每日一题

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

答案和解析

答案：C

解析：

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-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-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-n) plus (12-n) equals 13. Solving this equation gives n equals 7, so 7 students belong to both clubs.