Let's do the math.
Your teacher is correct that the half-life is clearly 15 minutes.
We are looking for a function in the form of C = A(1/2)^(t/15).
We can calculate the value of A with any one of these points.
800 = A (1/2)^(20/15)
I get the value of A as 2015.87. Since A corresponds to the value of the count at T=0... looking at the graph makes me feel good (it makes sense).
So then I plug in 60 for t.
C = 2015.87*(1/2)^(60/15)
I get 126 (I am doing this quickly... I could be making a mistake).
I believe 126 makes sense.... because it is a little less than 2 half-lives from 400 (and should be a little more than a quarter of this value).
50--- is clearly NOT the correct answer. Unless maybe they mean an hour after the origin... in which case they would really mean t = 75?
This is a horribly written problem.