There are 4 related suttas, but they may not fit your description precisely.

[Pañhapuccha Sutta (AN 5.165)][1] describes 5 types of questions based on their motivations:

 - Stupidity and bewilderment
 - Evil desires and greed
 - Contempt
 - Desire for knowledge
 - 'If, when asked, he answers correctly, well & good. If not, then I will answer correctly [for him].'

The last type of question is normally asked by the Buddha and Arahant teachers to their students.

[Pañha Sutta (AN 4.42)][2] describes 4 ways of answering questions:

 - There are questions that should be answered categorically [straightforwardly yes, no, this, that].
 - There are questions that should be answered with an analytical (qualified) answer [defining or redefining the terms].
 - There are questions that should be answered with a counter-question.
 - There are questions that should be put aside. 

[Kathavatthu Sutta (AN 3.67)][3] describes persons who are fit and unfit to talk with:

 - A person who does not answer a question with the type of answer that is fitting to it (based on [AN4.42][2]), is unfit to talk with.
 - A person who, in his answer, does not stand by what is possible and impossible, doesn't stand by agreed-upon assumptions, doesn't stand by teachings known to be true, doesn't stand by standard procedure, then he is unfit to talk with.
 - A person, when asked a question, wanders from one thing to another, pulls the discussion off the topic, shows anger & aversion and sulks, then he is unfit to talk with.
 - A person, when asked a question, puts down [the questioner], crushes him, ridicules him, grasps at his little mistakes, then he is unfit to talk with.

A person who is fit to talk with, is the opposite of the above.

The Buddha concludes the purpose of teaching and discussing, as quoted by Samana Johann in his answer:

> For that's the purpose of discussion, that's the purpose of counsel,
> that's the purpose of drawing near, that's the purpose of lending ear:
> i.e., **the liberation of the mind through no clinging.**

The [Kesi Sutta (AN 4.111)][4] describes the four approaches the Buddha has towards a student:

 - Gentleness or mild training.
 - Harshness or harsh training.
 - Both gentleness and harshness, or both mild and harsh training.
 - Give up teaching the student for whom the 3 methods above do not work.

  [1]: https://www.accesstoinsight.org/tipitaka/an/an05/an05.165.than.html
  [2]: https://www.accesstoinsight.org/tipitaka/an/an04/an04.042.than.html
  [3]: https://www.accesstoinsight.org/tipitaka/an/an03/an03.067.than.html
  [4]: https://www.accesstoinsight.org/tipitaka/an/an04/an04.111.than.html