In the state of minnesota or even on the federal level, is it true that a company does not have to pay you overtime if the forty plus hours are not at the same pay rate?

EX:
If you are paid fifteen dollars, get a promotion so in training you get seventeen dollars, then after training you get twenty all in one pay period and end the week with fifty something hours.

You may want to contact your local labor board. I am sorry, I just don't know. Depending on how you are classified, you may not be entitled to overtime.