Interviews are always stressful moments, especially when it comes to interviews in investment banking. The reason is that a lot is at stake, and, the CV is not anymore an asset to extol since the interview's essence does not rely on questions about your grades, internships or university, the interviewer already knows that after the CV screening process. The main goal of the interview is to check your communication skills. One of my co-worker told me that for JP Morgan, he had to go through 5 interviews, 3 were technical knowledge checks, one was a party with all the applicants to assess their/his sociability and the last interview was a dinner with the head of the department where no work-related topic was evoked. Social skills are definitely what interviewers try to evaluate since most of the IB jobs are network-related: networking skills are a necessity.
Not only technical, communication and social skills are appreciated during the interview, capacities to deal with the unknown is also required. The interviewer will ask you a question to which he knows you do not have the answer, though what he looks for is how you drag the unknown domain to your perimeter of knowledge.
Most of IB interviews end with finance enigmas, which are in fact common enigmas. My IT friend developing/testing the automaton's trading strategies in the trading room of the BNP Paribas Tokyo told me that after his 3rd interview, his last questions were the two following riddles:
"You have a big cube, composed of little cubes, 10 on each edge, therefore 10^3 cubes in total. If the big cube is dipped into paint, how many little cubes are painted, regardless of the number a painted faces the small cube has ?"
The second riddle he was asked was:
"There are three 3 envelopes on the table, one contains your contract and two are empty. You do not know which envelopes are empty but I (interviewer) know, you have to find your contract. After you chose one envelope, I will remove one empty envelope from the table. I will then give you the choice to exchange your envelope with the one on the table or to keep your first choice. Will you chose to change or not?"
Some of the enigmas are famous, the one previously cited can be found in 21, the MIT blackjack-hacker's movie. An other IB riddle can be found in Die Hard 3:
"You have a jug of 3L and one of 5L. You need exactly 4L, how do you do it?"
Another famous riddle, frequently asked in IB interviews is:
"There are 9 balls: 8 having the same weight and 1 heavier than the others. How can you determine which is the heavy ball by using only twice a pair of scales?"
You can find more IB riddles in the attached e-book called Heard on the street: quantitative questions from Wall Street job interviews which Chapter 1 is full of. The rest of the book is very interesting but too more mathematical/statistical.
So, if it is too late to work on your background to reach a top IB, you can still work on your riddle's skills ;)
Guillaume