Before reading the replies, my guesses are:
http://www.personalitypage.com/html/ENTJ.htmlENTJs are natural born leaders. They live in a world of possibilities where they see all sorts challenges to be surmounted, and they want to be the ones responsible for surmounting them. They have a drive for leadership, which is well-served by their quickness to grasp complexities, their ability to absorb a large amount of impersonal information, and their quick and decisive judgments. They are "take charge" people.
http://www.personalitypage.com/html/ESTP.htmlESTPs are outgoing, straight-shooting types. Enthusiastic and excitable, ESTPs are "doers" who live in the world of action. Blunt, straight-forward risk-takers, they are willing to plunge right into things and get their hands dirty. They live in the here-and-now, and place little importance on introspection or theory. They look at the facts of a situation, quickly decide what should be done, execute the action, and move on to the next thing.
http://www.personalitypage.com/html/ISTP.htmlISTPs are excellent in a crisis situations. They're usually good athletes, and have very good hand-eye coordination. They are good at following through with a project, and tying up loose ends. They usually don't have much trouble with school, because they are introverts who can think logically. They are usually patient individuals, although they may be prone to occasional emotional outbursts due to their inattention to their own feelings.
http://www.personalitypage.com/html/ENTP.htmlENTPs are fluent conversationalists, mentally quick, and enjoy verbal sparring with others. They love to debate issues, and may even switch sides sometimes just for the love of the debate. When they express their underlying principles, however, they may feel awkward and speak abruptly and intensely.
After reading the replies, I really like INTJ for Jake. I wouldn't have thought of him as an introvert, but the INTJ description fits him really well. ESTP for Rachel is actually the one I'm most sure about. None of the others really fit her, and ESTP fits really well. I didn't even consider Ax for some reason (maybe because the test is intended for humans, but he's not that different mentally...) After reading over the types again I'm thinking ISTJ too.
And yes, this is a fun thread! I feel like such a dork, but in a good way, I promise...
Here's another personality test I like:
https://www.enneagraminstitute.com/