Question

In a group of 150 students, more students are taking a math class than are taking a science class this semester. If 80 are taking a science class and 25 are not taking either math or science this semester, what is the minimum number of students who could be taking both math and science this semester?

Answer 1

I think it is 45 students but I am not sure. Try to google the question, maybe there is a similar question solved. Good luck.

Answer 2

Right, there are 150 students. Strike out the 25 who are taking neither math nor science. That leaves 125.

Answer 3

And then, there are 80 students who take science, and there are more who take math. That means there must be at least 81 students that take math. An extreme case is that all those who take science also take math, means there are 80 students who take both, but that's not the minimum.

Another extreme case is if you consider the 45 students who don't take science (and are not part of the 25 originally struck out) and have them all take math. Then there must be at least 36 more students who take math from the 80 students who take science so that there will be more "math-takers" than "science-takers". Thus, the minimum is for 36 students to take both math and science.