T102 Supplement Problems on Venn
Diagrams
1. NEW Gadgets
A recent
survey of 600 families revealed that 348 of them had a video cassette recorder
(VCR), 198 had a microwave oven, and 75 had both a VCR and a microwave
oven. Based upon this information,
a) How many families had neither a VCR nor a
microwave oven?
b) How many families had only a VCR?
c) How many families had only a microwave oven?
2. Thirsty?
Lemonmobiles
are available with two possible options:
radio and air conditioning. The
owner of the Lemonmobile Emporium is studying a recent inventory of his lot,
which shows
50 Lemonmobiles on hand in all
25 Lemonmobiles have radios
13 have both
options, radios and air conditioning
15 have neither option
a) How many of the Lemonmobiles on hand have air
conditioning?
b) How many of the Lemonmobiles on hand have
radios but no air conditioning?
3. Musicians
In a music
club with 15 members, 7 people played piano, 6 people played guitar, and 4
people didn’t play either of these two instruments. How many people played both piano and guitar?
4. Flawed Data
A
sociologist surveyed 100 college students and came up with these data:
72 own cars
60 own stereos
20 own both items.
On seeing
these results, another sociologist claimed that the doing the survey was either
a fraud or incompetent (or both). Is
this correct? Why?
5. High School
Background
The student government at
28
took physics,
31 took biology,
42 took
geometry,
9 took physics and biology,
10 took
physics and geometry,
6 took biology and geometry, and
4 took all three subjects.
On the
basis of these figures,
a)
How many students took none of the three subjects?
b)
How many students took physics, but not biology or geometry?
c)
How many students took biology and physics but not geometry?
6. Science Anyone?
A
survey was taken of students at the university concerning their enrollment in
liberal arts courses. Each of 600
students was asked to answer yes or no to each of the questions:
Are you enrolled in a humanities
course?
Are you enrolled in a natural
science course?
Are you enrolled in a social science
course?
So far the
following data from the survey have been tabulated.
250 of the students
survey are enrolled in natural science courses
100 are enrolled both in a
humanities course and a social science course
130 are enrolled in a natural
science course but not in a humanities course
120 are enrolled only in a social
science course
30 are enrolled in all three course areas
270 are enrolled in a social science
course
300 are enrolled in only one of the
three areas
The dean of
liberal arts is interested in know the answers to the questions.
a) How many of the students surveyed are
enrolled in none of these three areas?
b) How many of the student surveyed are enrolled in at least one of the three areas?
c) How many of the students surveyed are
enrolled in at least two of the three areas?
d) How many of the students
survey are enrolled in a humanities course?
Bonus - TVs
At
a large TV appliance store you can purchase a TV in two sizes: Large or small. Each TV has either a black and white or a
color screen the owner of the store has checked her stock and found out that
she has
23 large TVs
6 small black and white TVs
19 color TVs
21 black and white TVs
How many
large color TVs are there?
How many
small TVs are there?
How many
TVs are there in all?
Solutions
1. a)
129, b) 273, c) 123
2. a) 23, b) 12
3. 2
4. Flawed, sum is greater than 100
5. a)
20, b) 13,
c) 5
6. a)
60, b) 540,
c) 240, d) 290
Bonus - 8, 17, 40