I like the substance of Marcab's response, and he's very sharp to recognize an absolute phrase in the right answer, but I'd like to add a couple of notes on process here. First, let me reproduce the question with underlining.

Margaret Courtney-Clarke has traveled to remote dwellings in the Transvaal to photograph the art of Ndebele women, whose murals are brilliantly colored, their geometrical symmetries embellished with old and new iconography and in a style that varies from woman to woman and house to house.
(A) whose murals are brilliantly colored, their geometrical symmetries embellished with old and new iconography and in a style that varies from woman to woman and house to house
(B) whose murals are brilliantly colored, their geometrical symmetries are embellished with old and new iconography, and their style is varying among women and houses
(C) whose murals are brilliantly colored, their geometrical symmetries are embellished with old and new iconography, and they are in styles that vary from woman to woman and house to house
(D) with murals brilliantly colored, their geometrical symmetries embellished with old and new iconography, and their style varies among women and houses
(E) with murals that are brilliantly colored, their geometrical symmetries embellished with old and new iconography, and their styles vary among women and houses

As most forum regulars know, Manhattan GMAT's approach to SC relies on splits, differences among the answers choices. Once in a great while you may hear something specific wrong as you read the original sentence, and more often than that you will recognize a certain structure (e.g., a list) and know that the sentence will test a certain issue (e.g., parallelism), but usually you don't know what's at issue until you see the differences among the answer choices.

When a very big portion of the sentence is underlined, as here, you'll often find problems with parallelism, modifiers, or what the OG explanations calls rhetorical construction. I more or less expected such problems in the answers to this question , but I hoped for some very clear splits among those answers, and didn't dwell at all on these likely issues ahead of time. So how do the answer choices differ?

I. The first split is between whose in A, B, and C and with in D and E. Since whose correctly modifies women--it is their murals which are brilliantly colored--I eliminated D and E. That might seem rash; just because whose is acceptable doesn't mean with is unacceptable, right? I don't want to get off track here, but I'll explain below why I was so confident that D and E were wrong.

II. The next split is between symmetries embellished in A and symmetries are embellished in B and C. In A embellished modifies the noun symmetries, while in B and C are embellished is a verb whose subject is symmetries. Just as Marcab suggests, B and C are wrong in part because they contain so-called comma splices, commas used to join independent clauses. In both B and C, the independent clauses inappropriately joined by the comma are Margaret Courtney-Clarke has traveled and symmetries are embellished. (By the way, a sentence containing a comma splice is often called a run-on sentence, and that's fine with me, but grammarians usually reserve run-on sentence to talk about other problems.)

III. So that leaves A.

IV. As Marcab suggested, A uses a device called an absolute phrase, a noun+modifier, to modify an entire clause. You can read about absolute phrases on pages 242 and 243 of the Manhattan GMAT SC Strategy Guide, 5th edition (or pages 237 and 238 of the 4th Edition). Honestly, I've never seen a real GMAT SC question that really demanded that you understand absolute phrases. If you can confidently eliminate four wrong answers, even if the remaining answer is a bit of a head-scratcher, it must be right.

V. For what it's worth, absolute phrases are pretty rare on the GMAT. They're also sufficiently abstruse that many years ago, when I was teaching at a school for English-learners, a student asked me, "Could we use an absolute phrase here?", and I had no idea what he meant.

VI. Finally, in the first numbered section above I blithely eliminated D and E, just because whose correctly modifies women. Why so quick? Although prepositions, such as with, can be either noun modifiers or adverbial modifiers, when the GMAT gives you a split between a relative clause and a prepositional phrase in the very same spot, they're using the prepositional phrase to modify a clause. They're giving you a choice between a noun modifier and an adverbial modifier. If you want to modify the preceding noun, choose the relative clause. Otherwise, choose the prepositional phrase.
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It's A. In C they refers to Ndebele women
in A => to their geometrical symmetries embellished in a style that varies from woman to woman and house to house

I would go with A

surely D & E are out of the picture

B is wrong
and their style varies "among" women and houses

C is wrong
and they are in styles that vary from woman to woman and house to house

what does "they" refer to?
here we are talking abt art.. and definitely "they" cannot refer to art

A is the only option that makes sense.

Eliminate D/E due to the clause starting with "with murals"

B and C are both run-on sentences. Especially C...
"Margaret Courtney-Clarke has traveled to remote dwellings in the Transvaal to photograph the art of Ndebele women, whose murals are brilliantly colored, their geometrical symmetries are embellished with old and new iconography, and their style is varying among women and houses"

The clause their geometrical symmetries is an independent clause and can't be connected by just a comma.

HI mikeCoolBoy
Thanx for your effort.
Can you answer, is it ok to omit TO BE from the passive? I agree that it's ok to omit the verb, but here we have to be+PII
Don't you think that this action could make the sentence ambiguous? Looks like active voice.
...their geometrical symmetries embellished
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the pronoun WHOSE tells you that all the analogies must be parallel and structured.
oNLY A seems to fit the bill...i dont see how can the remaining options even come close....(well,i think the same about questions which i get wrong )

D and E wrong, should start with "whose"
C is wrong, it is not clear what "they" is referring to.
B is also wrong, because of the use of "among women and houses".
A is correct, because "their geometrical..." until the end modifies the murals. When in B and C there is an effort to create an artificial parallelism that changes the meaning of the original sentence.

I think that A is the correct answer.
C is awkward, wordy. "They" refers to geometrical symmetries so "they" could be eliminated to have a more concise sentence.
In option A, "their geometrical symmetries embellished with old and new iconography and in a style that varies from woman to woman and house to house" is an absolute phrase.

http://grammar.about.com/od/ab/g/absoluteterm.htm

Definition:
A group of words that modifies an independent clause as a whole.

An absolute is made up of a noun and its modifiers. It may precede, follow, or interrupt the main clause:
Example:
Their slender bodies sleek and black against the orange sky, the storks circled high above us.
The storks circled high above us, their slender bodies sleek and black against the orange sky.
The storks, their slender bodies sleek and black against the orange sky, circled high above us.

Margaret Courtney-Clarke has traveled to remote dwellings in the Transvaal to photograph the art of Ndebele women, whose murals are brilliantly colored, their geometrical symmetries embellished with old and new iconography and in a style that varies from woman to woman and house to house.
(A) whose murals are brilliantly colored, their geometrical symmetries embellished with old and new iconography and in a style that varies from woman to woman and house to house
(B) whose murals are brilliantly colored, their geometrical symmetries are embellished with old and new iconography, and their style is varying among women and houses
(C) whose murals are brilliantly colored, their geometrical symmetries are embellished with old and new iconography, and they are in styles that vary from woman to woman and house to house
(D) with murals brilliantly colored, their geometrical symmetries embellished with old and new iconography, and their style varies among women and houses
(E) with murals that are brilliantly colored, their geometrical symmetries embellished with old and new iconography, and their styles vary among women and houses

my 2 cents here :
women are not with murals -> eliminate D and E. Among A,B and C . In C 'they' is ambiguous -> it refer to geometrical symmteries or mural -> Eliminated.
In B , their is repetitive , that's an error. Eliminated. A wins.

Let me express what I consider about that AND part.
In original choice "in a style" is modifying GEOMETRICAL SYMMETRIES, but in choice proposed by you "in a style" is modifying iconography.
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