditions:
- Only one person sits between B and C.
- A sits to the immediate right of C.
Let's analyze these conditions using the four positions (1, 2, 3, 4) from their left end to right end:
- Condition 1: If there is exactly one person between B and C, possible pairs of positions are (1, 3), (2, 4), (3, 1), (4, 2).
- Condition 2: A sits to the immediate right of C (from their perspective). This means if C is at a certain position, A is at the position immediately to its right (one position higher in our numbering 1-4).
Let's test the possibilities from Condition 1 with Condition 2:
- Case A: B is at Position 1, C is at Position 3.
Arrangement: B _ C _
According to Condition 2, A is immediately right of C (Position 3). So A is at Position 4.
Arrangement becomes: B _ C A. The remaining person D must be at Position 2.
Complete arrangement: (B, D, C, A). Their right end is Position 4, where A is sitting. - Case B: B is at Position 2, C is at Position 4.
Arrangement: _ B _ C
According to Condition 2, A is immediately right of C (Position 4). But Position 4 is their rightmost position; there is no position to its right. This case is impossible. - Case C: C is at Position 1, B is at Position 3.
Arrangement: C _ B _
According to Condition 2, A is immediately right of C (Position 1). So A is at Position 2.
Arrangement becomes: C A B _. The remaining person D must be at Position 4.
Complete arrangement: (C, A, B, D). Their right end is Position 4, where D is sitting. - Case D: C is at Position 2, B is at Position 4.
Arrangement: _ C _ B
According to Condition 2, A is immediately right of C (Position 2). So A is at Position 3.
Arrangement becomes: _ C A B. The remaining person D must be at Position 1.
Complete arrangement: (D, C, A, B). Their right end is Position 4, where B is sitting.
From Statement II, we found three possible arrangements for who is sitting from their left end to right end: (B, D, C, A), (C, A, B, D), and (D, C, A, B). The person at their right end (Position 4) could be A, D, or B.
Since Statement II leads to multiple possible answers for the question, Statement II alone is not sufficient.
Conclusion
Statement I alone is sufficient to determine who is sitting at the right end (it is B). Statement II alone is not sufficient as it leads to multiple possibilities (A, D, or B could be at the right end).
| Statement | Is it sufficient to answer the question? | Reason |
|---|---|---|
| I | Yes | Leads to a unique arrangement D C A B (from their left to right), placing B at the right end. |
| II | No | Leads to multiple possible arrangements (B D C A, C A B D, D C A B), where the person at the right end can be A, D, or B. |
Therefore, the data in statement I alone is sufficient, while the data in statement II is not sufficient.
Revision Table: Linear Seating Arrangement Concepts
| Concept | Description | Facing Direction Impact |
|---|---|---|
| Linear Arrangement | People/objects placed in a straight line. | Direction affects 'left' and 'right' relative positions. |
| Relative Position | Describing someone's place based on others (e.g., 'left of', 'right of', 'between'). | Crucially depends on the facing direction. |
| Immediate Left/Right | The very next person on one's left or right side. | Depends on facing direction and arrangement order. |
| Ends of the Line | The first and last positions in the straight line. | The 'left end' and 'right end' are determined by the facing direction. |
Additional Information: Solving Direction-Based Seating Puzzles
Solving seating arrangement problems, especially those involving direction, requires careful consideration of perspective.
- Establish a Frame of Reference: Decide whether you will draw/note positions from your perspective (viewer's left/right) or the perspective of the people in the arrangement (their left/right). Be consistent.
- Visualize or Draw: Drawing the line and filling in positions as you deduce them can be very helpful. Use placeholders like underscores (\_ \_ \_ \_) for unknown positions.
- Interpret Directions Carefully: Pay close attention to the facing direction (North, South, East, West). This dictates how 'left' and 'right' are interpreted.
- Facing North: Their left is our left, their right is our right.
- Facing South: Their left is our right, their right is our left.
- Facing East: Their left is our upward, their right is our downward (on paper).
- Facing West: Their left is our downward, their right is our upward (on paper).
- Break Down Statements: Analyze each condition in the statements separately before trying to combine them.
- Test All Possibilities: If a condition presents multiple initial scenarios (like B _ _ D or D _ _ B), explore each scenario fully with the other conditions from the same statement.
- Check for Sufficiency: A statement is sufficient only if it leads to one unique, definite answer to the question asked. If it leads to multiple possible answers, it is not sufficient.
Similar Questions
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: Six people sit in two parallel rows. In Row 1 - J, K and L sit facing towards north, and in Row 2 - F, G and H sit facing towards south. Each person in a row faces a person in the other row. Who faces G?
Statements:
(I) H faces K; L faces an immediate neighbour of H.
(II) G sits at one of the extreme ends of the row; J sits to the immediate left of L.
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: A, B, C and D are sitting around a circular table facing the centre. Who sits to the immediate right of A?
Statements:
(I) C sits to the immediate left of A; only one person sits between C and D.
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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.
In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statement/s are sufficient to answer the question. Read both the statements and choose your answer carefully.
Question: P, Q, R, S, T, U and V are 7 people standing in a row all facing North (not necessarily in the same order). Who is standing second to the right of T?
Statements:
(I) U is standing 3rd from the right end and 2nd to the left of R.
(II) Q is standing to the immediate right of T. Q is standing 2nd to the left of P
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?
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?
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?
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?
Important Questions from Linear Arrangement
M, N, L, O, Q and H are sitting in a row. Q and H are in the centre. M and N are at the ends. L is sitting to the immediate left of N. Who is to the right of M?
Five friends, Shruti, Shreya, Anup, Ankit and Kiran, are sitting in a row facing towards the south. Shruti is between Shreya and Anup. Kiran and Shreya are sitting at the extreme ends of the west and east, respectively. Who is sitting in the middle?
Five students are standing in a line. Suman is standing next to Pranav but not next to Deena. Kumar is standing next to Raju, who is standing on the extreme left, and Deena is not standing next to Kumar.
Who is standing in the middle?Eight friends, A, B, C, D, E, F, G and H, are sitting in a straight line, all facing the north. F is sitting between D and G. B is sitting between H and A. E is third to the left of G. G is sitting at one of the corners. H is third to the left of C. Who is sitting between A and E?
Five students are sitting in a row. Akbar is to the left of the person sitting in the middle, but to the right of Sekar. Prakash is to the right of Deva, and Ram is to the right of Prakash. Ram is second from the person sitting in the middle. Who is the person sitting in the middle?
