Problem Solving

Question: Of the 100 athletes in a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes playing both midfield and defense could be any number between:

A: 10 to 20
B: 10 to 40
C: 30 to 40
D: 30 to 70
E: 40 to 70

I got the question wrong, got caught up in the time crunch and picked "D". The answer is actually C. When I went back to review my answers, I couldn't figure out how they could possibly have 40 players playing both positions??

If you have 100 bodies, 20 play neither, so that leaves 80 bodies playing Midfield only, Defense only, or both Midfield and Defense.

Now:

30 players (Both - Mid and Def) + 10 Def only (since it must add up to 40) + 40 MF only (since it must add up to 70) = 80 bodies.

If there are 40 players who play both ways:

40 (both mid and def) + 0 def only (must add up to 40, and all are two position players) + 30 MF only (must add up to 70) = 70 bodies! It doesn't add up. It doesn't work.

Am I missing something here? Please advise.