Introduction / Context:
Determine the exact middle person in a linear arrangement using positional clues. Data Sufficiency requires finding whether the given statements, alone or together, uniquely determine the middle seat (position 3 out of 5).
Given Data / Assumptions:
- Five seats in a row labeled 1 (leftmost) to 5 (rightmost).
- “Between” is interpreted as in-order with the middle person somewhere strictly between the two named persons.
- Goal: Identify the unique middle person.
Concept / Approach:
Translate constraints into relative orders and test feasible placements. If more than one arrangement remains with different middles, the data is insufficient. If exactly one arrangement satisfies all, the data is sufficient.
Step-by-Step Solution:
From I and II: B is between E and C, and B is to the right of E ⇒ the left-to-right order among these three is E ... B ... C. From III: D is between A and E ⇒ A ... D ... E (left-to-right). Try E at seat 3: Then A and D must be to the left with A-D-E occupying seats 1-2-3. Since E ... B ... C, B and C occupy seats 4 and 5 with B before C. Unique arrangement: 1=A, 2=D, 3=E, 4=B, 5=C. Try E at seat 4: Then A and D must be left of E, leaving only one seat to the right for both B and C, which is impossible given E ... B ... C. Other E positions also fail except seat 3. Therefore, the only arrangement satisfying all three statements has E in the middle.
Verification / Alternative check:
Check subsequences: E-B-C holds (3-4-5) and A-D-E holds (1-2-3). Consistent and unique.
Why Other Options Are Wrong:
- Any pair among I, II, III leaves multiple valid seating orders; the middle is not fixed.
- Hence only the combination of all three conclusively yields the middle person.
Common Pitfalls:
Treating “between” as “adjacent” (not required); not testing all feasible E positions; overlooking the uniqueness requirement for Data Sufficiency.
Final Answer:
All I, II and III.
Discussion & Comments