Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question; Give answer (b) if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question; Give answer (c) if the data either in statement I or in statement II alone are sufficient to answer the question; Give answer (d) if the data even in both statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both statements I and II together are necessary to answer the question. How much minimum marks will be required to pass an examination? I. Student A secured 32% marks in that examination and he failed by 1 mark. Student B secured 36% marks in the same examination and his marks were 1 more than the minimum pass marks. II. Student A secured 30% of full marks in the examination and he failed by 2 marks. If he had secured 5 more marks his percentage of marks would have been 40%.

Concept & Logic The minimum pass mark can be found if we can set up a linear equation that allows us to find the total marks. Once total marks are known, any relative percentage condition can be used to find the exact pass marks. Step-by-Step Solution * Given: We need the absolute value of the minimum passing marks. Let total marks = $T$ and pass marks = $P$. Calculation / Deduction: * Analyzing Statement I: Student A: $0.32T = P - 1 \implies P = 0.32T + 1$ Student B: $0.36T = P + 1 \implies P = 0.36T - 1$ Equating both expressions for $P$: $0.32T + 1 = 0.36T - 1 \implies 0.04T = 2 \implies T = 50$. Since we can find $T$, we can substitute it back to find $P = 0.32(50) + 1 = 17$. Statement I alone is sufficient. * Analyzing Statement II: Student A condition: $P = 0.30T + 2$. Hypothetical condition: If he scored 5 more marks, he would hit $40\%$. Currently, he has $30\%$. Adding 5 marks jumps his score by $10\%$ (from $30\%$ to $40\%$). Therefore, $10\%$ of Total Marks = $5 \implies 0.10T = 5 \implies T = 50$. Since we can find $T$, we can substitute it into the first condition: $P = 0.30(50) + 2 = 17$. Statement II alone is sufficient. Exam Strategy & Shortcut For Statement I, recognize the "Difference of Percentages = Difference of Marks" shortcut. The difference between $36\%$ and $32\%$ is $4\%$. The mark difference is $1 - (-1) = 2$ marks. So, $4\% = 2$ marks, meaning Total = $50$. For Statement II, jumping from $30\%$ to $40\%$ takes exactly $5$ marks. So, $10\% = 5$ marks, meaning Total = $50$. Both statements independently provide a path to find the total marks, and thus the pass marks. Common Pitfall Failing to properly assign negative and positive signs when translating "failed by" and "more than". "Failed by $1$" means his score was $P - 1$. "More than pass marks" means his score was $P + 1$. Misaligning these signs will ruin the linear equation. Final Answer **Therefore, the correct answer is If the data either in statement I or in statement II alone are sufficient.**