Data Sufficiency – Linear arrangement of five buildings (find the middle) Question: In a row of five buildings P, Q, R, S and T, which building is exactly in the middle? Statements: I. Buildings S and Q are at the two extreme ends of the row. II.

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:This is a DS problem on linear arrangements. We must determine if the given constraints uniquely identify the building in the central (3rd) position of a row of five distinct buildings. Given Data / Assumptions: Buildings: P, Q, R, S, T arranged left-to-right in a straight row. Exactly five positions; no duplicates. Middle means the 3rd position from the left. Concept / Approach:Check each statement's implications separately, then together. If more than one valid lineup satisfies the statements but yields different middles, the information is insufficient. Step-by-Step Solution: Using I alone: S and Q occupy the two ends (order unknown). The middle could be P or R or T. Multiple possibilities ⇒ not sufficient.Using II alone: T is somewhere to the right of R (not necessarily adjacent). Without fixed end positions, the middle varies widely ⇒ not sufficient.Using I and II together: The ends are S and Q. The remaining middle three positions are some permutation of P, R, T with the constraint R left of T. Examples: (1) S R P T Q → middle is P; (2) S P R T Q → middle is R. Both satisfy I and II but give different middles. Therefore, even together the statements are not sufficient. Verification / Alternative check:Systematically enumerate permutations of the three middle buildings under R–left–of–T and confirm that the 3rd position changes across valid arrangements. Why Other Options Are Wrong: I alone / II alone / Both: none of these fix a unique middle building; multiple solutions persist. Either I or II: false because neither alone suffices. Common Pitfalls:Assuming 'to the right' means 'immediately to the right'. It does not; without adjacency, many orders remain possible. Final Answer:Neither I nor II is sufficient

Data Sufficiency – Linear arrangement of five buildings (find the middle) Question: In a row of five buildings P, Q, R, S and T, which building is exactly in the middle? Statements: I. Buildings S and Q are at the two extreme ends of the row. II. Building T is to the right of building R.

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