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Quiz 6
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Question 1
You did not answer the question.
Given the following Venn diagram, find n[ A ∪ ( B ∩ C ) ].
a)
63
b)
66
c)
62
d)
59
e)
60
f)
None of the above.
Question 2
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You did not answer the question.
Given the following Venn diagram, find n[ ( A ∪ B )c ∩ C ) ].
a)
44
b)
20
c)
49
d)
47
e)
48
f)
None of the above.
Question 3
You did not answer the question.
Given the following Venn diagram, find n[ A ∪ ( B ∩ C )c].
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a)
86
b)
90
c)
91
d)
87
e)
84
f)
None of the above.
Question 4
You did not answer the question.
Given the following Venn diagram, find n[ ( B ∩ C)c].
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a)
80
b)
3
c)
47
d)
101
e)
26
f)
None of the above.
Question 5
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Let U represent the set of people in a certain community who were asked if they subscribe to an
information source.
Let D ={ x ∈ U | x subscribes to The Daily Informer }
and
N ={ x ∈ U | x subscribes to News Magazine }
(Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who
subscribe to exactly one of the two news sources given.
a)
N∪D
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b)
( N ∩ D )c
c)
(Nc∩D)∪( N∩Dc)
d)
( Nc ∪ D) ∩(N ∪Dc)
e)
Nc∩D
f)
None of the above.
Question 6
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Let U represent the set of all people that frequently visit a certain restaurant, surveyed about which food
they like best. Let
B = { x ∈ U | x likes Hamburgers }
C = { x ∈ U | x likes Corn Dogs }
P = { x ∈ U | x likes Pizza }
(Assume these sets are not disjoint.) Write the statement that refers to: P ∩ ( C ∪ B ) c .
a)
The set of customers who like Pizza or Corn Dogs or Burgers.
b)
The set of customers who like all three foods given.
c)
The set of customers who like Pizza but not Corn Dogs or Burgers.
d)
The set of customers who like Pizza and Corn Dogs but not Burgers.
e)
The set of customers who do not like any of these foods given.
f)
None of the above.
Question 7
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Suppose that S is the set of successful students in a classroom, and that F stands for the set of freshmen
students in that classroom. Find n(S ∩ F) given that
n(S) = 51, n(F) = 23 and n(S ∪ F) = 60
a)
111
b)
0
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c)
14
d)
74
e)
134
f)
None of the above.
Question 8
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Suppose that n(U) = 200, n(A) = 105, n(B) = 110, and n( A ∩ B ) = 30. Find n( A c ∪ B ).
a)
80
b)
110
c)
125
d)
95
e)
75
f)
None of the above.
Question 9
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A survey of 398 children given at a local elementary school showed that 175 like chocolate ice cream, 150
like pistachio ice cream, and 123 do not like chocolate or pistachio ice cream. How many children like
both chocolate ice cream and pistachio ice cream?
a)
50
b)
275
c)
225
d)
125
e)
325
f)
None of the above.
Question 10
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337 car stereos were recently sold in a car audio store. 104 had a CD player, 126 had a cassette player,
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and 40 had both a CD and a cassette player. How many had a CD player only?
a)
24
b)
54
c)
64
d)
56
e)
74
f)
None of the above.
Question 11
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412 students were surveyed about their preferences of sports. 115 students like football, 100 students like
baseball, and 45 students like both sports. How many students like exactly one of the two sports?
a)
115
b)
215
c)
125
d)
70
e)
55
f)
None of the above.
Question 12
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A campus radio station surveyed 500 students to determine the types of music they like. The survey
revealed that 204 like rock,160 like country, and 120 like jazz. Moreover, 27 like rock and country, 27
like rock and jazz, 23 like country and jazz, and 10 like all three types of music. How many students
surveyed liked exactly one of the three types of music? (Note: A Venn diagram may be useful here.)
a)
10
b)
360
c)
200
d)
147
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e)
500
f)
None of the above.
Question 13
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A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500
students surveyed, 42 like Snickers, 110 like Twix, 124 like Reese's Peanut Butter Cups, 33 like Snickers
and Twix, 62 like Twix and Reese's Peanut Butter Cups, 26 like Snickers and Reese's Peanut Butter Cups,
and 22 like all three kinds of chocolate candy. How many students like no more than one kind of these
chocolate candies?
a)
100
b)
155
c)
77
d)
323
e)
423
f)
None of the above.
Question 14
You did not answer the question.
A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500
students surveyed, 143 like Snickers, 130 like Twix, 163 like Reese's Peanut Butter Cups, 51 like Snickers
and Twix, 43 like Twix and Reese's Peanut Butter Cups, 86 like Snickers and Reese's Peanut Butter Cups,
and 34 like all three kinds of chocolate candy. How many students like Reese's Peanut Butter Cups or
Snickers, but not Twix?
a)
186
b)
92
c)
160
d)
108
e)
194
f)
None of the above.
Question 15
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(Car Sales) Of the cars sold during the month of July, 94 had air conditioning, 96 had automatic
transmission, and 80 had power steering. 6 cars had all three of these extras. 18 cars had none of these
extras. 21 cars had only air conditioning, 62 cars had only automatic transmissions, and 25 cars had only
power steering. 11 cars had both automatic transmission and power steering. How many cars had air
conditioning and automatic transmission but not power steering?
a)
23
b)
44
c)
29
d)
6
e)
5
f)
None of the above.
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