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 is the speed of the train? (Bank P.O., 2003) I. 280 metres long train crosses a signal pole in 18 seconds. II. 280 metres long train crosses a platform in 45 seconds.

### Concept & Independence of Variables To determine if a statement is sufficient, evaluate if it alone contains all the necessary variables to compute a final, unique numerical answer for the question asked. $$Speed = \frac{Distance}{Time}$$ ### Step-by-Step Solution * **Question Stem:** We are looking for the numerical speed of the train. * **Analyze Statement I:** A 280 m train crosses a signal pole in 18 seconds. * Distance = Length of train = 280 m. * Time = 18 seconds. * $Speed = \frac{280}{18}$ m/s. This yields a specific numerical answer. Statement I alone is sufficient. * **Analyze Statement II:** A 280 m train crosses a platform in 45 seconds. * Equation: $Speed = \frac{280 + Length\ of\ Platform}{45}$. * Because the length of the platform is an unknown variable, we cannot find the speed. Statement II alone is insufficient. ### Exam Strategy & Shortcut Always test the statements independently. Statement I gives you the two exact pieces of information needed for speed: distance (train length against a point object) and time. You can instantly mark it as sufficient without looking at Statement II. Statement II introduces a new unknown (platform length), making it useless on its own. ### Common Pitfall A common trap is merging the data from Statement II with Statement I automatically without testing them independently first. Some students might try to calculate the length of the platform, completely forgetting the question only asked for the speed. ### Final Answer Therefore, the correct answer is **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;**.