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 percentage of families in the city have telephones? I. 50% of the families of the city possess television. II. 30% of the television owners of the city have telephones.

Concept & Logic Data sufficiency requires determining if a unique answer can be logically deduced, not necessarily calculating the final answer itself. To find the overall percentage of families with telephones, we must account for every segment of the population (those with TVs, and those without TVs). Step-by-Step Solution Given: We need the percentage of families with telephones out of the entire city. Let total families = $100$. Calculation / Deduction: * Analyzing Statement I: $50\%$ of families own a television. (TV owners = $50$). This gives absolutely no information about telephones. Statement I alone is insufficient. * Analyzing Statement II: $30\%$ of television owners have telephones. This only gives us a subset. Statement II alone is insufficient. * Combining both statements: If total families = $100$, TV owners = $50$. The number of families having both a TV and a telephone is $30\%$ of $50 = 15$. * Crucial Missing Data: We know $15\%$ of families have both. However, we have absolutely no data regarding families who own a telephone but DO NOT own a television. * Because this unknown segment exists, we cannot determine the total percentage of families with telephones. Exam Strategy & Shortcut Venn Diagram visualization is the fastest method here. Draw two intersecting circles for "TV" and "Phone". Statement I gives the total value of the TV circle. Statement II gives the value of the intersection. We are entirely missing the "Phone only" section. Hence, the data is clearly insufficient. Common Pitfall Assuming that only TV owners can have telephones. Students hastily calculate $30\%$ of $50\%$ (which is $15\%$) and assume it is the final answer, incorrectly marking that both statements are necessary. Always check for elements outside the explicitly given sets. Final Answer **Therefore, the correct answer is If the data even in both statements I and II together are not sufficient.**