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.
Correct Answer: Both Statements I and II together are not sufficient.
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:
From I alone: youngest is P (unique).From II alone: youngest is R (unique).Taken together, there is a contradiction regarding who is youngest. Since the task is to answer using the given statements (which must both hold if used together), the joint use does not yield a consistent unique answer.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.