Honors Geometry Page 6
Venn Diagrams III
In a survey of children who saw three different shows at Walt Disney World, the following information was gathered:
· 39 children liked The Little Mermaid
· 43 children liked 101 Dalmatians
· 56 children liked Mickey Mouse
· 7 children liked The Little Mermaid and 101 Dalmatians
· 10 children liked The Little Mermaid and Mickey Mouse
· 16 children liked 101 Dalmatians and Mickey Mouse
· 4 children liked all three shows
· 6 children did not like any of the shows
Answer the following questions:
· How many students were surveyed?
· How many liked The Little Mermaid only?
· How many liked 101 Dalmatians only?
· How many liked Mickey Mouse only?
A class has 175 students. The following is the description of students studying one or more of the following subjects in this class. Mathematics 100, Physics 70, Chemistry 46, Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students are enrolled in Mathematics alone, Physics alone and Chemistry alone?
In a Canadian hospital, the blood of 500 patients was tested. It was found that 228 patients had the A antigen, 64 had the B antigen and 422 had the Rh antigen, while 35 had none of these. In addition, it was found that 18 had the A and B antigens, 51 had the B and Rh antigens, 193 had the A and Rh antigens and 13 had all three.
Draw a Venn diagram to illustrate the above situation.
200 people were asked which of these grand slam tournaments that they have attended. The tournaments inquired about were: US Open, Wimbledon, or Australian Open.
· 30 people have not attended any of these tournaments.
· 10 people have been to all thee tournaments.
· 25 people have been to Wimbledon and the Australian Open.
· 20 people have been to the US Open and the Australian Open but not to Wimbledon.
· 65 people have been to exactly two of the tournaments.
· 165 people have been to the US Open or to Wimbledon.
· 120 people have been to Wimbledon or to the Australian Open.
A survey of 80 sophomores at a certain western college showed the following:
· 36 take English
· 32 take history
· 32 take political science
· 16 take history and English
· 16 take political science and history
· 14 take political science and English
· 6 take all three
How many students:
a) take English and neither of the other two? ____
b) Take none of the three courses? ____
c) take history, but neither of the other two? ____
d) take political science and history but not English? ____
e) do not take political science? ____
Country-Western songs emphasize three basic themes: love, prison and trucks. A survey or the local Country-Western radio station produced the following data:
12 songs about a truck driver who is in love while in prison
2 about people in prison who are not in love and do not drive trucks
8 about people who are out of prison, are not in love, and do not drive a truck
13 about a prisoner in love
28 about a person in love
18 about a truck driver in love
16 about truck drivers who are not in prison
3 about a truck driver in prison who is not in love
Find the number of songs about:
a) How many songs were surveyed? ____
b) truck drivers? ____
c) prisoners? ____
d) truck drivers in prison? ____
e) people not in prison? ____
f) people not in love? ____