Ages — Among P, Q, R, S, T (all different ages), who is the youngest? Statements: I. Q is younger than only P. II. S is older than only R.

Introduction / Context:We must find the youngest person using partial order statements that may even conflict.

Given Data / Assumptions:

• I: 'Q is younger than only P' ⇒ only P is younger than Q, so P is the youngest and Q is second youngest.
• II: 'S is older than only R' ⇒ only R is younger than S, so R is the youngest and S is second youngest.

Concept / Approach:Check consistency; if I implies youngest=P and II implies youngest=R, then the two cannot simultaneously be true unless P=R (not allowed).

Step-by-Step Solution:

Verification / Alternative check:If we try to reconcile by reinterpreting phrasing, we would be adding assumptions. The DS framework disallows that.

Why Other Options Are Wrong:

• I alone sufficient / II alone sufficient: each is sufficient individually, but the question's options are about sufficiency classification; contradiction between them means we cannot pick 'either alone' as sufficient to the DS prompt of which option describes sufficiency generally.
• Both together sufficient: false due to inconsistency.

Common Pitfalls:Overlooking that contradictory statements make the pair unusable; misreading 'younger than only P' vs 'older than only R'.

Final Answer:Both Statements I and II together are not sufficient.