# Math homework

**QUESTION 1**

In a survey of 380 households regarding the ownership of VCRs and DVD players, the following data was obtained:

350 households own one or more VCRs.

180 households own one or more VCRs and one or more DVD players.

13 households do not own a VCR or a DVD player.

How many households only own one or more DVD players?

a. 29 households

b. 17 households

c. 20 households

d. 30 households

e. 16 households

f. 19 households

**QUESTION 2**

On a certain day, the Wilton County Jail had 184 prisoners. Of these, 128 were accused of felonies, and 117 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor?

a. 81 prisoners

b. 61 prisoners

c. 71 prisoners

d. 82 prisoners

e. 76 prisoners

f. 62 prisoners

**QUESTION 3**

In a survey of 122 consumers conducted in a shopping mall, 82 consumers indicated that they buy brand A of a certain product, 71 buy brand B, and 46 buy both brands. How many consumers participating in the survey buy only brand A?

a. 87 consumers

b. 56 consumers

c. 36 consumers

d. 51 consumers

e. 17 consumers

f. 35 consumers

**QUESTION 4**

The 130 consumers were asked about their buying preferences concerning another product that is sold in the market under three labels. The results were

12 buy only those sold under label A.

24 buy only those sold under label B.

27 buy only those sold under label C.

14 buy only those sold under labels A and B.

9 buy only those sold under labels A and C.

11 buy only those sold under labels B and C.

7 buy the product sold under all three labels.

How many of the consumers surveyed buy the product sold under none of these labels?

a. 106

b. 89

c. 26

d. 19

e. 41

**QUESTION 5**

Let A and B be subsets of a universal set U and suppose , , , and . Compute .

a. 200

b. 180

c. 90

d. 150

e. 80

f. 100

**QUESTION 6**

Of 110 clock radios sold recently in a department store, 60 had FM circuitry, and 80 had AM circuitry. How many could receive FM transmission only?

a. 30

b. 60

c. 10

d. 50

e. 40

**QUESTION 7**

Let and . Compute n(A).

a. 8

b. 14

c. 5

d. 4

e. 17

f. 1

**QUESTION 8**

If , , and , what is ?

a. 2

b. 5

c. 9

d. 12

e. 1

f. 3

**QUESTION 9**

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and .

Compute .

a. 89

b. 14

c. 10

d. 70

e. 39

f. 64

**QUESTION 10**

If , , and , what is ?

a. 8

b. 5

c. 15

d. 9

e. 17

f. 13

**QUESTION 11**

Of 55 employees of a store located in downtown Boston, 16 people take the subway to work, 11 take the bus, and 6 take both the subway and the bus. How many employees take either the bus or the subway to work?

a. 34

b. 21

c. 5

d. 10

e. 15

**QUESTION 12**

In a survey of members of a local sports club, members indicated that they plan to attend the next Summer Olympic Games, indicated that they plan to attend the next Winter Olympic Games, and indicated that they plan to attend both games. How many members of the club plan to attend at least one of the two game?

**QUESTION 13**

Let . If and , find .

a. 19

b. 3

c. 7

d. 2

e. 8

f. 11

**QUESTION 15**

Let A and B be subsets of a universal set U and suppose , , , and . Compute .

a. 10

b. 40

c. 20

d. 90

e. 170

f. 30

**QUESTION 16**

To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained:

132 students ate breakfast.

182 students ate lunch.

279 students ate dinner.

68 students ate breakfast and lunch.

112 students ate breakfast and dinner.

91 students ate lunch and dinner.

59 students ate all three meals.

How many of the students ate exactly two meals in the cafeteria?

a. 187

b. 111

c. 119

d. 94

e. 174

f. 251

**QUESTION 17**

A survey of the opinions of leading Economists in a certain country showed that, because oil prices were expected to drop in that country over the next 12 months,

had lowered their estimate of the consumer inflation rate,

had raised their estimate of the gross national product (GNP) growth rate.

had lowered their estimate of the consumer inflation rate but had not raised their estimate of the GNP growth rate.

How many Economists had raised their estimate of GNP growth rate and lowered their estimate of the consumer inflation rate for that period?

a. 8

b. 3

c. 12

d. 5

e. 7

**QUESTION 18**

In a survey of 250 households regarding the ownership of desktop and laptop computers, the following information was obtained:

130 households own only desktop computers.

30 households own only laptop computers.

50 households own neither desktop nor laptop computers.

How many households own both desktop and laptop computers?

a. 100 households

b. 40 households

c. 10 households

d. 90 households

e. 80 households

f. 50 households

**QUESTION 19**

Data released by the Department of Education regarding the rate (percentage) of ninth-grade students that don’t graduate showed that out of 50 states,

16 states had an increase in the dropout rate during the past 2 years.

18 states had a dropout rate of at least 30% during the past 2 years.

20 states had an increase in the dropout rate and/or a dropout rate of at least 30% during the past 2 years.

How many states had a dropout rate that was less than 30% but that had increased over the 2-year period?

a. 4

b. 14

c. 2

d. 30

e. 32

**QUESTION 20**

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and .

Compute .

a. 38

b. 34

c. 33

d. 9

e. 24

f. 19

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