Directions: Each of the questions 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 statements 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; and Give answer (e) if the data in both Statements I and II together are necessary to answer the question. How much time did X take to reach the destination? I. The ratio between the speeds of X and Y is 3 : 4. II. Y takes 36 minutes to reach the same destination.

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

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

if the data either in Statement I or in Statement II alone are sufficient to answer the question

if the data even in both Statements I and II together are not sufficient to answer the question

[Solved] Directions: Each of the questions below consists of

Answer

Correct Answer: if the data in both Statements I and II together are necessary to answer the question

Explanation

### Concept & Logic When the distance is constant, the time taken to cover the distance is inversely proportional to the speed. $$ \text{Speed} \propto \frac{1}{\text{Time}} $$ ### Step-by-Step Solution From Statement I: * The ratio of the speeds of X and Y is 3 : 4. * Because distance is constant, the ratio of the time taken by X and Y will be 4 : 3. * This statement alone does not provide the actual time taken by X. From Statement II: * Time taken by Y = 36 minutes. * This statement alone does not provide information about X. Combining Statements I and II: * Time ratio X : Y = 4 : 3. * Let the time taken by X be $4k$ and by Y be $3k$. * We are given $3k = 36 \Rightarrow k = 12$. * Time taken by X = $4k = 4 \times 12 = 48$ minutes. * Since combining both statements gives the exact time, both statements are necessary. ### Exam Strategy & Shortcut For Data Sufficiency, you do not need to calculate the final numerical answer. As soon as you see a ratio connecting the two subjects (Statement I) and an absolute value for one of them (Statement II), you know the system is solvable. Mark the answer combining both. ### Common Pitfall Attempting to solve for the exact distance. Distance is not required to find the time here, and it cannot be calculated with the given data. Do not waste time looking for it. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question**.