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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.

Difficulty: Easy

Statement I alone is sufficient to answer the question.
Statement II alone is sufficient to answer the question.
Both statements I and II together are necessary to answer the question.
Both statements I and II together are not sufficient to answer the question.
Either statement I alone or statement II alone is sufficient to answer the question.

Correct Answer: Statement I alone is sufficient to answer the question.

Explanation:

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.

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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