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.

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:

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.