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Chinese Girl: Within the first minute or so of the exam, after The Invigilator goes over the rules, the Chinese Girl starts writing on her sheet of paper. The camera spots this, and appears to be able to see what she's writing at which point the guard hauls her out of the room. There are two theories; one because she "spoiled her paper" by writing on it, or two, because the Invigilator saw what she was writing on the sheet and anything other than "Yes" or "No" meant she didn't understand the question, didn't want to work with the others, didn't have enough attention to detail, was over-eager, etc... and therefore was disqualified.
Brunette: Tries to get the sprinkler system going in order to see if that would get some form of invisible ink on the paper to show. However, White tricks her by giving Brunette her own sheet instead of the scraps of Chinese Girl's. Seeing as how she spoiled her paper by burning it, meaning she was too trusting or didn't pay attention to the simple details that the sheet wasn't torn up, nor checking to make sure the sheet wasn't hers, therefore she was disqualified.
Deaf: White convinces Deaf to tear up his sheet and eat it. For an unknown reason, Deaf complies and is therefore disqualified.
Dark: When White starts having a seizure, in a moment of panic, she shouts at the camera for help. Which disqualifies her.
Brown: Volunteers to leave the room instead of getting shot by White, disqualifying himself.
White: The time counter runs out and so White starts shouting at the window which is considered communicating with the Invigilator. The guard shows him his watch which still has 40 seconds on the clock. White then notices there's a second button on the time counter that can speed up the time when pressed. Realizing that Deaf and pushed this button earlier, he then figures out he just disqualified himself as 80 minutes had not yet come to pass. He is then escorted out of the room. Edit
Black gets shot by White and is seemingly dead. Blonde was hiding just outside the doorway but kept her toe just inside the frame of the door so she wasn't considered to have left the room. After White disqualified himself, Blonde enters back into the room and finally figures out what the question was. The Invigilator enters the room along with Deaf who turned out to actually be the CEO. She answers the question but nearly refuses the job because it wasn't worth dying for or killing over. At which point The Invigilator reveals that Black was shot with a "magic bullet" that held a brand new medicine that contained rapid cell regeneration. At this point Black awakens and Blonde agrees to take the job. It's possible that Black also managed to gain a position in the company as well. Because he appeared to have several of the traits that Blonde had, which The Invigilator said the position required, except attention to detail required to have found the question (though he may have figured it out, had he not been shot). While Black didn't answer the question, he had been shot and was unconscious for the remainder of the time limit of the exam. So even if he didn't get the job along with Blonde, he was still cured of his disease not to mention his bullet wound. Not a bad prize for runner-up.
Also, it is entirely possible that Blonde, seeing how Black has all the qualities needed for the new job (something that both the Vigilator and the CEO may have noticed too), she will simply use her new position in the Company to hire him as her assistant through normal channels. Edit
There are two possibilities: The first possibility is that they simply waited until the clock ran out and when the Invigilator came back into the room, they'd be allowed to talk to him once the time was up, and they could verbally answer. The second possibility is that they were in fact allowed to write on their paper, but they would only be allowed to answer "Yes", "No", or write a question. The Chinese Girl starts writing more of an essay on why she felt she deserved the job, and was disqualified. Edit
The Invigilator mentions that they all passed the first rounds of testing to get to the final exam. We have no idea what those tests were, however they were likely basic, possibly testing their mental prowess, assessing their attributes, their strengths and weaknesses, etc.
White is shown throughout the film to be ruthless, arrogant and selfish. Yet he's also willing to take risks and do whatever it takes to succeed. It's possible he got to where he was by passing the previous rounds of testing, however he could, by lying, cheating, bullying, etc. It's also entirely possible he was deliberately put there to shake things up, knowing he'd be a wild card, unstable and dangerous. After all, he was the one who got everyone talking and working together, albeit to serve his own agenda. The CEO may have anticipated this, hence giving the guard in the room a gun loaded with a miracle cure as opposed to lethal rounds. Edit
Most likely; depending on the question, he would have said "That will be answered after the exam", as the actual answering of the question wasn't that important. Some viewers have pointed out that the invigilator asked "Are there any questions?" before actually starting the clock. So had someone asked a question, he could have answered it, then started the clock...so during the 80 minutes, there were no questions, so the answer to "Question 1:" is "No."
The test was simply a social experiment to determine who embodied specific traits; working well with others, compassion, can follow instructions, attention to detail, problem solving, etc.
The testing was extreme in this scenario because the job was incredibly important to humanity. Edit
Yes. It is discovered at the end, on each sheet of paper, in incredibly small, fine print the words "Question 1." was written. Which if you were paying attention, goes back to the very start of the exam, when the Invigilator says "There is one question before you, and one answer is required. If you try to communicate with myself or the guard, you will be disqualified. If you spoil your paper, intentionally or accidentally, you will be disqualified. If you choose to leave this room for any reason, you will be disqualified. Are there any questions?" So to put it quite simply, the answer was "No". Edit