Premise #1: Funding is less in geology research.
Step conclusion (or Premise #2): Fewer students are making career in geology research.
Main Conclusion: The number of postgraduate students enrolling in geology courses will decline.
Key objects: number of postgraduate students that enroll in geology courses, less funding, and fewer students that go on geology research career.
A), This is irrelevant. This talks about the number of undergraduate students. However, the connection among the number of undergraduate students and the key objects is too casual. The question doesn't explicitly or implicitly express how the number of undergraduate students will kick in this argument.
B), This is a tempting option. The logic behind this option may get you to the right answer in some questions. I am keeping it for now. Basically if the connection between research funding and number of students, in general, is casual - not absolute, then the current argument could be undermined. But this option goes extra miles to achieve the weakening. I am not sure at this point.
C), This is better than B. Remember the argument's logic - because fewer students are going to pick careers in geology research, the number of postgraduate students who choose geology courses will decrease. There is a difference between careers in geology research and geology courses in general. Geology courses may include courses in geology research but geology research doesn't represent geology courses as a whole. This option clearly points out that most of the postgraduate students still need geology courses even though they are not going on geology research career path.
D), Same as A, the object here - teacher staffing, is irrelevant to the argument.
E), The comparison of budget size between science department and arts department is irrelevant. How will these two big departments' budgets impact geology group?
Answer should be C.
Feel free to discuss.