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. Are at least 20% of the people in City X who are 30 years old or older bilingual? I. In City X, 30% of the population is at least 30 years old. II. In City X, of the population 30 years old or older, 18 percent of the women and 17 percent of the men are bilingual.

Concept & Logic In Data Sufficiency, a definitive "No" is just as sufficient as a definitive "Yes". The overall percentage of a combined group (men and women) must strictly fall between the percentages of the individual groups. Step-by-Step Solution Given: We need to determine if the bilingual percentage of the $\ge 30$ years old population is $\ge 20\%$. Calculation / Deduction: * Analyzing Statement I: It tells us the size of the $\ge 30$ population relative to the whole city ($30\%$). However, it provides absolutely no information regarding bilingualism. Statement I alone is insufficient. * Analyzing Statement II: It states that among the population 30 years or older, $18\%$ of women are bilingual and $17\%$ of men are bilingual. * Since the entire $\ge 30$ population is made up of men and women, the overall average of bilingual individuals MUST be a weighted average of $17\%$ and $18\%$. * Therefore, the overall bilingual percentage must be strictly between $17\%$ and $18\%$. * Because the maximum possible value is $18\%$, we can definitively answer the question: "No, the percentage is NOT at least $20\%$." Since we can confidently answer the question, Statement II alone is sufficient. Exam Strategy & Shortcut Recognize the bounds of weighted averages instantly. If Group A is $17\%$ and Group B is $18\%$, the total combination can never exceed $18\%$. Since the question asks if it hits $20\%$, you can immediately conclude "No" and mark Statement II as sufficient without any algebraic setup. Common Pitfall Assuming that because you can't find the *exact* percentage (since the ratio of men to women is unknown), the statement is insufficient. In Data Sufficiency, answering "No" definitively means the data is sufficient. Final Answer **Therefore, the correct answer is If the data in statement II alone are sufficient.**