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. What is the value of 20 percent of $x$? I. One-fourth of 20 percent of $x$ is 5. II. $4x = S$, $5y = S$ and $y = 80$.

### Concept & Logic The target is to find the value of $20\%$ of $x$, which is simply $0.2x$ or $\frac{x}{5}$. Any statement that allows us to find a unique numerical value for $x$ (or directly gives the value of the expression) will be sufficient. ### Step-by-step Solution **Evaluating Statement I:** * "One-fourth of 20 percent of $x$ is 5." * Translating into math: $\frac{1}{4} \times (20\% \text{ of } x) = 5$ * Multiplying both sides by 4 gives: $20\% \text{ of } x = 20$. * This directly answers the target question without even solving for $x$. Statement I alone is sufficient. **Evaluating Statement II:** * "$4x = S$, $5y = S$ and $y = 80$." * Since $y = 80$, we can find $S$: $S = 5y = 5(80) = 400$. * Since $4x = S$, we have $4x = 400 \Rightarrow x = 100$. * Now we can find $20\%$ of $x$: $20\% \text{ of } 100 = 20$. * Statement II alone provides a unique answer. Statement II alone is sufficient. **Conclusion:** Since both statements individually provide enough information to find the answer, either statement alone is sufficient. ### Exam Strategy & Shortcut Look for direct algebraic solvability. In Statement I, the phrase "One-fourth of [Target] = 5" clearly means [Target] = 20. Sufficient. In Statement II, a simple chain of linear equations ($y \rightarrow S \rightarrow x$) means $x$ is fully determined. Sufficient. You can mark "Either I or II" within 10 seconds without calculating $x = 100$. ### Common Pitfall A major trap is solving for $x$ in Statement I ($x = 100$) and thinking that because both give $x = 100$, you need both. Remember, Data Sufficiency asks if a statement *alone* can answer the question. Evaluate them completely independently before combining. ### Final Answer **Therefore, the correct answer is Data either in statement I or in statement II alone are sufficient to answer the question.**