I made a video today that I hope will help you understand something I get asked about an awful lot. The SAT loves asking a particular kind of Venn diagram question—not so common that it appears on every test, but common enough that high scorers need to know it. The test writers keep coming back to this kind of question because it’s so easy to trick students with it. Here’s an example:

17. In a certain neighborhood, 11 children play baseball and 13 children play soccer. If 16 of the children play only one of the two sports, how many children play both sports?(A) 1
    (B) 3
    (C) 4
    (D) 8
    (E) 10

I solve this two ways in the video above (beginning at 4:05)—first I backsolve, then I do the algebra. My general preference is to backsolve a question like this because once you’ve practiced doing so it’s really fast and easy, but it’s good to know the algebra in case you ever come across such a question as a grid-in.

Think you’ve got this question type mastered? Try this short, 3-question quiz:

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