Data Sufficiency – Ordering by height (find the middle position) Question: Who among P, Q, T, V, and M stands exactly in the middle when arranged in ascending order of height? Statements: I. V is taller than Q but shorter than M. II. T is taller than Q and M but shorter than P.

Introduction / Context:
This DS problem asks for the exact person at the middle position when five people are ordered by height (shortest to tallest). We must judge whether each statement independently, or both together, determine the middle person uniquely.

Given Data / Assumptions:

• Set of persons: P, Q, T, V, M (all distinct).
• Ascending order means position 3 of 5 (middle) from shortest to tallest.
• No two persons have exactly the same height (standard assumption unless stated otherwise).

Concept / Approach:
Translate each statement into inequality chains and see whether a complete linear order results. If a single statement leaves multiple possible lineups, it is not sufficient. If the combination gives a unique lineup, both together are sufficient.

Step-by-Step Solution:

Verification / Alternative check:
Try to construct any alternative consistent ordering that changes the middle. All constraints force V between M and Q and T above M but below P, leaving no flexibility; M must be in the middle.

Why Other Options Are Wrong:

• I alone or II alone: each leaves at least one person's position undetermined; the middle can vary.
• Either I or II: false since neither alone suffices.
• Neither I nor II: false because together they fix a unique order.

Common Pitfalls:
Mixing up ascending with descending order; ignoring that five distinct heights imply a unique middle position once the chain is fully specified.

Final Answer:
Both I and II are sufficient