The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 500 graduate

Question

207 had at least one year of Spanish.
171 had at least one year of French.
140 had at least one year of German.
40 had at least one year of Spanish and French.
25 had at least one year of Spanish and German.
22 had at least one year of French and German.
4 had at least one year of all three languages.

(a) How many of the graduates had at least 1 yr of at least one of the three languages?
(b) How many of the graduates had at least 1 yr of exactly one of the three languages?
(c) How many of the graduates had less than 1 yr of any of the three languages?

Answer 1

This is a typical 3-circle Venn diagram. When you fill in the areas, the question should be easy.

Start with the central 3-circle intersection. That is 4.

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