Disclaimer: I don't own any of the characters or settings. Pet Girl of Sakurasou is owned by Hajime Kamoshida. Divergent is owned by Veronica Roth. My name is not Hajime or Veronica.
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Misaki Kamiigusa
Born: Dauntless
Aptitude test result: Amity and Dauntless
Chosen faction: Dauntless
Her story: Since before the Choosing Ceremony, she had already been in a relationship with a guy who transferred from Candor the previous year. She was planning to move in with him once she had passed initiation. Sadly, even though she's brave enough for Dauntless, she's not physically strong - she lost two fights during the first stage of initiation, and was cut along with a few other initiates.
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Jin Mitaka
Born: Candor
Aptitude test result: Amity
Chosen faction: Dauntless
His story: He chose Dauntless only because his (then-)girlfriend had chosen it as well. They both managed to pass through initiation, and they dated for a few more months after that. But then they broke up. Later on, he developed a crush on a slightly younger Dauntless-born girl who he saw quite often. It turned out she had feelings for him too, and they started dating. He was overjoyed when she chose to stay in Dauntless in the Choosing Ceremony. A week after that, as soon as he heard the news that she got cut, he decided to leave Dauntless and join her.
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Sorata Kanda
Born: Erudite
Aptitude test result: Amity
Chosen faction: Erudite
His story: He chose Erudite because he wanted to stay with his family. He found a stray cat on the first day of initiation. When an instructor caught him, she told him that initiates couldn't keep pets, and gave him two choices: leave the cat alone, or keep the cat and be kicked out of Erudite. He chose the latter, because being born in Erudite himself, he had seen his faction's scientists use stray animals as test subjects. (A/N: I don't know if Erudite scientists would actually do that)
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Ryuunosuke Akasaka
Born: Candor
Aptitude test result: Candor and Erudite
Chosen faction: Erudite
His story: On the third day of initiation, he decided that the daily lectures were all the same, and they were boring. He skipped the rest of the lectures, but he showed up for the final exam and did very well. He was about to be officially accepted as an Erudite member when another initiate pointed out that he hadn't been to most of the lectures. He was scolded for not taking initiation seriously, and his punishment was to become factionless.
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Nanami Aoyama
Born: Abnegation
Aptitude test result: Abnegation
Chosen faction: None
Her story: Although she's not Divergent, she didn't want to be tied down to any particular faction. At the Choosing Ceremony, when given her knife, she just put it in her pocket and walked away. She is the only person known to have openly refused to choose a faction. Reports from Erudite state that she did this because her parents abused her, but she has denied these claims.
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Mashiro Shiina
Born: Amity
Aptitude test result: Not tested
Chosen faction: No test, therefore not applicable
Her story: She's an extremely talented artist. But for some reason, she has never been able to take care of herself properly, and therefore wouldn't be able to pass any faction's initiation. Her parents tried asking if she could just live with them for a longer time, but their request was refused. They took the case to court and sued for discrimination, but to no avail. She was ordered to leave Amity and instantly become factionless on the day of the Choosing Ceremony.
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(A/N: I hope the faction test results were accurate enough! Sorata's was pretty hard, he's really kind and peaceful but overreacts a lot so I don't know whether he's actually 100% Amity or Divergent. I'm not sure if he fits any other faction though. Ryuunosuke's was the easiest, his was the first that I thought of! The others were alright I guess)