Data Sufficiency — Linear Seating (Who Sits in the Middle?) Among P, Q, R, S, and T in a straight line facing North, who sits exactly in the middle? I. P sits third to the left of S. T is an immediate neighbour of both P and R. II. T sits second to the left of S. Q is not an immediate neighbour of T or S.
Correct Answer: Both statements I and II together are sufficient, but neither alone is sufficient.
Introduction / Context:We must identify the exact middle seat using two incomplete linear constraints.
Given Data / Assumptions:
- I gives a 3-left relation between P and S and binds T to both P and R, leaving multiple valid permutations.
- II fixes T two-left of S and restricts Q’s adjacency, but still allows multiple permutations.
Concept / Approach:Each statement alone permits more than one arrangement; combining them typically collapses to a unique layout, hence a unique middle person.
Step-by-Step Solution:
1) Build candidates from I (positions of P,S,T,R relative).2) Intersect with II (T two-left of S; Q not adjacent to T,S).3) Unique configuration emerges ⇒ unique middle seat.Verification / Alternative check:Quick backtracking shows single consistent ordering when both are enforced.
Why Other Options Are Wrong:I alone or II alone: multiple possibilities; either alone false; “even both not sufficient” is false.
Common Pitfalls:Forgetting everyone faces North (left/right are absolute), or placing two people in one seat.
Final Answer:Both statements together are sufficient; neither alone is sufficient.