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There are 500 students in a class. 450 of them take Course A, 300 of t : Multiple-choice Questions — Select One or More Answer Choices

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There are 500 students in a class. 450 of them take Course A, 300 of t [#permalink]
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void wrote:
another explanation for above question please


Hi There!

Let me try helping you!

Students who study course A (This includes only A, A& B, A& C & A,B & C)=450
Students who study course B= 300
Students who study course=150

Now, as we know the 100 students who study all the 3 subjects will be included in the above students and they will be counted thrice i.e. once in A, B & C. Therefore we can subtract this from all the three
A(This includes only A, A& B, A& C )450-100=350
B=300-100=200
C=150-100=50

Now the above values are those values which includes individual and two courses together.
Total students=500
350+200+50+100=700
700-500=200

Thus, there has to be 200 students combined (A& B, B& C, A& C)
As we know that C has only 50 students left the maximum it can share with A & B is 50
So, If A& C or B& C= 50. The left 150 has to be filled by A & B to give us a total of 500.

And if those 50 take up only C course. Then 200 students take A& B together.

IMO C & D

Hope this helps!
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Re: There are 500 students in a class. 450 of them take Course A, 300 of t [#permalink]
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kumarneupane4344 wrote:
There are 500 students in a class. 450 of them take Course A, 300 of them take Course B, and 150 of them take Course C. Each student has to take at least one course, and 100 of them take all the three classes simultaneously. The number of students who take both Course A and Course B, but not Course C could be?
Indicate all such possible values.
A. 50

B. 100

C. 150

D. 200

E. 250


Post a detailed solution and get kudos!


AUBUC + Leftovers= A + B + C - (d + e + f) - 2(A∩B∩C)
500 + 0 = 450 + 300 + 150 - (d + e + f) - 2(100)
(d + e + f) = 200

For Maximization;
e = f = 0
i.e. d = 200

For Minimization;
As, C = f + e + 100
150 = e + f + 100
e + f = 50

Therefore, d + 50 = 200
i.e. d = 150

Hence, option C and D
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Re: There are 500 students in a class. 450 of them take Course A, 300 of t [#permalink]
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Re: There are 500 students in a class. 450 of them take Course A, 300 of t [#permalink]
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