Data Sufficiency — Marks of P (Total of P,Q,R,S is 360) How many marks did P score in Mathematics? I. P scored one-third of the total of Q, R, and S. II. The average of Q and R is 20 more than S.

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:We use totals and linear relations among marks. Given Data / Assumptions: Total: P + Q + R + S = 360. I: P = (1/3)*(Q + R + S). II: (Q + R)/2 = S + 20 ⇒ Q + R = 2S + 40. Concept / Approach:From I alone we can directly solve for P using the total. Step-by-Step Solution: 1) From I: P = (1/3)(Q+R+S).2) Total ⇒ P + (Q+R+S) = 360 ⇒ Since P = (1/3)(Q+R+S), let X = (Q+R+S). Then P = X/3 and P + X = 360 ⇒ (X/3) + X = 360 ⇒ (4X/3) = 360 ⇒ X = 270.3) Hence P = X/3 = 90 (unique). Verification / Alternative check:II is not needed to compute P. It provides another relation among Q,R,S but P is already determined. Why Other Options Are Wrong:II alone cannot fix P without the total; “both together necessary” is false; “not sufficient even together” is false. Final Answer:I alone sufficient; P = 90.

Data Sufficiency — Marks of P (Total of P,Q,R,S is 360) How many marks did P score in Mathematics? I. P scored one-third of the total of Q, R, and S. II. The average of Q and R is 20 more than S.

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