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

Pañhapuccha Sutta (AN 5.165) 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) 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) 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), 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) 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.

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

Pañhapuccha Sutta (AN 5.165) describes 5 types of motivations for asking questions:

• 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 motivation for questioning usually applies to the Buddha and Arahant teachers toward their students.

Pañha Sutta (AN 4.42) 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) describes 4 types of 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), 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) 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.