About bubble sort vs merge sort
I just googled the algorithms. The bubble sort wins in both situations because of the largest benefit of only having to run through it once. Merge sort can not cut any short cuts for only having to calculate the largest number. Merge takes the length of the list, finds the middle, and then all the numbers below the middle compare to the left and all above compare to the right; in oppose to creating unique pairs to compare. Meaning for every number left in the array an equal number of comparisons need to be made. In addition to that each number is compared twice so the lowest numbers of the array will most likely get eliminated in both of their comparisons. Meaning only one less number in the array after doing two comparisons in many situations. Bubble would dominate
It's a trick question. If you just want the maximum, (or indeed, the kth value for any k, which includes finding the median), there's a perfectly good O(n) algorithm. Sorting is a waste of time. That's what they want to hear.
As you say, the algorithm for maximum is really trivial. To ace a question like this, you should have the quick-select algorithm ready, and also be able to suggest a heap datastructure in case you need to be able to mutate the list of values and always be able to produce the maximum rapidly.
Firstly I agree with everything you have said, but perhaps it is asking about knowing time complexity's of the algorithms and how the input size is a big factor in which will be fastest.
Bubble sort is O(n2) and Merge Sort is O(nlogn). So, on a small set it wont be that different but on a lot of data Bubble sort will be much slower.
Barring the maximum part, bubble sort is slower asymptotically, but it has a big advantage for small n in that it doesn't require the merging/creation of new arrays. In some implementations, this might make it faster in real time.