Explanation

In this question, we have 9 recordings, with a recording of 7.5 seconds in the middle. Call the duration of the shortest recording x. Then, the question tells us, the longest is . We want to find the largest possible maximum recording. In other words, there are different possible maximums, and we want to know the greatest of them. The average of 5.7 is known; to maximize the longest recording, we want to minimize the other ones, so that it has the most negative offset possible to have to net out and generate an average of 5.7. In the case in which everything else is minimal, not just the shortest, but all four recordings shorter than 7.5 seconds are x seconds long. Meanwhile, the recordings past the median have to be at least 7.5 seconds, but they could be only 7.5 seconds, so we'll make all three of them between the median and the longest 7.5 seconds. Then we can compute the sum of all the recordings



The right side comes from the fact that











When , .

The correct answer is (D).