" You may notice that I prefer to use "who" when referring to people, rather than "that," though "that" is not wrong. I just think "who" sounds very much better.
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If you are going to say "I'd gotten," which is correct, as opposed to "I got," which is also acceptable, you should be consistent and use the past perfect in the second clause: "...everyone who had taken that exam..." You may notice that I prefer to use "who" when referring to people, rather than "that," though "that" is not wrong. I just think "who" sounds very much better.