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.

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:

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