Question

Students are in clubs as follows:

Science - $20$, Drama - $30$, and Band - $12$. No student is in all three clubs, but $8$ are in both Science and Drama, $6$ are in both Science and Band and $4$ are in Drama and Band. How many different students are in at least one of the three clubs ?

• A. $50$
• B. $55$
• C. $42$
• D. $44$

Answer 1

The correct option is D $44$

$44$ different students: There are three overlapping sets here. Therefore, use a Venn diagram to solve Science the problem. First, fill in the numbers given in the problem, working from the inside out: no students in all three clubs, $8$ in Science and Drama, $6$ in Science and Band, and $4$ in Drama and Band. Then, use the totals for each club to determine how many students are in only one club. For example,you know that there are $30$ students in the Drama club. So far, you have placed $12$ students in the circle that represents the Drama club ($8$ who are in Science and Drama, and $4$ who are in Band and Drama). Therefore, $30-12=18$, the number of students who are in only the Drama Club. Use this process to determine the number of students in just the Science and Band clubs as well. To find the number of students in at least one of the clubs, sum all the numbers in the diagram:

$6+18+2+6+8+4=44$.