How to Solve a Group problem involving Both/Neither

Eli S.

Whether it’s the GRE or the GMAT, there are some classic word problems that you’ll face. One classic set of word problems will involve two groups with overlapping members and possibly elements that belong to neither group. It’s easy to identify this type of question because the words both and/or neither appear in the question.  These problems are quite workable if you just remember the following formula.

Eli S. Kaplan Expert

Group Formula

Group 1 + Group 2 + Neither – Both = Total              Remember This!

Try it yourself:

Of the 120 students at a language school, 65 are studying Russian, 51 are studying Polish, and 53 are studying neither Russian nor Polish. How many are studying both Russian and Polish?


Group 1 + Group 2 + Neither – Both = Total

65 + 51 + 53 – both = 120

169 – both = 120

both = 49

49 students are studying both Russian and Portuguese.