A student of mine recently asked me for help with the following GRE quantitative question from one of the practice tests in The Official Guide to the GRE, 3rd Ed:

In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?

It’s a student-response question, meaning you have to come up with your own answer. No help from the answer choices!

Now, this is obviously an example of a “Sets” question involving two groups, which I teach in detail in our Common GRE Word Problems video course. But what makes this problem particularly interesting — and challenging — is that it’s also a Max/Min question since it asks for the greatest possible number of students who could have taken both classes.

Unfortunately the book’s answer key only gives the correct answer without any sort of explanation. As such, I’ve taken the liberty of recording a video where I solve the problem while providing some important teaching points not only about how to tackle two-sets word problems in general on the GRE, but also how to use Venn Diagrams to your advantage on Max/Min problems like this one.

Give this problem a try on your own first and then check out this video where I break it all down for you:

Spoiler alert: The correct answer is 121. Well done if you got that!

Questions? Comments? Please post them below! And check out our a-la-carte GRE video courses for additional strategies to dominate all types of quant and verbal questions that you’ll encounter on test day. Enjoy!