# Sets

As always, remember to follow the Knowsys method for math. Read the problem carefully and identify the bottom line (what you are looking for). Then, consider your options. How could you solve it? How should you solve it? Next, attack the problem using the method that you selected. Finally, loop back and verify that your answer matches the bottom line.

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?

This problem involves sets. The easiest way to solve this problem is to look at the information that you are given and make deductions. By working step by step from the information given, you can find the answer. First of all, you know that there are a total of 15+12=27 memberships. Notice that this isn't the number of students since some students belong to both the chess and math clubs. This is simply the number of memberships. Secondly, you know that 13 students belong to only one club. 27 (the total number of memberships of both clubs) minus 13 (the number of students in only one club) is 14 (this is the number of memberships that come from students who are in both clubs). Since 14 is the number of memberships that come from students who are in both clubs, there must only be 7 students who are members of both clubs (1 student=2 memberships). Now, look at the answers and see which one matches your prediction.

(A) 2
(B) 6
(C) 7
(D) 12
(E) 14

(C) matches your prediction exactly. Interestingly, you can see that (E) is a trap answer. If you had failed to divide 14 by 2 (to account for the fact that the 14 memberships came from students who were in both clubs), you would have chosen (E). Remember to take your time and work the problem carefully. If you work a problem and make a sloppy mistake, you will not only lose a chance to earn a point, but you will also be penalized a quarter of a point (and you will waste valuable time on that problem).

The correct Answer Choice is (C).

On sat.collegeboard.com 37% of the responses were correct.

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