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?

(A) 2

(B) 6

(C) 7

(D) 12

(E) 14

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The correct answer is C

Explanation

Let  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  students in this category) and those who are in the math club only (there are   students in this category).

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

Since a total of  students belong to only one of the two clubs, you know that . Solving this equation gives , so 7 students belong to both clubs.