Directions: Each of the following questions consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. How many children are there in the class? I. $20\%$ children in the class can speak only Hindi. II. 44 children can speak languages other than Hindi. III. There are 30 boys in the class.

### Concept & Logic This problem relies on complementary percentages. In a defined population, if a certain percentage falls into an exclusive category (e.g., "only Hindi"), the remaining percentage must fall into the exact inverse category (e.g., "languages other than Hindi"). ### Step-by-Step Solution * Target: Find the total number of children ($T$). * Evaluate Statement I: Tells us $20\%$ speak *only* Hindi. This implies the remaining $100\% - 20\% = 80\%$ of the class must speak a language *other than* Hindi. (Insufficient alone). * Evaluate Statement II: Gives the absolute number of children who speak languages other than Hindi as 44. (Insufficient alone). * Evaluate Statement III: States there are 30 boys. (Irrelevant to the language demographics without further context). * Calculation / Deduction: Combining Statement I and II gives us both the percentage and the numerical value for the exact same group of children. * $80\%$ of Total Children = 44 * $$0.80 \times T = 44 \implies T = \frac{44}{0.80} = 55$$ * Statements I and II together are sufficient to find the answer. ### Exam Strategy & Shortcut Look for direct complements. "Only X" and "Other than X" are perfect complements that add up to $100\%$. Whenever you have a statement providing the percentage of a group, and another statement providing the absolute number of the complementary group, those two statements together are always sufficient to find the total. ### Common Pitfall Getting distracted by irrelevant data points like gender breakdown (Statement III). Just because data is provided does not mean it fits into the mathematical model required to solve the specific question asked. ### Final Answer **Therefore, the correct answer is I and II only.**