kant said:
What is this qualifying examination? Is this like a GRE subject test?
Please refer to this as an example - http://www.rpi.edu/dept/phys/graduate/exam_handbook.html,
http://www.rpi.edu/dept/phys/graduate/exam_qualifying.html
The qualifying exam is unique to the particular department and university, and the particulars will vary among different institutions, but usually there a written exam, and there may be an oral exam as well. The written exam involves solving detailed problems in a way that one demonstrates one's basic knowledge in a particluar field. In an oral exam, one stands in front of several faculty members as they pose problems and questions on basic and specialized knowledge.
When I qualified for a PhD, I took an 8 hr written test in 2 4-hr sessions much like that described in RPI's handbook. The problems presented are much like homework problems in which one has to apply forumulas, reasoning, perform calculations, and basically demonstrate a certain level of competency.
The qualifying exam is in addition to the GRE. When a took the GRE, IIRC it was a multiple choice exam, much like the SAT in the US.
One can apply for a PhD program and take the qualifiers during the program, however that would assume one has fulfilled admission requirements, such as application, letters of recommendation, completion of an undergrad program, usually in the same or related field, or Master's program. Coming from a completely different field or from similar or unrelated professional field, one would likely have to take the qualifiers as part of the admissions process.
Perhaps our PhD members can elaborate on their experiences. There are perhaps differences between US and foreign universities.