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Five friends P, Q, R, S and T are standing in a row. Is P at one of the extreme ends? I. Q is to the immediate right of P. II. T is standing between S and R.
Data in statement I alone is sufficient
Data in statement II alone is sufficient
Data in both I and II together are necessary
Data in both I and II are not sufficient
Data in both I and II are not sufficient
Test if combining the statements allows multiple arrangements; if conflicting outcomes arise regarding the target, the data is insufficient.
Test if combining the statements allows multiple arrangements; if conflicting outcomes arise regarding the target, the data is insufficient.
Analyze Statement I
Statement I states that Q is to the immediate right of P, forming the block [P, Q]. This leaves the positions of R, S, and T completely undetermined.
Analyze Statement II
Statement II states that T is between S and R, forming the block [S, T, R] or [R, T, S]. This provides no information regarding the positions of P and Q.
Combine Statements I and II
Combining both statements gives the blocks [P, Q] and either [S, T, R] or [R, T, S]. We can arrange them as P-Q-S-T-R (where P is at the extreme left end) or S-T-R-P-Q (where P is fourth from the left, not at an extreme end), leading to conflicting answers.
A: Statement I alone does not determine the positions of R, S, and T. B: Statement II alone provides no information about P and Q. C: Both statements combined still yield multiple valid arrangements with conflicting answers for P's position.
D is correct because even when combining both statements, multiple arrangements are possible where P is either at an extreme end or not, making the data insufficient.
Always test for alternative valid arrangements when evaluating data sufficiency in puzzle and seating problems.
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