some difficult problems (with hints)

1
some difficult problems (with hints)
Pamela Leutwyler
2
12.)
There are 45 people at a college reunion. All of
the women are smart. (hint ) All of the men are
rich. (hint ) All of the lawyers are smart
men. Everyone is a doctor or a lawyer. (hint
) There are 12 rich women. 10 have both law and
medical degrees. There are 30 rich
doctors. There are 15 lawyers. There are 26 men.
1.) How many women are there?___ 2.) How many
men are not lawyers?___ 3.) How many men are
smart?_____
next problem
3
S
W
return to the problem
4
All the men are rich. M ? R if and only if
R? ? M? if and only if R? ? W
S
W
R?
return to the problem
5
Everyone is a doctor or a lawyer. D ? L U
if and only if D? ? L
ie if you are not a doctor then you must be a
lawyer
L
D?
return to the problem
6
13.) In a survey of 100 students, it was noted
that Everyone was taking English or Math All
those taking Biology were also taking English and
Math Everyone was taking History or
Biology Everyone was taking History or
Math Everyone was taking English or History 17
were enrolled in English, Math, History, and
Biology 28 were enrolled in Biology 88 were
enrolled in Math 76 were enrolled in English
How many students were enrolled in 1.)
History?_________ 2.) History but not
English?_______ 3.) Math and History?________
hint
P?QU if and only if P'?Q' ? if and only
if P ' ? Q if and only if Q ' ? P
7
14.)
In a recent survey of students, it was noted
that Everyone was enrolled in Math or
History All those taking Math were also taking
Physics 8 were taking both Math and History 19
were taking Math 26 were taking Physics 20 were
taking History How many students were
surveyed?_______ How many were taking Physics
and History?_______
8
15.) In a recent survey of 100 people, it was
noted that All of the men watch football All of
the women are happy 20 women watch football 30
men are happy 10 people do not watch
football How many people are happy?______ How
many people watch football?________
9
16.) In a recent survey of people shopping at
the mall, it was noted that None of the men are
happy All of the men are rich All of the happy
people are teachers There are 50 men There are 90
rich people There are 85 teachers There are 20
happy rich people 10 men are teachers There are
45 rich teachers There are 30 unhappy
teachers There are 95 women How many rich women
are unhappy?________ How many happy people are
not rich?_________