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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

At Central High School, the math club has 15 members and the chess club has 12 members. If a total of 13 students belong to only one of the two clubs, how many students belong to both clubs?

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Let n stand for the number of students who belong to both clubs. The 15 members of the math club can be broken down into two groups: those who are in both clubs (there are n students in this category) and those who are in the math club only (there are 15 minus n students in this category).

The 12 members of the chess club can also be broken down into two groups: n students who are in both clubs and 12 minus n students who are in the chess club only.

Since a total of 13 students belong to only one of the two clubs, you know that (15 minus n) plus (12 minus n) equals 13. Solving this equation gives n equals 7, so 7 students belong to both clubs.

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