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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!

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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