Question

In a class of 40 students, 15 watched television last night, 32 did homework, 9 atepizza, 11 watched television and did homework, 7 watched television and atepizza, 4 ate pizza and did homework and 3 did all three. (Note: When we say11 students watched television and did homework, some of those students mayhave also eaten pizza. Likewise, for the other numbers.)How many students did none of these activities?

Answer 1

We know that

• There are 40 students in total.

,

• 15 watched television last night.

,

• 32 did homework.

,

• 9 ate pizza.

,

• 11 watched television and did homework.

,

• 7 watched television and ate pizza.

,

• 4 ate pizza and did homework.

,

• 3 did all three.

Let represent this problem as a Venn diagram.

As you can see in the diagram above, 27 students did those activities, and just 3 didn't do any activities.

Notice that to solve this kind of problem, we just have to pay close attention to the elaboration of the diagram, we must place the right numbers on each intersection in order to not have more students than we should have.

When the problem states 11 students watched television and did homework, it means that from those 11 in total we can find that some of them also ate pizza as the triple intersection can suggest.

Therefore, the right answer is "3 students did none of these activities".