Question

From a survey of 100 college students, a marketing research company found that 40 students owned iPods, 40 owned cars, and 20 owned both cars and iPods.(a) How many students owned either a car or an iPod (but not both)?

Answer 1

To solve that question let's draw a Venn's Diagram:

The left circle represents all students that owned a car, and the right circle represents all students that owned an iPod. The intersection of the two circles represents students that owned both. We know that the intersection has 20 students, then

We also know that there are a total of 40 students that owned cars, 20 of them are in the intersection, which means that they owned both, then, there are 20 students that only owned a car

Now we can repeat the same logic to the iPod, there are a total of 40 students that owned iPods, 20 of them are in the intersection, then only 20 students only owned an iPod,

Then, there are 20 students that only owned an iPod, and 20 students that only owned a car. Then there are 40 students that owned either a car or an iPod.