Equivalency exams do the trick.
Equivalency exams?
Who will sanction these exams, how will recognize which exams are legitimate, and which ones aren't? It'll come down to which exams are considered more prestigious, and those will be used to separate the cream from the crop. You'll have "prepatory schools" for the better exams, and someone will charge a lot of money for those--it'll be no different than the Ivy League is today.
Higher education should not be solely about choosing the correct answers on an exam. There are too many intangibles that an institution of higher learning should provide that a multiple choice exam could never duplicate.