Prosaic conjures up a beautiful mosaic for some. For others, the pro- is clearly positive. So if somebody or something is prosaic, it must surely be good.
Once again the GRE confounds expectations. Prosaic means dull and lacking imagination. It can be used to describe plans, life, language, or just about anything inanimate that has become dull (it is not used to describe people).
A good mnemonic: prose is the opposite of poetry. And where poetry, ideally, bursts force with imagination, prose (think of text-book writing), lacks imagination. Hence, prose-aic.
Commonly, when we think of begging, we think of money, or a favor. But, one can also beg a question, and that's where things start to get complicated. To beg a question can mean to evade a question, invite an obvious question, or, and this is where it starts to get really tricky, to ask a question that in itself makes unwarranted assumptions.
For instance, let's say you are not really sure if you are going to take the GRE. If somebody asks you when you are going to take the GRE, then that person is assuming you are going to take the GRE. That is, they are begging the question. If you avoid giving a direct answer, then you are also begging the question (albeit in a different sense). Which finally begs the question, how did this whole question begging business get so complicated in the first place?
This is perhaps the most commonly confused secondary meaning and the one that is most important to learn for the GRE. To qualify is to limit, and is usually used in the context of a statement or an opinion.
I love San Francisco.
I love San Francisco, but it is always windy.
The first statement shows my unqualified love for San Francisco. In the second statement I qualify, or limit, my love for San Francisco.
In the context of the GRE, the concept of qualification is usually found in the Reading Comprehension passage. For example, an author usually expresses qualified approval or some qualified opinion in the passage. As you may have noticed, the authors of reading comprehension passages never feel 100% about something. They always think in a nuanced fashion. Therefore, they are unlikely to be gung-ho or downright contemptuous. That is, they qualify, or limit, their praise/approval/disapproval.