#36:

1. we know tanB is 3/4

2. tan=opposite/adjacent, so the AC will be a multiple of 3 and AB will be a multiple of 4

3. Pythagorean theorem baby! 15^2=(4x)^2 + (3x)^2 The x is just a place holder.

4. Solve and get x=3

5. now we know AC=3*3=9 and AB=3*4=12

6. Now proportions! But first we need BD which we can find by simply subtracting AB-DA=12-4=8

7.Now we set up a proportion. (12/8)=(9/DE)

8. Solve and get DE=6

#38

This one is tricky and took me a while to get but the concept is simple. 

1. There are 7 possible people who got 5's in the 3 Days.

2. Out of the 7, 5 got a 5 on day 2 and 3

3. Possible/total = 5/7

TIP: You don't have to look at the 20 or 60, there only there to trick you. The question said the contestant cannot get the same score twice and that he or she must have a 5, implying that it has to be one of the 7 who got 5's on one of the days.