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.
Correct Answer: Both statements I and II together are sufficient, but neither alone is sufficient.
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:
From I: Let total marks be M. Raman = 0.25 M. Sunil = Raman + 128 = 288 ⇒ Raman = 160 ⇒ 0.25 M = 160 ⇒ M = 640.From II: Passing marks P_min = Raman + 64 = 160 + 64 = 224.Passing percentage = (P_min / M) * 100 = (224 / 640)*100 = 35% (unique).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.