Question 1

If  ,  ,  ,  ,  ,  , and  , find  . ​
A) 18
B) 15
C) 20
D) 11
E) 10
F) 14

Accepted Answer

The answer of If  ,  ,  ,...

Question 2

Let A and B be subsets of a universal set U and suppose  ,  ,  , and  . Compute  . ​
A) 40
B) 90
C) 30
D) 20
E) 170
F) 10

Accepted Answer

The answer of Let A and B be subsets of...

Question 3

A survey of 100 college students who frequent the reading lounge of a university revealed the following results:
​
47 read Time.
​
36 read Newsweek.
​
31 read U.S. News & World Report.
​
19 read Time and Newsweek.
​
16 read Time and U.S. News & World Report.
​
12 read Newsweek and U.S. News & World Report.
​
6 read all three magazines.
​
How many of the students surveyed read none of these magazines?
​
__________ students

Accepted Answer

The answer of A survey of 100 college students who...

Question 4

In a poll conducted among  active investors, it was found that  use discount brokers,  use full-service brokers, and  use both discount and full-service brokers. How many investors use only discount brokers? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of In a poll conducted among  active...

Question 5

In a survey of 300 individual investors regarding subscriptions to the New York Times (NYT), Wall Street Journal (WSJ), and USA Today (UST), the following data were obtained: ​
122 subscribe to the NYT.
​
151 subscribe to the WSJ.
​
63 subscribe to the UST.
​
39 subscribe to the NYT and WSJ.
​
29 subscribe to the WSJ and UST.
​
18 subscribe to the NYT and UST.
​
35 do not subscribe to any of these newspapers.
​
How many subscribe to only one of these newspapers?
​
A) 244
B) 229
C) 179
D) 209
E) 194

Accepted Answer

The answer of In a survey of 300 individual investors...

Question 6

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) 
B) 
C) 
D) 
E)

Accepted Answer

According to the information given, 11eab448_e7fa_3238_acdb_cb1f75b3cb92_TB6027_11 lowered their estimate of consumer inflation rate and raised their estimate of GNP growth rate. 
11eab448_e7fa_323b_acdb_93636c6d41cc_TB6027_11 also lowered their estimate of consumer inflation rate but did not raise their estimate of GNP growth rate. 
Therefore, there are only two economists who lowered their estimate of consumer inflation rate. Out of these two, only one raised their estimate of GNP growth rate. 
Hence, the answer is C.

Question 7

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) 10
C) 21
D) 15
E) 5

Accepted Answer

The answer of Of 55 employees of a store located...

Question 8

The 120 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) 81
B) 16
C) 12
D) 32
E) 104

Accepted Answer

To find the number of consumers who buy the product sold under none of these labels, we can use the formula:

Total consumers = Only A + Only B + Only C + A and B + A and C + B and C + All three + None

We know that:
Only A = 12
Only B = 24
Only C = 27
A and B = 14
A and C = 9
B and C = 11
All three = 7
Total consumers = 120

Substituting these values in the formula, we get:

120 = 12 + 24 + 27 + 14 + 9 + 11 + 7 + None
None = 16

Therefore, 16 of the consumers surveyed buy the product sold under none of these labels. The answer is option B.

Question 9

Of 100 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) 50
B) 10
C) 20
D) 60
E) 40

Accepted Answer

Given that 60 radios had FM and 80 had AM, and assuming all 100 radios had at least one of these features, the maximum overlap (radios that have both AM and FM) would be the minimum of the two numbers given, which is 60. This means at least 20 of the FM radios could only receive FM (100 total - 80 AM = 20 could be FM only). However, to directly calculate the FM only radios: if all 60 FM radios also had AM, that leaves 20 AM radios without FM, implying the rest of the radios (100 - 80 = 20) could receive FM only, matching the conditions given.

Question 10

If  ,  , and  , what is  ? ​
A) 17
B) 8
C) 15
D) 13
E) 6
F) 14

Accepted Answer

The answer of If  ,  , and ...

Question 11

In a survey of 370 households regarding the ownership of VCRs and DVD players, the following data was obtained:
​
340 households own one or more VCRs.
​
170 households own one or more VCRs and one or more DVD players.
​
18 households do not own a VCR or a DVD player.
​
How many households only own one or more DVD players?
​
__________ households

Accepted Answer

The answer of In a survey of 370 households regarding...

Question 12

If  ,  , and  , what is  ? ​
A) 1
B) 12
C) 5
D) 2
E) 3
F) 9

Accepted Answer

The answer of If  ,  , and ...

Question 13

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) 14
B) 32
C) 30
D) 2
E) 4

Accepted Answer

Given that 20 states had either an increase in dropout rate or a dropout rate of at least 30%, it implies that 30 states did not meet either condition. Since 16 states had an increase and 18 had a rate of at least 30%, but only 20 states are accounted for in these categories combined, it means there's an overlap of 14 states (16 + 18 = 34, but only 20 states are mentioned, so 34 - 20 = 14). Therefore, only 2 states (16 - 14) had an increase in the dropout rate but did not reach the 30% threshold.

Question 14

In a survey of 200 households regarding the ownership of desktop and laptop computers, the following information was obtained:
​
110 households own only desktop computers.
​
10 households own only laptop computers.
​
50 households own neither desktop nor laptop computers.
​
How many households own both desktop and laptop computers?
​
__________ households

Accepted Answer

The answer of In a survey of 200 households regarding...

Question 15

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? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of In a survey of  members of...

Question 16

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) 76 prisoners
B) 61 prisoners
C) 71 prisoners
D) 82 prisoners
E) 62 prisoners
F) 81 prisoners

Accepted Answer

61 prisoners are accused of both a felony and a misdemeanor. This is found by adding the number of prisoners accused of felonies (128) and misdemeanors (117) which gives 245. Since there are only 184 prisoners in total, the difference (245 - 184 = 61) must be those accused of both.

Question 17

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor?
​
__________ prisoners

Accepted Answer

The answer of On a certain day, the Wilton County...

Question 18

If  ,  ,  ,  ,  ,  , and  find  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If  ,  ,  ,...

Question 19

To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained:
​
133 students ate breakfast.
​
184 students ate lunch.
​
278 students ate dinner.
​
71 students ate breakfast and lunch.
​
113 students ate breakfast and dinner.
​
92 students ate lunch and dinner.
​
59 students ate all three meals.
​
How many of the students ate exactly one meal in the cafeteria?
​
__________ students

Accepted Answer

The answer of To help plan the number of meals...

Question 20

Let A and B be subsets of a universal set U and suppose  ,  ,  , and  . Compute  . ​
A) 80
B) 100
C) 90
D) 200
E) 150
F) 180

Accepted Answer

The answer of Let A and B be subsets of...

Quiz 6: Sets and Counting

If , , , , , , and , find .

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

In a poll conducted among active investors, it was found that use discount brokers, use full-service brokers, and use both discount and full-service brokers. How many investors use only discount brokers?

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?

Of 100 clock radios sold recently in a department store, 60 had FM circuitry, and 80 had AM circuitry. How many could receive FM transmission only?

If , , and , what is ?

If , , and , what is ?

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?

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? __________ prisoners

If , , , , , , and find .

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

Quiz 6: Sets and Counting

If , , , , , , and , find . ​

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

In a poll conducted among active investors, it was found that use discount brokers, use full-service brokers, and use both discount and full-service brokers. How many investors use only discount brokers? ​

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? ​

Of 100 clock radios sold recently in a department store, 60 had FM circuitry, and 80 had AM circuitry. How many could receive FM transmission only? ​

If , , and , what is ? ​

If , , and , what is ? ​

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? ​

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? ​ __________ prisoners

If , , , , , , and find . ​

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

If , , , , , , and , find .

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

In a poll conducted among active investors, it was found that use discount brokers, use full-service brokers, and use both discount and full-service brokers. How many investors use only discount brokers?

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?

Of 100 clock radios sold recently in a department store, 60 had FM circuitry, and 80 had AM circuitry. How many could receive FM transmission only?

If , , and , what is ?

If , , and , what is ?

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?

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? __________ prisoners

If , , , , , , and find .

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