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As a former City Training Principal … and to pick up on a few points made: we received scores of applications for each trainee position. From as many as 1600 applications for 4 places, to as few as 600 for 8. Most had a 2.1 from a decent Uni (not all Russell Group I might add), and the CVs were stuffed with all the usual extra curricular: DoE gold, work experience, travel...
To weed the applications to a realistic number for interview meant things like typos - any typos - were usually fatal, and so were editorial errors, such as a cut and paste from another application from which it was plain my firm was not meant.

Once down to interview stage, we'd scour the internet for interview techniques and questions: not to copy, but to see what candidates might be researching and to try and avoid the same stuff. Hence, in part, quirky questions. Also, quirky questions allow an interviewer to see how the interviewees mind works (allowing for stress), and avoids parroted answers. The answer itself doesn't matter, so long as it is coherent.

I looked at aptitude tests, but decided that, for the money, they didn't add anything worthwhile.

Overall, and unsurprisingly, the trainees who worked out best (although not necessarily staying with my firm longer term) were those who had more previous life experience in one form or another.

The system is a bit crazy, but it is difficult to see how it could usefully be bettered (which isn't to say it can't be improved). One bug in the City at any rate is making offers to people two years ahead - a lot can change in two years.