Question 1

A large inpatient addiction treatment facility houses 80 patients. Thirty-two are addicted to alcohol, 25 to narcotics, and 4 to both. How many patients are addicted only to narcotics?

Accepted Answer

$$21$$

Question 2

Given the same facility: How many patients are not addicted to narcotics?

Accepted Answer

$$55$$

Question 3

How many patients are addicted to something other than alcohol or narcotics?

Accepted Answer

$$23$$

Question 4

There are 18 states with at least one mountain but no coastline, 7 with coastline but no mountains, and 9 with neither. If there are 50 states, how many states have both a mountain and a coastline?

Accepted Answer

$$16$$

Question 5

Based on the previous scenario, how many states have at least one mountain?

Accepted Answer

$$34$$

Question 6

How many states have a coastline?

Accepted Answer

$$23$$

Question 7

In a survey of 230 cities, 119 have an art museum, 75 have a ballet company, and 41 have an orchestra but no ballet. If 30 cities have neither ballet nor orchestra, how many cities have only an orchestra?

Accepted Answer

$$22$$

Question 8

How many cities have an art museum?

Accepted Answer

$$119$$

Question 9

How many cities have an orchestra?

Accepted Answer

$$73$$

Question 10

How many cities have none of the three: art museum, orchestra, or ballet?

Accepted Answer

$$30$$

Question 11

How many cities have all three: an art museum, an orchestra, and a ballet company?

Accepted Answer

$$7$$

Question 12

If $$A$$ and $$B$$ are sets such that $$n(A) = 32$$, $$n(B) = 25$$, and $$n(A \cap B) = 4$$, what is $$n(A \cup B)$$?

Accepted Answer

$$53$$

Question 13

If $$U is $$the universal set of 80 patients, $$A is $$the set of alcohol addiction, $$N is $$narcotics, and $$n(A \cup N) = 53$$, how many are in the complement $$U - (A \cup N)$$?

Accepted Answer

$$27$$

Question 14

If a city is randomly selected from the 230 surveyed, what is the probability it has neither a ballet nor an orchestra?

Accepted Answer

$$\frac{30}{230}$$

Question 15

If $$A$$, $$B$$, and $$C$$ are sets representing art museum, orchestra, and ballet, respectively, which expression represents the number of cities with only an art museum?

Accepted Answer

$$n(A) - n(A \cap B) - n(A \cap C) + n(A \cap B \cap C)$$

College Algebra Study Guide: Sets and Venn Diagrams

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