The question consists of 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.

Let the total work be 'W' units. Statement I: A alone can complete the work in 15 days. So, A's 1 day's work = W / 15. Since B's efficiency is unknown, data in statement I alone is not sufficient to answer the question. Statement II: B is 50% more efficient than A. So, ratio of efficiency of A to B = 100 : 150 = 2 : 3. Since the actual time taken by A or B is unknown, data in statement II alone is not sufficient to answer the question. Combining Statement I and II: A's 1 day's work = W / 15. Since B is 50% more efficient than A, B's 1 day's work = (W / 15) × 1.5 = W / 10. ATQ, 1 day's work of A and B together = (W / 15) + (W / 10). Or, 1 day's work of A and B together = (2W + 3W) / 30 = 5W / 30 = W / 6. So, A and B together can complete the work in 6 days. So, data in both statements I and II together is necessary to answer the question. Hence, the correct answer is E.