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10 Nov 2023, 09:16
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (02:23) correct
24%
(03:07)
wrong
based on 131
sessions
History
Date
Time
Result
Not Attempted Yet
Out of 75 students, 17 students enrolled in a Physics class, 28 students enrolled in a Chemistry class, and 39 students enrolled in a Biology class. 5 students enrolled in both the Physics and Chemistry classes, 7 students enrolled in both the Chemistry and Biology classes, and 6 students enrolled in both the Biology and Physics classes. If 4 students enrolled in Physics, Chemistry, and Biology, how many students did not enroll in any of the three science classes?
A. 2
B. 3
C. 4
D. 5
E. 6
A. 2
B. 3
C. 4
D. 5
E. 6
10 Nov 2023, 20:09
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Bunuel
To solve this type of questions create a set and then solve by giving variable
OA is D
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10 Nov 2023, 22:13
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This question is asking us to find out how many students are not enrolled in any of the three science classes. This can be found by removing the number of students who have enrolled in at least one class from the total student.
The number of students enrolled in the Physics class, P = 17
The number of students enrolled in the Chemistry class, C = 28
The number of students enrolled in the Biology class, B = 39
The number of students enrolled in both Physics and Chemistry classes, P∩C = 5
The number of students enrolled in both Chemistry and Biology classes, C∩B = 7
The number of students enrolled in both Biology and Physics classes, B∩P = 6
The number of students enrolled in all three classes, P∩C∩B = 4
We can calculate the total number of students enrolled in at least one class as
P+C+B−(P∩C)−(C∩B)−(B∩P)+(P∩C∩B) = 17+28+39−5−7−6+4 = 70
So, 70 students are enrolled in at least one of the three classes. Since there are 75 students in total, the number of students not enrolled in any of the three classes is 75−70 = 5
Thus, 5 students are not enrolled in any of the three science classes
The number of students enrolled in the Physics class, P = 17
The number of students enrolled in the Chemistry class, C = 28
The number of students enrolled in the Biology class, B = 39
The number of students enrolled in both Physics and Chemistry classes, P∩C = 5
The number of students enrolled in both Chemistry and Biology classes, C∩B = 7
The number of students enrolled in both Biology and Physics classes, B∩P = 6
The number of students enrolled in all three classes, P∩C∩B = 4
We can calculate the total number of students enrolled in at least one class as
P+C+B−(P∩C)−(C∩B)−(B∩P)+(P∩C∩B) = 17+28+39−5−7−6+4 = 70
So, 70 students are enrolled in at least one of the three classes. Since there are 75 students in total, the number of students not enrolled in any of the three classes is 75−70 = 5
Thus, 5 students are not enrolled in any of the three science classes
