While Martha Hornblatch was working as a cook for Gary's Diner

Can you please explain why C is out?

C is out because if 'as' is used for comparisons, it should always be followed by a clause. Here we are comparing the abilities. and In C, we donot have any clause after as. Hence, incorrect.

I agree with lowryder for B.

"Not unlike" should be fine, it's a standard construct to emphasize the nature of something being "not different" from that of something else.
I dug out another strikingly similar question for comparison purposes.

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While Jackie Robinson was a Brooklyn Dodger, his courage in the face of physical threats and verbal attacks was not unlike that of Rosa Parks, who refused to move to the back of a bus in Montgomery,Alabama

(A) not unlike that of Rosa Parks, who refused
(B) not unlike Rosa Parks, who refused
(C) like Rosa Parks and her refusal
(D) like that of Rosa Parks for refusing
(E) as that of Rosa Parks, who refused

In this case the OA is, again, A.
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For C "the ability was as that of someone else" should be unidiomatic here; "like" - or, well, "not unlike" - would be appropriate. In comparisons between "things" you have to use "like", "as" is used for behavior or characteristics pertaining to one in particular. Furthermore, this tends to avoid confusion in sentences like these:

* As your father, I wish you well. -> I am your father, and I wish you well.
* Like your father, I wish you well. -> I am [your uncle/teacher/friend/etc.], and I wish you well.

Unfortunately I can't post links because of my low post count, but it's easy to check out on Google: just search "as or like" or something like that.

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