Introduction / Context:
We have five persons seated in a row facing North. We must identify the person in the exact middle position using Data Sufficiency logic—checking each statement alone and then both together.
Given Data / Assumptions:
- Row has 5 positions, indexed left→right for North-facing seats.
- I: A is third to the left of D; B is immediately to the right of C.
- II: B is second to the right of A; E is not adjacent to D.
Concept / Approach:
For North-facing rows, ‘‘to the right’’ means higher index. We attempt placements consistent with each statement and test uniqueness of the middle seat occupant.
Step-by-Step Solution:
1) Statement I alone: A = D − 3 forces A to be at most position 2 (since D must be ≤5). Possible pairs: (A=1, D=4) or (A=2, D=5). Also “B right of C” only fixes adjacency direction (C,B). Multiple seatings exist with different middle occupants. So I alone is insufficient.2) Statement II alone: B = A + 2 narrows relative positions of A and B (valid pairs: (A,B) = (1,3), (2,4), (3,5)). “E not neighbour of D” still allows multiple layouts; the middle seat varies across valid arrangements. So II alone is insufficient.3) Combine I + II: Test A=1 scenario. From II, B=3. From I, D=A+3=4 and C is immediately left of B (since B is immediately right of C), so C=2, placing E=5 (only seat remaining). This satisfies “E not neighbour of D” (E=5 not adjacent to D=4 is false), so A=1 is invalid due to II's E–D condition? Check: II states E is not an immediate neighbour of D—indeed 5 is neighbour of 4, so invalid. Now try A=2: Then B=4 (from II), D=5 (from I), and C=3 (since B is immediately right of C). E must be 1. E is not adjacent to D (1 not neighbour of 5) satisfied. The seating becomes [1:E, 2:A, 3:C, 4:B, 5:D], uniquely fixing the middle seat as C.
Verification / Alternative check:
No other A–B pair works with I + II simultaneously without violating adjacency or row bounds. Hence the combined information yields a single consistent arrangement with C in the middle.
Why Other Options Are Wrong:
- A/B: Each alone admits multiple layouts—no unique middle person.
- C: “Either alone” is false because neither alone suffices.
- D: Together they are sufficient (unique layout), so “not sufficient” is false.
Common Pitfalls:
Confusing left/right with South-facing logic; forgetting the 5-seat boundary when applying ‘‘third to the left’’; ignoring the non-neighbour constraint for E and D when combining statements.
Final Answer:
Both statements together are sufficient, but NEITHER alone is sufficient.
Discussion & Comments