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. (II) Only one person sits between A and B; C sits to the immediate right of B.
Understanding the Circular Arrangement Question
The problem asks us to identify the person sitting immediately to the right of A, given that A, B, C, and D are sitting around a circular table and facing the center. In a circular arrangement with people facing the center, "immediate right" refers to the person encountered when moving in the anti-clockwise direction from the person in question (A).
We need to determine if the information in Statement I alone, Statement II alone, or both statements together are sufficient to pinpoint the person to A's immediate right.
Analyzing Statement I Data
Statement I provides two pieces of information about the seating arrangement:
- C sits to the immediate left of A.
- Only one person sits between C and D.
Let's interpret these conditions for a circular table with 4 people facing the center:
- "C sits to the immediate left of A" means C is the person immediately clockwise to A.
- "Only one person sits between C and D" in a 4-person circular arrangement implies that C and D are seated opposite each other. If there was zero person between them, they would be adjacent. If there were two people between them (which would mean zero people the other way), they would also be adjacent. With 4 people, one person between along one arc means they are opposite.
Based on Statement I, we know the relative positions of A, C, and D:
- C is clockwise to A.
- C is opposite D.
Let's place A at an arbitrary position. Since C is immediately clockwise to A, C's position is fixed relative to A. Since D is opposite C, D's position is also fixed relative to C and A. With 4 positions around the table, the fourth person, B, must occupy the only remaining spot. This uniquely determines the relative seating arrangement.
Let's illustrate a possible arrangement (reading clockwise):
- Place A at the bottom. Immediate left of A (clockwise) is C, so C is to the left of A.
- C is opposite D, so D is above C's opposite position.
- The remaining person, B, takes the last spot.
Arrangement (clockwise): A, C, B, D.
Let's check the conditions from Statement I:
- C sits to the immediate left of A: In the arrangement A → C → B → D, C is indeed immediately clockwise (left) of A. This is correct.
- Only one person sits between C and D: Starting from C (clockwise), we have C → B → D. One person (B) is between C and D. Starting from C (anti-clockwise), we have C → A → D. One person (A) is between C and D. C and D are opposite, which fits the condition. This is correct.
The arrangement A → C → B → D (clockwise) is consistent with Statement I and is uniquely determined (up to rotation). In this arrangement, moving anti-clockwise from A, the immediate next person is D.
Therefore, Statement I alone is sufficient to determine who sits to the immediate right of A (it's D).
Analyzing Statement II Data
Statement II provides two pieces of information:
- Only one person sits between A and B.
- C sits to the immediate right of B.
Let's interpret these conditions for a circular table with 4 people:
- "Only one person sits between A and B" means A and B are sitting opposite to each other.
- "C sits to the immediate right of B" means C is the person immediately anti-clockwise to B.
Based on Statement II, we know the relative positions of A, B, and C:
- A is opposite B.
- C is anti-clockwise to B.
Let's place A. Since A is opposite B, B's position is fixed relative to A. Since C is immediately anti-clockwise to B, C's position is fixed relative to B and A. The fourth person, D, must occupy the remaining spot. This uniquely determines the relative seating arrangement.
Let's illustrate a possible arrangement based on Statement II (reading clockwise):
- Place A at the bottom. A is opposite B, so B is at the top.
- C sits to the immediate right of B (anti-clockwise). From B at the top, moving anti-clockwise places C to B's right.
- The remaining person, D, takes the last spot.
Arrangement (clockwise): A, C, B, D.
Let's check the conditions from Statement II:
- Only one person sits between A and B: In the arrangement A → C → B → D, A is opposite B. This is correct.
- C sits to the immediate right of B: From B, moving anti-clockwise encounters C. This is correct.
The arrangement A → C → B → D (clockwise) is consistent with Statement II and is uniquely determined (up to rotation). In this arrangement, moving anti-clockwise from A, the immediate next person is D.
Therefore, Statement II alone is sufficient to determine who sits to the immediate right of A (it's D).
Concluding on Sufficiency
Both Statement I alone and Statement II alone provide enough information to uniquely determine the seating arrangement relative to A and thus identify the person sitting immediately to A's right (which is D in both cases).
| Statement | Information Provided | Is it Sufficient to Determine Immediate Right of A? |
|---|---|---|
| I alone | C immediate left of A; One person between C and D. | Yes, uniquely determines arrangement relative to A. |
| II alone | One person between A and B; C immediate right of B. | Yes, uniquely determines arrangement relative to A. |
Since either statement alone is sufficient to answer the question, the appropriate answer choice is "Data in either statement I alone or statement II alone is sufficient to answer the question".
Revision Table: Circular Seating Concepts
| Term | Meaning (4 people, facing center) |
|---|---|
| Immediate Left | Next person clockwise. |
| Immediate Right | Next person anti-clockwise. |
| One person between X and Y | X and Y are opposite each other. |
Additional Information: Solving Data Sufficiency Puzzles
Data sufficiency questions in logical reasoning require careful analysis of each statement independently first. Only if neither statement alone is sufficient do you combine them. It's crucial to determine if the information leads to a single, unique solution for the question asked.
For seating arrangement puzzles, sketching the possibilities based on the conditions is very helpful. Remember that relative positions are key in circular arrangements. If the data fixes the position of every person relative to one another, it is sufficient.
In this problem, although both statements led to the same arrangement (A-C-B-D clockwise), the sufficiency is determined by whether *each statement independently* allows you to answer the question uniquely, regardless of whether the answers from each statement are identical.
Similar Questions
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