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Of 40 employees at a firm, 25 can read Spanish and 18 can read French. If 5 of the employees can read neither language, how many employees can read exactly one of the two languages?
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Correct answer
D
Start with how many read at least one language: 40 total − 5 who read neither = 35. By inclusion-exclusion, those reading at least one equal Spanish plus French minus both, so 25 + 18 − both = 35, giving both = 43 − 35 = 8.
Exactly one excludes the 8 who read both from each language group: Spanish-only is 25 − 8 = 17 and French-only is 18 − 8 = 10, for 17 + 10 = 27, choice (D). Equivalently, exactly one = (at least one) − both = 35 − 8 = 27.
The big trap is (E) 35, the at-least-one count, which still double-counts the both-readers.
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