There are 15,000 students in college X. Of those students, 1,700 are taking both ethics and metaphysics this semester. There are 2,200 total students taking ethics. 9,500 students are taking neither of these classes. What is the maximum number of students that are taking metaphysics this term?
There are 15,000 students in college X. Of those students, 1,700 are taking both ethics and metaphysics this semester. There are 2,200 total students taking ethics. 9,500 students are taking neither of these classes. What is the maximum number of students that are taking metaphysics this term?
The correct option is D 5000
The easiest way to understand this problem is to draw a Venn diagram:
Where,
S = Total number of students
A = Total students taking ethics
B = Total students taking metaphysics
A – B = Students taking only ethics
B – A = Students taking only metaphysics
A ∪ B = Total students taking either ethics or metaphysics
A ∩ B = Total students taking both ethics and metaphysics
We know that there are a total of 15,000 students and that 9,500 are taking neither class.
Therefore, 15,000 – 9,500 = 5,500 are taking at least one of the classes.
Based on our prompt, there are 1,700 taking both, and 2,200 students are taking ethics.
Number of students picking only ethics
= 2200 – 1700
= 500
Finally, if we know that there are 5,500 taking at least one of these classes, the maximum number of students picking metaphysics will be
= 5,500 – 500
= 5,000.
The easiest way to understand this problem is to draw a Venn diagram:
Where,
S = Total number of students
A = Total students taking ethics
B = Total students taking metaphysics
A – B = Students taking only ethics
B – A = Students taking only metaphysics
A ∪ B = Total students taking either ethics or metaphysics
A ∩ B = Total students taking both ethics and metaphysics
We know that there are a total of 15,000 students and that 9,500 are taking neither class.
Therefore, 15,000 – 9,500 = 5,500 are taking at least one of the classes.
Based on our prompt, there are 1,700 taking both, and 2,200 students are taking ethics.
Number of students picking only ethics
= 2200 – 1700
= 500
Finally, if we know that there are 5,500 taking at least one of these classes, the maximum number of students picking metaphysics will be
= 5,500 – 500
= 5,000.
