Data Sufficiency — Heaviest Bag (P, Q, R, S, T) Which bag is the heaviest? I. Q is heavier than R and S. T is heavier than only P. II. Exactly three bags are lighter than R. Also, Q weighs 50 kg, which is 2 kg more than R.
Correct Answer: Statement II alone is sufficient; Statement I alone is not sufficient.
Introduction / Context:We rank five bags by weight to identify the heaviest using partial order and one numeric gap.
Given Data / Assumptions:
- I: Q>R,S and T>only P (so T is second-lightest). Heaviest remains ambiguous among Q and perhaps another bag.
- II: Three bags lighter than R ⇒ only one heavier than R. Also Q = R + 2 kg ⇒ Q is heavier than R.
Concept / Approach:If only one bag is heavier than R and Q is heavier than R, then Q must be that unique heavier bag, i.e., Q is the heaviest.
Step-by-Step Solution:
1) From II: position R as second heaviest (only one heavier).2) With Q = R + 2 kg ⇒ Q is heavier than R; thus Q is the unique heaviest.3) From I alone, candidates remain; cannot fix the heaviest.Verification / Alternative check:No other bag can exceed Q under II without violating “exactly three lighter than R”.
Why Other Options Are Wrong:I alone insufficient; both together not needed; either alone false since only II suffices.
Common Pitfalls:Misreading “exactly three lighter than R” (it places R second highest).
Final Answer:Statement II alone is sufficient.