Analyzing Seating Arrangement Sufficiency

The question asks us to determine who is sitting next to person B, given that five people (A, B, C, D, and F) are sitting around a round table. We need to evaluate whether the provided statements, individually or together, are sufficient to answer this question.

Let's break down the analysis of each statement.

Analysis of Statement 1: D is sitting between A and F.

Statement 1 tells us the relative positions of A, D, and F. At a round table with 5 people, if D is between A and F, the arrangement segment is A - D - F or F - D - A. The remaining two people are B and C. We don't have any information from this statement about where B and C are positioned relative to A, D, or F, and specifically not relative to B itself.

For example, if we have A-D-F, the remaining two spots could be occupied by B and C in different ways. Two possible arrangements that satisfy Statement 1 are:

• A - D - F - B - C (around the table)
• A - D - F - C - B (around the table)

In the arrangement A-D-F-B-C, the neighbours of B are F and C. In the arrangement A-D-F-C-B, the neighbours of B are C and A.

Since Statement 1 alone does not give a unique set of neighbours for B, Statement 1 alone is not sufficient to answer the question.

Analysis of Statement 2: C is sitting between B and F.

Statement 2 tells us the relative positions of B, C, and F. At a round table with 5 people, if C is between B and F, the arrangement segment is B - C - F or F - C - B. The remaining two people are A and D. We don't have any information from this statement about where A and D are positioned relative to B, C, or F, and specifically not relative to B's neighbours other than C and F.

For example, if we have B-C-F, the remaining two spots could be occupied by A and D in different ways. Two possible arrangements that satisfy Statement 2 are:

• B - C - F - A - D (around the table)
• B - C - F - D - A (around the table)

In the arrangement B-C-F-A-D, the neighbours of B are D and C. In the arrangement B-C-F-D-A, the neighbours of B are A and C.

Since Statement 2 alone does not give a unique set of neighbours for B, Statement 2 alone is not sufficient to answer the question.

Analysis of Statements 1 and 2 Together

Now let's consider both statements together:

1. D is sitting between A and F. This means A and F are neighbours of D.
2. C is sitting between B and F. This means B and F are neighbours of C.

From Statement 1, we know that F is next to D. From Statement 2, we know that F is next to C. Since F is at a round table, it can have two neighbours. These neighbours must be D and C based on the statements.

So, around F, the arrangement must be D - F - C or C - F - D (clockwise). Let's follow these arrangements to complete the circle with the remaining people (A and B).

Case 1: Arrangement around F is D - F - C (clockwise)

• We have D - F - C.
• From Statement 1: D is between A and F. Since D is followed by F, A must be before D. So we get A - D - F.
• From Statement 2: C is between B and F. Since C is preceded by F, B must be after C. So we get F - C - B.

Combining A - D - F and F - C - B around the common person F, we get the arrangement A - D - F - C - B around the round table.

In this arrangement (A - D - F - C - B), the people next to B are C and A.

Case 2: Arrangement around F is C - F - D (clockwise)

• We have C - F - D.
• From Statement 2: C is between B and F. Since C is followed by F, B must be before C. So we get B - C - F.
• From Statement 1: D is between A and F. Since D is preceded by F, A must be after D. So we get F - D - A.

Combining B - C - F and F - D - A around the common person F, we get the arrangement B - C - F - D - A around the round table.

In this arrangement (B - C - F - D - A), the people next to B are A and C.

In both possible orientations resulting from combining the statements (A-D-F-C-B and B-C-F-D-A), the people sitting next to B are A and C. While the direction might be reversed, the pair of neighbours for B (A and C) is uniquely determined.

Therefore, both statements 1 and 2 together are sufficient to answer the question: "who is sitting next to B?".

Conclusion on Sufficiency

Statement 1 alone is not sufficient. Statement 2 alone is not sufficient. However, both statements 1 and 2 together are sufficient to determine the neighbours of B.

Revision Table: Seating Arrangement Questions

When tackling seating arrangement data sufficiency questions, keep these points in mind:

• Understand the type of arrangement (linear, circular, square, etc.) and the number of people.
• For circular arrangements, remember that only relative positions matter unless a specific orientation (e.g., 'facing the center') is given.
• Analyze each statement independently first to see if it provides a unique answer.
• If individual statements are insufficient, combine them and see if the combined information leads to a unique solution.
• Draw diagrams or use position numbers to visualize the arrangements derived from the statements.
• Be mindful of clockwise vs. anti-clockwise possibilities in circular arrangements and how they might be equivalent in terms of relative positions.

Additional Information: Data Sufficiency Tips

Data sufficiency questions test your ability to determine if the given data is enough to answer a specific question, not necessarily to find the actual answer. Here are some tips:

• Read the question carefully to understand exactly what information is required to answer it.
• Analyze Statement 1 assuming only Statement 1 is true. Ignore Statement 2 completely for this step.
• Analyze Statement 2 assuming only Statement 2 is true. Ignore Statement 1 completely for this step.
• If neither statement alone is sufficient, combine the information from both statements. See if the combined information allows you to answer the question uniquely.
• Do not use external knowledge or make assumptions not explicitly given in the question or statements.
• The answer choices are standard:
  1. Statement 1 alone is sufficient.
  2. Statement 2 alone is sufficient.
  3. Both statements together are sufficient, but neither alone is sufficient.
  4. Either statement alone is sufficient.
  5. Neither statement alone nor both statements together are sufficient.
• For this particular question, the given options match one of these standard types.