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 given 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 was the speed of a running train X? I. The relative speed of train X and another train Y running in opposite direction is 160 kmph. II. The train Y crosses a signal post in 9 seconds.

### Concept & Logic To find the speed of train X, we need to know the relationship between its speed and other variables like length or time taken to cross objects. Relative speed in opposite directions is given by: $$S_{rel} = S_x + S_y$$ ### Step-by-Step Solution * Let the speed of train X be $S_x$ and train Y be $S_y$. Let the length of train Y be $L_y$. * From Statement I: $S_x + S_y = 160$. This alone is insufficient as we have two variables. * From Statement II: Train Y crosses a signal post in 9 seconds. So, $L_y = S_y \times 9$. This introduces another variable $L_y$ but doesn't connect to $S_x$. * Combining both statements: We have equations $S_x + S_y = 160$ and $S_y = \frac{L_y}{9}$. We have three unknowns ($S_x, S_y, L_y$) and only two equations. We cannot determine the value of $S_x$. ### Exam Strategy & Shortcut In Data Sufficiency, do not solve the equations completely. Merely count the number of independent equations and the number of unknown variables. Since unknowns (3) > equations (2), it is unsolvable. ### Common Pitfall A common mistake is assuming standard lengths or speeds for trains when they are not provided, leading to an incorrect conclusion that the data is sufficient. ### Final Answer Therefore, the correct answer is **if the data even in both Statements I and II together are not sufficient to answer the question**.