Each of 25 people is enrolled in history, mathematics, or both. If 20 are enrolled in history and 18 are enrolled in mathematics, how many are enrolled in both history and mathematics?

15

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16

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13

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14

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Solution

The correct option is C $13$
The 25 people can be divided into three sets : those who study history only, those who study mathematics only, and those who study history and mathematics. Thus a Venn diagram may be drawn as follows, where n is the number of people enrolled in both courses, 20 - n is the number enrolled in history only, and 18 - n is the number enrolled in mathematics only.
Since there is a total of 25 people, (20 - n) + n + (18 - n) = 25, or n = 13. Thirteen people are enrolled in both history and mathematics.

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