Seating/ordering — which house is exactly in the middle? Five houses A–E in a row. A is to the right of B. E is to the left of C and to the right of A. B is to the right of D. Which house is in the middle position?

Introduction / Context:Determine a linear arrangement that satisfies all the relative position constraints.

Given Data / Assumptions:

• A is to the right of B (A > B).
• E is to the left of C and to the right of A (A < E < C).
• B is to the right of D (B > D).

Concept / Approach:Use inequality chaining and try positions 1–5 from left to right.

Step-by-Step Solution:1) Choose A=3, E=4, C=5 to satisfy A < E < C.2) Then B and D must occupy positions 1 and 2 with B > D ⇒ D=1, B=2.3) Order is: 1=D, 2=B, 3=A, 4=E, 5=C.

Verification / Alternative check:All constraints hold: A right of B (3>2); E left of C and right of A (4 between 3 and 5); B right of D (2>1).

Why Other Options Are Wrong:They conflict with one or more constraints in any consistent arrangement.

Final Answer:A