ExplanationThis overlapping sets question can be solved with the following equation:
Total # of people = Group 1 + Group 2 + Group 3 – (# of people in two groups) – (2)(# of people in all three groups) + (# of people in no groups)
The problem indicates that everyone studies at least one language, so the number of people in no groups is zero. The problem also indicates that nobody studies all three languages, so that value is also zero:
Total # of students = 100 + 80 + 40 – 22 – (2)(0) + 0 = 198.
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