Two football teams, A and B, each played ten games in a season

This solution is not correct; for one, we don't necessarily need to know all of our values to compare the medians of two sets (in fact you often need to know very few values in two sets to do that), and for another, the question doesn't ask you to "find the median" of either set - it only asks you to compare the medians, and you might be able to do that even without knowing the exact value of either median. Lastly the information in Statement 2 is definitely "relevant" -- in fact, combining the two statements almost gives us sufficient information, and if the "14" were changed to "17", say, in Statement 2, the answer would be C, not E.

The problem here is that from Statement 1, if team A's total points was almost double team B's, the values in set A must generally be much larger than the values in set B. With the given numbers, it's not straightforward to come up with two sets A and B where A has almost twice as many total points as B, but at the same time has a lower median point total than B. If we want to construct two sets like that, we'll want to make B's median as large as possible, while making B's total points as low as possible (since that will let us make the scores for team A, and especially the median for A, as low as possible). So for team B, we should make the four lowest-scoring games 10 point games, then make every other score besides the largest one equal to the median:

B: 10, 10, 10, 10, m, m, m, m, m, 49

For team A, we want the largest point total with the lowest median, so the four highest scores should equal the maximum. If we make the remaining scores besides the lowest equal to the median, we have this set:

A: 14, M, M, M, M, M, 56, 56, 56, 56

and if the total of A's points is 20 less than twice the total of B's points, we have

14 + 5M + (4)(56) = 2(40 + 5m + 49) - 20
238 + 5M = 158 + 10m
5M + 80 = 10m
M + 16 = 2m

We want to make M < m (or M = m) true, if we want to prove the information is insufficient. M is at least 14, but that value works, because m = 15 can be true. So we can have these sets:

A = 14, 14, 14, 14, 14, 14, 56, 56, 56, 56
B = 10, 10, 10, 10, 15, 15, 15, 15, 15, 49

and here the two Statements are true, and the median of set A is slightly less than the median of set B, so the answer is E. But if the numbers are changed even slightly, the answer could easily be C here, and there's no way to tell without doing quite a lot of work.