In a class of 30 students, 25 play soccer and 20 play basketball. What

I solved this in a less rigorous manner than globaldesi has indicated above. I simply parsed the question and quantified each part as a counting number before I took the difference.

Question, Part 1) What is the greatest number of students who play neither soccer nor basketball?
Answer: If there are 30 students, and at least 25 of them play soccer (but only 20 play basketball), then there can only be 30 - 25, or up to 5 students who play neither sport.

Question, Part 2) What is the least number of students who play neither soccer nor basketball?
Answer: Since 25 and 20 sum to more than 30, it is clear that some students must play both sports, but we could come up with a way to ensure that all 30 students played one or the other. We could, for instance, say that 15 play both sports; 25 - 15, or 10 play soccer exclusively; and 20 - 15, or 5 play basketball exclusively. This is a valid solution, since 15 + 10 + 5 = 30. Although I did NOT actually work this part out when solving, I am just pointing to the fact that it could be done to show that there could be 0 students who play neither sport (i.e. all 30 students could play one sport, the other, or both).

Solution: 5 - 0 = 5. The answer must be (C).

- Andrew