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A question is given, followed by two statements labelled I and II. Identify which of the statements is/are sufficient to answer the question. A, B, C, D and E are sitting in a straight line facing North. Who sits on the extreme right end? (I) Exactly three people sit between B and C. (II) A sits immediately to the left of B.
Both Statements I and II put together are not sufficient to answer the question.
Both Statements I and II put together (and not independently) are sufficient to answer the question.
Data in Statement I alone is sufficient to answer the question, while data in Statement II is not.
Data in Statement II alone is sufficient to answer the question, while data in Statement I is not.
Both Statements I and II put together (and not independently) are sufficient to answer the question.
In seating puzzles with 5 slots, if you have a fixed relative distance (3 between B and C) and a fixed adjacency (A-B), test the absolute boundary positions for the A-B-C block.
In seating puzzles with 5 slots, if you have a fixed relative distance (3 between B and C) and a fixed adjacency (A-B), test the absolute boundary positions for the A-B-C block.
Analyze Statement I
With 5 people, if there are exactly 3 people between B and C, they must occupy the extreme ends (Position 1 and Position 5). So, {B, C} are at {1, 5} or {5, 1}. This is insufficient.
Analyze Statement II
A sits immediately to the left of B. This only provides the sequence AB, but their absolute positions are unknown. This is insufficient.
Combine Statements I and II
From (I), B and C are at 1 and 5. If B is at 1, A is at 0 (impossible, as there is no position 0). Therefore, B must be at 5, which means C is at 1. Since A is immediately left of B, A must be at position 4. The arrangement is C, _, _, A, B. D and E fill the remaining spots 2 and 3. Thus, B is at the extreme right.
A: Both statements together solve the arrangement, so this is false. C: Statement I only tells us the endpoints, not the specific identity of the rightmost seat. D: Statement II only gives a relative pair without reference to the full line boundaries.
B is correct because combining the extreme-end constraint from Statement I with the relative adjacency constraint from Statement II fixes B at the 5th position.
In data sufficiency, always check for 'boundary conditions' (e.g., first or last seats) first, as they often limit the available space for the remaining variables.
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