Pilots can be tested for the stresses of flying high-speed jets in a whirling "human centrifuge," which takes 1.2min to turn through 23 complete revolutions before reaching its final speed.
a. what was its angular acceleration (assumed constant)? i got 32 rev/min 2 and it was rightb. what was its final angular speed in rpm? i tried 27 and 32 rpm but they are both wrong. any ideas?

Sure.
Can I use your answer to part-'a' ?

If the angular acceleration is actually 32 rev/min², than
after 1.2 min, it has reached the speed of

                 (32 rev/min²) x (1.2 min)  =  38.4 rev/min .

Check:

If the initial speed is zero and the final speed is 38.4 rpm,
then the average speed during the acceleration period is

                   (1/2) (0 + 38.4)  =  19.2 rpm  average

At an average speed of  19.2 rpm for 1.2 min,
it covers

                   (19.2 rev/min) x (1.2 min)  =  23.04 revs .

That's pretty close to the "23" in the question, so I think that
everything here is in order.

The answer is  a.first and third quarters