Each of the following questions consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. In how many days can A and B together complete a piece of work? Statement I: A alone can complete the work in 15 days. Statement II: B is 50% more efficient than
A.

From I, A alone can complete the work in 15 days. So, A's 1 day's work = 1/15 Since we do not have any information about B's efficiency or time, Statement I alone is not sufficient. From II, B is 50% more efficient than A. So, the ratio of efficiency of A to B = 100 : 150 = 2 : 3 Since the actual time taken by either of them is not known, Statement II alone is not sufficient. From I and II, A takes 15 days to complete the work. Since B is 50% more efficient than A, the ratio of time taken by A to B = 3 : 2 ATQ, 3 units = 15 days So, 1 unit = 5 days So, B takes 2 * 5 = 10 days to complete the work. Now, 1 day's work of A and B together = 1/15 + 1/10 Or, (2 + 3) / 30 = 5/30 = 1/6 So, A and B together can complete the work in 6 days. Therefore, both statements I and II together are necessary to answer the question. Hence, the correct answer is E.