Quant problems

I was about to give a big long answer and then you said "meltdown" so I don't think my original answer would have been helpful, so I'm going to try to keep it short.

First, notice that if we were to pretend that no one took both classes and we tried to count the total students, we'd end up with a graduating class of 142 + 121 = 263. The graduating class has 236 students, not 263. What this demonstrated to us is that we can't just give any value for the number of students who take both classes-- whatever number we choose, it must be something that allows the total number of students to equal 236.

When we add 142 + 121 and get 263, the "extra" number of students we get above the "true" student population of 236 is a the result of the overlap in enrollment between the two classes. Thus, you can figure out how many students are enrolled in both by subtracting 236 from 263.

263 - 236 = 27

Thus, 27 students have taken both algebra and chemistry.

The reason they ask for a maximum is because technically it's possible that there are also some students who have taken neither of the two courses. In other words, there are two unknown values-- students who have taken both classes and students who have taken none. The total is the same regardless, so to find the maximum number of students who have taken both, we need to assume that there are no students who have taken neither.

This makes life easier, because it allows the entire calculation to be 263 - 236 = 27.

/r/GRE Thread