In a class, every student knows french or german (or both). 15 students know french, and 17 students know german. what is the largest possible number of students in that class?

If you apply the or both
Only 1 of the students would need to know the "or both", therefore maximizing the remaining amount of students you can put in.

Gerald, let's call him, knows French AND German, so there's only one less student that knows french and german. Gerald is 1 student.

MAXIMUM:
There are now 14 monolinguistic French speakers and 16 monolinguistic German's, 30 students + Gerald=31.

Minimum:
As a bonus, the minimum is 15 students knowing french AND German and only 2 monolinguistic German speakers, so 17.