No one can give you a real estimate. It all depends on how much time you have per day and how high score you want to achieve. I would say roughly at least one month full time if you don't have any experience in ejb. The exam gives you an overall conceptual knowledge of EJB, that is all. To be able to write real world EJB, you will have to spend more time, mainly because there is another part the exam does not cover, application server.