Data Sufficiency — Minimum Passing Percentage What is the minimum passing percentage in a test? I. Raman scored 25% marks in the test, and Sunil scored 288 marks, which is 128 more than Raman. II. Raman scored 64 marks less than the minimum passing marks.

Introduction / Context:
The task is to determine the minimum passing percentage (passing marks expressed as a percentage of total marks). This is a sufficiency check, not merely arithmetic.

Given Data / Assumptions:

• Statement I: Raman has 25% of total marks; Sunil = 288, which is 128 more than Raman.
• Statement II: Raman scored 64 marks less than the minimum passing marks.

Concept / Approach:
To get the passing percentage, we need both the total marks (denominator) and the minimum passing marks (numerator). Statement I can reveal total marks; Statement II can relate passing marks to Raman’s score.

Step-by-Step Solution:

Verification / Alternative check:
Neither statement alone suffices: I yields M but not P_min; II yields a difference relative to Raman but not M. Together they fix both.

Why Other Options Are Wrong:

• I alone sufficient: Lacks the passing threshold.
• II alone sufficient: Lacks total marks M.
• Either alone sufficient: False.
• Even both not sufficient: False — together they give 35%.

Common Pitfalls:
Misreading “128 more than Raman” as a percentage; or treating passing marks as a fixed number across tests without computing from given data.

Final Answer:
Both statements together are sufficient; neither alone is sufficient.