Considered a pseudoscience or false science even during the height

OFFICIAL EXPLANATION



Just for the sake of an accurate historical record, phrenology was much more mainstream in certain countries such as Scotland and the United States than this sentence suggests.

According to Oxford Dictionary online, phrenology is the detailed study of the shape and size of the cranium as a supposed indication of character and mental abilities.
What were practitioners looking for when they examined other human beings' heads?
Bumps and hollows, the size of the cranium, or the slope of the lower skull, to name just a few things.

• Split #1 - Dangling modifier

What was considered a pseudoscience, or false science? Phrenology.
-- Phrenology, the noun, should immediately follow the introductory description; otherwise, we have a dangling or misplaced modifier.
(I don't care whether you know the jargon. Just understand how these modifiers work.)
-- The noun modifier "Touch Rule" states that a noun should be as close as possible to the noun that it modifies.
When an intro is anchored by a past or present participle (a verbED or a verbING word), the noun it modifies must be the subject of the immediately following clause. Almost always, that noun will show up right after the comma.

Options B and D use some psychiatrists and neurologists rather than the correct noun, phrenology. Wrong noun. Modifier error.
Eliminate B and D

• Split #2: fragment - or, the case of the Missing Verb

If we strip this sentence and insert option E, we have this sentence:

Considered a pseudoscience, phrenology being taken seriously by some psychiatrists and neurologists that felt a patient’s head for bumps.
This sentence has no working verb.
Sentences without working verbs are called fragments.

Option E also uses the word that rather than the correct who to refer to some psychiatrists and neurologists.
GMAC is very strict about this rule: who refers to people and may not refer to things, whereas that refers to things and may not refer to people.

Typically I have seen exceptions to rules at least in non-underlined portions of official questions.
I have never seen a single exception to this rule in an official question.
In jargon, the relative pronoun who refers only to human beings whereas the relative pronoun that refers to things and non-human living beings.

Eliminate option E

• Split #3: logic and clarity

The only difference between options A and C is the presence of the word yet in option A.
This split is a lot harder than it seems.

Here's the problem with option A: the word yet is being used as a subordinating conjunction, in the sense of "but," or "nevertheless," or even "but nevertheless."

Those kinds of words start "subordinate" clauses that are dependent on another full independent clause, a "main clause"—and in the case of option A, there isn't such a main clause.
This clause cannot stand on its own:
Yet phrenology was taken seriously by some psychiatrists and neurologists, who would feel a patient’s head for bumps.
Now look at Considered a pseudoscience, or false science, even during the height of its popularity.
-- That one is not a full sentence, either. It is not an independent clause with a subject and a verb that can stand on its own.

Option A lacks an independent clause.
Eliminate option A.

The answer is C.

Notes

→ Would feel is okay
We can use the helping verb would + base form of verb to indicate repeated or habitual actions in the past; such use is common when we are describing "contradictory" or unexpected behavior.

→ When an introduction is anchored by a participle, past (verbED) or present (verbING), look for noun modifier problems.
-- the noun described by the intro phrase should be the subject of the subsequent clause, and most of the time, that noun will be the first word after the comma
-- a "dangling modifier" is a descriptive phrase or clause that is inappropriately placed and appears to modify the wrong noun.

COMMENTS

I will give you the answer to my question from my last OE.

The only country ever to have defeated the armies and/or navies of the British, the Spanish, and the French is Haiti, which was the second country in the western hemisphere to win its independence from colonial England. (The first country to do so was the U.S.)

On a more topical note, these answers are good. Kudos to all.