Can I take a Class B test with a Class A permit?

You could, but the truck has to have air brakes and if the trailer is attached to the truck, you have to have someone else drive it to the examination.

 

If your vehicles are under 26k GVWR, you don't need a CDL. You can legally drive it on a regular operators license.

 

Airbrakes have nothing to do with weight classes.

 

That is true, but if you test without them, you have a restricted license.

 

Depending on the state.

 

All fifty have the same restrictions - 383.95

(a) Air brake.
(1) If an applicant either fails the air brake component of the knowledge test, or performs the skills test in a vehicle not equipped with air brakes, the State must indicate on the CLP or CDL, if issued, that the person is restricted from operating a CMV equipped with any type of air brakes.

(2) For the purposes of the skills test and the restriction, air brakes include any braking system operating fully or partially on the air brake principle.

 

If you are towing a vehicle, as an examiner I would not allow it, it has to be a combination with a truck and trailer not a tow truck and another truck.

See the entire purpose of the road test with the pre-trip is to make sure you can drive a combination vehicle - fifth wheel, air brakes on the trailer, etc. ... , and the truck in tow could be considered a drive-a-way setup which I'm told could not be used for a road test.