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B is incorrect...
B implies that the mountaineous regions were chiseled from rock...we want to pick a sentence that properly implies that the monasteries were chiseled from rock centuries ago and now dot the mountinous regions....
What's wrong with <monasteries are dotting> in choice C?
"Monasteries are dotting" means that "monasteries are in the process of dotting". It sounds strange that monasteries by themselves DOING that action, not to mention that "are dotting" is continuous tense.
According to explanation given at this link (which is very authentic source for American English), the absolute phrase usually occurs in the begining of a sentence.
However, even if we accept that absolute phrase can appear in some other place (as is the case with the given sentence), absolute phrase is supposed to modify an entire sentence and not ANY SPECIFIC ELEMENT of a sentence. In the given sentence, if we choose E as answer, there is no way that the phrase "many of them chiseled from solid rock centuries ago" will modify the entire preceding sentence. It seems to modify only "monesteries". Hence it does not fit into the definition of absolute phrase.
In my opinion, D should be the answer. Because there is nothing wrong with D. In "many of which", "which" certaily refers to monesteries because "which" usually modifies immediately preceding noun. So there is no way "which can refer to mountaineous regions.
Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...