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. What are the pass marks in an examination? I. A student secures 30% marks but fails by 10 marks. II. The total marks is 200.

Concept & Formula To find an exact absolute value (like pass marks) from a percentage condition, we need the total baseline (total marks) to apply the percentage to. $$ \text{Pass Marks} = (\text{Percentage Achieved} \times \text{Total Marks}) + \text{Marks Failed By} $$ Step-by-Step Solution * Given: The objective is to find the exact numerical value of the pass marks. Calculation / Deduction: * Analyzing Statement I: A student secures $30\%$ marks and fails by $10$ marks. Equation: $\text{Pass Marks} = 30\% \text{ of Total Marks} + 10$. Since "Total Marks" is unknown, we cannot solve this. Statement I is insufficient. * Analyzing Statement II: The total marks is $200$. This gives the maximum possible score but provides no passing criteria. Statement II is insufficient. * Combining Both Statements: Using the total from Statement II ($200$) in the equation from Statement I: $\text{Pass Marks} = (30\% \text{ of } 200) + 10$ $\text{Pass Marks} = 60 + 10 = 70$. We can uniquely determine the pass marks. Both statements are required. Exam Strategy & Shortcut Identify the missing variables. The core formula links Pass Marks, Total Marks, and the student's relative performance. Statement I gives relative performance. Statement II gives the Total Marks baseline. Instantly recognize that they are two halves of the same equation and choose "Both are necessary" without doing the arithmetic. Common Pitfall Thinking that finding a percentage is enough. Some might misinterpret Statement I and think $30\%$ is the passing percentage, ignoring the "fails by 10 marks" condition. Always read the failure condition carefully—it shifts the passing line linearly. Final Answer **Therefore, the correct answer is If the data in both statements I and II together are necessary.**