In a college, the science department has three disciplines.
In total, 280 students study chemistry, 254 students study
physics and 280 students study biology. 97 students study
both chemistry and physics, 138 students study both physics
and biology, 152 students study both chemistry and biology.
73 students study all three disciplines. Can you determine
how many students there are in the science department?
1) Five racing drivers, Alan, Bob, Chris, Don, and Eugene,
enter into a contest that consists of 6 races. The results
of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place
finish, four points for fourth, six points for third, eight
points for second, and ten points for first.
If Eugene finishes two places ahead of Chris in the first
race, all of the following will be true EXCEPT:
a) Bob finishes ahead of Don.
b) Chris finishes two places ahead of Alan.
c) Don finishes fourth.
d) Bob finishes immediately behind Eugene.
e) Chris finishes ahead of Bob.
2) Five racing drivers, Alan, Bob, Chris, Don, and Eugene,
enter into a contest that consists of 6 races. The results
of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place
finish, four points for fourth, six points for third, eight
points for second, and ten points for first.
If Don finishes third in the third race, which of the
following must be true of that race?
a) Alan finishes first.
b) Eugene finishes first.
c) Bob finishes second.
d) Chris finishes second.
e) Alan finishes fifth.
3) Five racing drivers, Alan, Bob, Chris, Don, and Eugene,
enter into a contest that consists of 6 races. The results
of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place
finish, four points for fourth, six points for third, eight
points for second, and ten points for first.
If Eugene's total for the six races is 36 points, which of
the following must be true?
a) Bob's total is more than 36 points.
b) Chris's total is more than 36 points.
c) Alan's total is 36 points.
d) Don's total is less than 36 points.
e) Don's total is 36 points.
4) Five racing drivers, Alan, Bob, Chris, Don, and Eugene,
enter into a contest that consists of 6 races. The results
of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place
finish, four points for fourth, six points for third, eight
points for second, and ten points for first.
If Alan finishes first only once, and Don finishes second
exactly twice, the lowest total number of points that Bob
can earn in the race is:
a) 32 points.
b) 38 points.
c) 40 points.
d) 44 points.
e) 48 points.
5) Five racing drivers, Alan, Bob, Chris, Don, and Eugene,
enter into a contest that consists of 6 races. The results
of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place
finish, four points for fourth, six points for third, eight
points for second, and ten points for first.
If Alan finishes first in four races, which of the following
could earn a total of fewer than 26 points in the six races?
a) Bob only.
b) Chris only.
c) Don only.
d) Eugene of Chris.
e) Don or Chris.
6) Five racing drivers, Alan, Bob, Chris, Don, and Eugene,
enter into a contest that consists of 6 races. The results
of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place
finish, four points for fourth, six points for third, eight
points for second, and ten points for first.
If Frank enters the third race and finishes behind Chris and
Don, which of the following must be true of that race?
a) Eugene finishes first.
b) Alan finishes sixth.
c) Don finishes second.
d) Frank finishes fifth.
e) Chris finishes third.
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