In maths, if you do well enough in the exam, you have to really mess up the interview to not get in though I would say. If you're borderline, the interview is important though - the interviews will usually be 95% maths questions so it's more like doing an oral exam where you have to explain your thinking process and answers.
I'm sure it probably depends on the discipline (and indeed the college, since some are harder to get into than others). I can see how this would be important in mathematics where it is hard to avoid rules and structure. In other areas, the decisions will be much more subjective.
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Entry is to Oxford and Cambridge is by interview. A lot hinges on that.
In maths, if you do well enough in the exam, you have to really mess up the interview to not get in though I would say. If you're borderline, the interview is important though - the interviews will usually be 95% maths questions so it's more like doing an oral exam where you have to explain your thinking process and answers.
I'm sure it probably depends on the discipline (and indeed the college, since some are harder to get into than others). I can see how this would be important in mathematics where it is hard to avoid rules and structure. In other areas, the decisions will be much more subjective.