The problem is that the RHCE is 100% hands-on. You wouldn't be answering multiple-choice questions, you'd actually be fixing a broken system. As such it's difficult to have "sample questions" on the web. Also, examinees sign an NDA and Red Hat is very protective of the specifics of the exam, so don't expect to find much about the exact problems.
Your best bet is to go through the material on Red Hat's outline, try to break your system accordingly, then fix it. Just learning how to break each component of the system is a good way to get better at fixing them. When you feel confident, if you know someone else knowlegable with Linux, have him/her break some things and see if you can fix them.
If you or your company have the money for it, Red Hat's training programs include hands-on troubleshooting exercises. Others may as well.