Solve this multiple-choice question and choose the correct option.

Concept & Data Sufficiency Logic: To find the speed of a boat in still water, we need both the upstream speed and the downstream speed, or one of those speeds along with the speed of the stream. Speed\ in\ still\ water = (Downstream\ Speed + Upstream\ Speed/2) Step-by-Step Solution: • From Statement I: We only know the time taken (2 hours) to travel downstream. Since the distance between A and B is unknown, we cannot calculate the downstream speed. • From Statement II: We only know the time taken (4 hours) to travel upstream. Again, the distance is unknown, so we cannot calculate the upstream speed. • Combining Statements I and II: Let the distance be d. • Downstream speed = d/2. Upstream speed = d/4. • Speed in still water = (1/2)(d/2 + d/4) = (3d/16). • Since the exact value of distance d is missing, we cannot determine a numerical value for the speed of the boat. Exam Strategy & Shortcut: In Data Sufficiency, whenever you are asked for a specific numerical value (like speed in km/hr) but are only given times and no absolute distances or other concrete speeds, you can immediately conclude that the exact value cannot be found. Common Pitfall: A common mistake is assuming a distance (like 100 km) to solve the problem. In Data Sufficiency, unless the value is given, you cannot assume it to find an absolute answer. 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;.

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., 2003) I. It takes 2 hours to cover the distance between A and B downstream. II. It takes 4 hours to cover the distance between A and B upstream.

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 in both Statements I and II together are necessary to answer the question.

[Solved] Directions: Each of the questions given below

Answer

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

Explanation

### Concept & Data Sufficiency Logic To find the speed of a boat in still water, we need both the upstream speed and the downstream speed, or one of those speeds along with the speed of the stream. $$Speed\ in\ still\ water = \frac{Downstream\ Speed + Upstream\ Speed}{2}$$ ### Step-by-Step Solution * From Statement I: We only know the time taken (2 hours) to travel downstream. Since the distance between A and B is unknown, we cannot calculate the downstream speed. * From Statement II: We only know the time taken (4 hours) to travel upstream. Again, the distance is unknown, so we cannot calculate the upstream speed. * Combining Statements I and II: Let the distance be $d$. * Downstream speed = $d/2$. Upstream speed = $d/4$. * Speed in still water = $\frac{1}{2}(d/2 + d/4) = \frac{3d}{16}$. * Since the exact value of distance $d$ is missing, we cannot determine a numerical value for the speed of the boat. ### Exam Strategy & Shortcut In Data Sufficiency, whenever you are asked for a specific numerical value (like speed in km/hr) but are only given times and no absolute distances or other concrete speeds, you can immediately conclude that the exact value cannot be found. ### Common Pitfall A common mistake is assuming a distance (like 100 km) to solve the problem. In Data Sufficiency, unless the value is given, you cannot assume it to find an absolute answer. ### 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;**.