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 many students are there in the class? I. There are 40 girls in the class. II. The boys are $80\%$ of the total number of students in the class.

### Concept & Logic This is a fundamental percentage composition problem. Finding the total class size requires knowing the absolute numerical value of one component (like the number of girls) and its corresponding percentage relative to the whole. ### Step-by-Step Solution * Let the total number of students in the class be $T$. * Evaluate Statement I: * Number of girls = 40. This gives no mathematical information about the boys or the total. Statement I alone is not sufficient. * Evaluate Statement II: * Boys are $80\%$ of $T$. This implies girls are $20\%$ of $T$. No absolute numbers are given to anchor the percentage. Statement II alone is not sufficient. * Evaluate Both Statements Together: * From II, we deduce that girls constitute $20\%$ of the class. * From I, the absolute number of girls is 40. * Equating the two yields a linear equation: * $$0.20 \times T = 40 \implies T = 200$$ * Combining both statements allows us to find a unique total. ### Exam Strategy & Shortcut Data sufficiency heavily relies on piecing together complementary information. Statement I gives the "value" of a part. Statement II gives the "percentage" of the parts. Connecting a percentage to its exact numerical equivalent is the standard mechanism to find a total. Once you see you have both pieces, mark "Both" and move on. ### Common Pitfall Assuming there are other variables (like teachers or other genders) in the class. In standard quantitative aptitude tests, student populations in such binary questions are strictly divided into boys and girls unless explicitly stated otherwise. ### Final Answer **Therefore, the correct answer is if the data in both statements I and II together are necessary to answer the question.**