gmat_winter wrote:Two football teams, A and B, each played ten games in a season, all against other teams. Was the median number of points scored higher for Team A than for Team B ?

(1) If Team A had scored 20 more points in total, Team A would have scored twice as many points as Team B.

(2) Team A's lowest score was 14 points and highest score was 56 points. Team B's lowest score was 10 points and highest score was 49 points.

To compare the median scores we need to have some indication of the exact number of points they scored in games.

Statement 1 tells us something, not very much, about the total points they scored in the season but gives us no way to determine the score for any particular game. So Statement 1 is insufficient.

Statement 2 gives us the range of the scores of each team, but the ranges overlap and therefore there is no way to use the information given to determine which team had a higher median score. If the ranges did not overlap, then even without knowing the median score of either, we could tell which must have had the higher median score, but as it stands Statement 2 is insufficient.

We can plug numbers into the combined Statements to see if there are multiple possible outcomes.

A Scores: 14 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 50 + 56 (+ 20) = 280 Median is 20.

B Scores: 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 11 + 49 = 140 Median is 10.

So A has a higher median.

A Scores: 14 + 14 + 14 + 14 + 15 + 15 + 56 + 56 + 56 + 56 (+ 20) = 330 Median is 15.

B Scores: 10 + 10 + 10 + 11 + 15 + 15 + 15 + 15 + 15 + 49 = 165 Median is 15.

Now the medians are the same.

So even combined the statements do not provide information sufficient for determining whether A had a higher median score.

So the answer is E.

This question is a little tedious and getting the answer took picking just the right numbers, twenty of them. So likely you won't see one much like it on the GMAT. Still the method described is applicable to handling GMAT questions of this type.