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. What is the speed of the boat in still water? (Bank P.O., 2006) I. The boat running downstream takes 6 hours from A to B. II. The boat running upstream takes 8 hours from B to C.

### Concept & Missing Variables To find a concrete speed (distance over time), we fundamentally need a defined distance. Times alone are insufficient to find absolute speeds. $$Speed = \frac{Distance}{Time}$$ ### Step-by-Step Solution * From Statement I: We only know the time (6 hours) for the downstream journey from A to B. The distance between A and B is completely unknown. Thus, downstream speed cannot be calculated. * From Statement II: We only know the time (8 hours) for the upstream journey from B to C. The distance between B and C is unknown. Thus, upstream speed cannot be calculated. * Combining both statements: We have times for two entirely different segments (A to B and B to C) with no known distances for either segment. There is no way to relate the two journey legs mathematically without distances. * Therefore, even combining both statements, we cannot find the speed of the boat. ### Exam Strategy & Shortcut If a Data Sufficiency question asks for a specific numerical rate (like km/hr) but provides zero concrete numbers for distance, it is automatically impossible to solve. You can mark "not sufficient" in just 5 seconds. ### Common Pitfall A common pitfall is incorrectly assuming that distances A to B and B to C are identical, and then setting up an arbitrary ratio. Even if they were identical, you would only find a ratio of speeds, not the exact numerical speed in still water. ### 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;**.