Do you have what it takes to be a quant? This article on quora lists two of the most commonly asked interview questions and answers in mathematical finance (quants also need increasingly strong computational skills, which this post does not address).
The first question (Feynman-Kac’s theorem) focuses on knowledge and the manipulation of the mathematics that quants apply every day. The skills required to answer are the same needed to follow financial modeling literature and conferences. The second question (model-free valuation of binary options) focuses on agility and reasoning, and tests the skills required to apply mathematics to resolve modeling problems.