There are 40 students at a summer camp that offers 2 courses: Mechanics and Statistics. Every student is in at least one of the two courses. If 22 students take Mechanics, and 31 students take Statistics, how many students take both Mechanics and Statistics?

Question

anonymous · Answer

use Venn Diagram

sirm3d · Answer

the total number of students enrolled in either Mechanics or Statistics is  53 (22 + 31), but there are only 40 of them in the summer camp. that means the excess in 40, which is 13, is the number of students counted twice, once in each subject.

anonymous · Answer

or if u want to do it mentally 
then 22+31 -40 =13 [bcoz  Every student is in at least one of the two courses]