Charlie got calls from two colleges. What could be the minimum marks obtained by him in a section?

We have to minimum marks obtained by him in a section which is possible only when Charlie  must have scored full marks in remaining 3 sections. Along with that we have to ensure that Charlie gets enough marks to clear aggregate cut off as well. 

For college 1, the minimum marks that Charlie needs to get a call = 176. To get the minimum marks in any section he has to score full marks in remaining 3 sections. Since he has to clear the cut off in sections A, B and C we can say that he can score a minimum marks in section D.

Minimum marks in section D despite which he will get call from college 1 = 176 - 3*50 = 26.
Similarly, minimum marks in one section out of  A and D despite which he will get call from college 2 = 175 - 3*50 = 25.
Similarly, minimum marks in one section out of A, B and Ddespite which he will get call from college 3 = 171 - 3*50 = 21.
Similarly, minimum marks in one section out of B and C despite which he will get call from college 4 = 178 - 3*50 = 28.
Similarly, minimum marks in one section out of B and D despite which he will get call from college 5 = 180 - 3*50 = 30.
Similarly, minimum marks in one section out of A and C despite which he will get call from college 6 = 176 - 3*50 = 26.

We can see that Charlie need to score at least 25 marks in one section out of A and D to get call from exactly 2 colleges. Therefore, option C is correct answer.