All students in the physics class also study mathematics. Half of those who study literature also study
mathematics. Half of the students in the mathematics class study physics. Thirty students study
literature and twenty study physics. Nobody who studies literature studies physics. How many
students in the mathematics class study neither physics nor literature?

Answer:

If there are 20 physics students who all take mathematics, and half of the mathematics students study
physics, there must be 40 students in the mathematics class. If half of the 30 literature students
take mathematics, then 15 of them take mathematics. Since none of the literature students study physics,
only five students in the mathematics class study neither physics nor literature.