Since it makes things easier to use the first letter of what
each set is composed of, and since Documents and Dramas both
start with D, I changed Dramas to Musicals. That way we can
use set D for documentaries, C for comedies, and M for musicals,
with no conflicts of letters.
CLUES
------------------------------------------------------------
1. 160 liked Comedies. (1 set is mentioned)
2. 160 liked to watch Documentaries, (1 set mentioned)
3 190 liked to watch Musicals, (1 set mentioned)
4. 20 campers like all three programs, (3 sets mentioned)
5. 50 watched Comedies and Documentaries, but not Musicals, (3 sets mentioned)
6. 70 liked to watch Documentaries and Musical, but not Comedies. (3 sets mentioned)
7. 130 watched Musicals, but not Comedies. (2 sets mentioned)
The little letters will represent how many are
in each of the 8 regions.
Region They
with watch do not
this these watch
many programs these
campers programs
------------------------------
a C D, M
b C,D M
e D C,M
f C,M D
g C,D,M ----
h D,M C
i M C,D
j ---- C,D,M
Since all participated in the survey, and none
did not like to watch any of the three kinds of
programs, so we know that j=0.
We begin with the clues that mention the most
number of sets.
Clue 4 tells us that g=20.
Clue 5 tells us that b=50.
Clue 6 tells us that h=70.
Now we can find e from clue 2
b+g+h+e = 120 and b+g+h=50+20+70=140,
so e=140-120=20.
We can find i from clue 7.
h+i = 130, and since h=70, i=130-70=60,
so now we have
Now we can find f from clue 3.
f+g+h+i=190, and g+h+i=20+70+60=150,
so f = 190-150=40. So we have
Finally we can find a from clue 1.
a+b+f+g=160, and b+f+g=50+40+20=110
so a=160-110=50. So now our Venn
diagram is complete:
Now to find the total number of campers we add
a+b+e+f+g+h+i+j =
50+50+20+40+20+70+60+0 = 310 campers.
Edwin