Maybe I'm a little out of the loop here. I have a senior auditioning soon at a university for their trumpet performance scholarship. One of the bullet points listing what they're expecting to hear is "sightreading and transposition".

Are they going to put a piece in front of the student and ask them to play it transposed, say, up a whole step on the fly?

What kind of piece might it be? Just a simple 4-measure exercise or an actual, like, C Trumpet Solo they're wanting played correctly on a Bb Trumpet?