20 teams play in a hockey tournament and get 3 points for a win and 1

My answer is B.

Long explanation to solve in mind or with minimum notes.
We have 20 teams playing with each other only ones, 2 ways to find "how many matches were". First, advanced: 2 out of 20 is 19*20 / 2 = 190 (Whoever knows knows). Easy way to calculate is understand sequence: 1st team play with other 19, 2nd team play with other 18 (because don't play with self and 1), 3rd team against 17 and so on until 19 with only one (20). So sequence is: 1*19 + 1*18+...1*1. we can write it like 19*(19+1) / 2 = 190. We can calculate that our average from sequence is 10, and we have 19 numbers in it, so all of this possible to do in mind, we comes to 190.
After that calculate score if they'd win every match 190*3 = 570 (300+270 easy to calc in mind).
now we can see an approximate situation that we need 530 points, we have set of our answers (35-55), and we have our maximum (570) for 190 games, we can find minimum but we don't really need it.
Now, we should pay attention on the fact, that when it's a draw they get 1 point BOTH. So it's 2 points for each draw.

Solution: we take some answer close to the middle, lets take 50. Then it comes to 140 win 50 draw. calculate - 140*3 + 50*2 = 520 < 530. we need less draws. Let's take 40, then 150*3 + 40*2 = 450 + 80 = 530. That's it.