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A question is followed by two statements (I) and (II). Are all five friends A, B, C, D, and E sitting in a row facing north? I. B sits at one end, and C is to his immediate right. II. D sits between A and E. Is it enough to determine the order?
Only I is sufficient
Only II is sufficient
Both I and II are needed
Neither I nor II is sufficient
Neither I nor II is sufficient
Analyze each statement independently for fixed anchor points, then test combined ambiguity for remaining positions.
Analyze each statement independently for fixed anchor points, then test combined ambiguity for remaining positions.
Analyze Statement I
B sits at the extreme left end (since C is to his immediate right, B cannot be at the right end), meaning B is at position 1 and C is at position 2. Positions 3, 4, and 5 remain completely undetermined.
Analyze Statement II
D sits between A and E, which can form either A-D-E or E-D-A, but the positions of B and C are unknown.
Combine Statements I and II
B and C take positions 1 and 2. A, D, and E take positions 3, 4, and 5 with D in the middle (position 4). However, the exact order can still be A-D-E or E-D-A, leaving the final arrangement ambiguous.
A: Statement I alone leaves three positions blank and undetermined. B: Statement II alone provides no information about B and C. C: Combining both still yields two possible arrangements for A and E, making them insufficient.
D is correct because even after combining both statements, the exact order of A and E (A-D-E versus E-D-A) cannot be uniquely determined.
In data sufficiency seating puzzles, always verify if remaining slots have multiple valid permutations before declaring combined statements sufficient.
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