The Kobayashi Maru scenario was a test given to Command-track line officer Starfleet cadets, but not science officers. It was a test of character to see what a potential captain would do in a no-win situation. While Spock was known to not have taken the scenario (as noted in Star Trek II: The Wrath of Khan), it seems probable that there were other examinations he must have undergone in order to have been more than an temporary first officer and, eventually, commanding officer.