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24 Apr 2020, 03:25
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A factory has 80 workers and 3 machines. Each worker knows to operate at least 1 machine. If there are 65 workers who know to operate machine 1, 60 who know to operate machine 2 and 55 who know to operate machine 3, what is the minimum number of workers who know to operate all the three machines?
A. 15
B. 20
C. 25
D. 30
E. 40
Are You Up For the Challenge: 700 Level Questions
A. 15
B. 20
C. 25
D. 30
E. 40
Are You Up For the Challenge: 700 Level Questions
24 Apr 2020, 10:03
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monikakumar
There are (80-65=) 15 workers who can't operate machine 1.
There are (80-60=) 20 workers who can't operate machine 2.
There are (80-55=) 25 workers who can't operate machine 3.
Since you have to minimize number of workers who know to operate all the three machines, you have to maximize number of workers who don't know to operate at least 1 of the machine. That can happen if there is no common worker in any of the above 3 cases or the above 3 sets are disjoint.
maximum number of workers who don't know to operate at least 1 of the machine = 15+20+25 = 60
Minimum value of workers who know to operate all the three machines = 80-60 = 20
There are (80-65=) 15 workers who can't operate machine 1.
There are (80-60=) 20 workers who can't operate machine 2.
There are (80-55=) 25 workers who can't operate machine 3.
Since you have to minimize number of workers who know to operate all the three machines, you have to maximize number of workers who don't know to operate at least 1 of the machine. That can happen if there is no common worker in any of the above 3 cases or the above 3 sets are disjoint.
maximum number of workers who don't know to operate at least 1 of the machine = 15+20+25 = 60
Minimum value of workers who know to operate all the three machines = 80-60 = 20
24 Apr 2020, 09:41
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Minimum value of workers who know to operate all the three machines
= 80- [(80-65) + (80-60) + (80-55)]
= 80- 60
=20
= 80- [(80-65) + (80-60) + (80-55)]
= 80- 60
=20
Bunuel
