Investment banking firms -- including large ones like Goldman Sachs and Morgan Stanley and tons of smaller firms that are lesser known -- often recruit students out of four-year colleges. Although studying business/economics/finance is helpful, many banks recruit students with various backgrounds. After graduating from college, my first job was as an investment banking analyst. Among the other recent grads who joined at the same time were people with college majors as diverse English, history, biology, and many others.
The banks are mainly looking for new employees who are smart, hard working and demonstrate an interest in a career on Wall Street. A test is not required to get such a job and most of the training happens once you join. However, it helps to work as an intern once or twice on Wall Street while you are still a college student, typically during the summer break. Fortunately, most universities help students obtain those spots.