Neither First Lady Eleanor Roosevelt nor Secretary of Labor

Thanks Daagh for pointing out the BLATANT SV error. In the process of arguing about all the other stuff, we all totally missed the SV agreement error that is so evident in the original choice.

In reality, had I followed my usual process (the e-GMAT 3 step process), I would have caught this error in the first place...See this is what happens when one takes short cuts or when one is looking for a smoking gun. Now since I did not follow the process myself, I will take this upon myself to give a detailed analysis of this question.

Meaning Analysis

The two ladies (ER and FP) did not seek recognition by the press for something.
They allowed other people to take credit for something.
Something = genesis of specific historic programs.
These two ladies were in fact largely responsible for the genesis of these programs.

Error Analysis

Clause 1 - Neither First Lady Eleanor Roosevelt nor Secretary of Labor Frances Perkins sought recognition by the press, and
Clause 2 - both cautiously allowed others of the Roosevelt brain trust to take credit for the genesis of historic programs in public employment, relief, and social security
Clause 3 - that were in large measure
Clause 4 - what they had been responsible for.

SV - SV pairs are marked as shown. Subject "that" in clause 3 refers to "genesis" and hence the verb "were" does not agree in number with the singular "genesis". SV Agreement Error

Verb - The sentence is established in past time frame. All verbs except verb in clause 4 are in simple past tense. Past perfect tense in clause 4 appears correct. The context of the sentence clearly indicates that the action of creation of the programs happened before anyone took credit for their creation. So in that sense past perfect tense seems ok.

Pronoun - Pronoun "they" should logically refer to the two ladies. Even the context indicates this reference. Why? because it would not make sense to first state that the ladies allowed others to take credit and then say that these other people were indeed responsible for the genesis of the programs. If the others were indeed responsible for this task, then why would the sentence say that the ladies ALLOWED then to take the credit. But that being said, if there is a choice that clarifies this reference i.e. a choice that does not use a pronoun, then we should consider that one if that choice does not have any other errors. Pronoun ambiguity is not something based on which you should eliminate a choice right away.

Modifier - Relative pronoun modifier "that" refers to singular "genesis". There is a large prepositional phrase describes genesis. So in that sense "that" refers to "genesis of programs in public employment, relief, and social security".

Parallelism - The list of programs is parallel.

So SV error is the primary error in this sentence. Other than that, the original choice is not very precisely written sentence. There may be a slight chance of pronoun ambiguity as well.

Based on this, now we find the correct answer from the 5 given choices.

Process of Elimination

Neither First Lady Eleanor Roosevelt nor Secretary of Labor Frances Perkins sought recognition by the press, and both cautiously allowed others of the Roosevelt brain trust to take credit for the genesis of historic programs in public employment, relief, and social security that were in large measure what they had been responsible for.

A. to take credit for the genesis of historic programs in public employment, relief, and social security that were in large measure what they had been responsible for
SV Error

B. to take credit for the genesis of historic programs in public employment, relief, and social security for which the two women were in large measure responsible
Correct

C. taking credit for the genesis of historic programs in public employment, relief, and social security for which the two women were in large measure responsible
Modifier error - Verb-ing modifier modifies the preceding noun, non-sensically implying that the programs took credit.

D. taking credit for the genesis of historic programs in public employment, relief, and social security that were in large measure what they were responsible for
SV error as in Choice A, Modifier Error as in Choice C

E. taking credit for the genesis of historic programs in public employment, relief, and social security which were largely their responsibility
SV error as in Choice A, Punctuation issue - which is always preceded by a comma.

Thus choice B is the correct answer.

Take Away

The biggest TAKE AWAY from this question is that do not lose sight of a step by step process. Thoroughly analyze the original sentence. Don't just find one thing that too something that is not as deterministic, e.g. pronoun ambiguity, stylists issues, word order issues. This entire exercise was a great case in point. Knowing the grammar rules is not sufficient - we all discussed pretty heavy grammatical rules here. But ultimately the main difference among several choices was SV error. So please please please follow a step by step method to solve any SC question. Do not take short cuts...

I would like to thank daagh and Ashish for a wonderful discussion here. This discussion was a pleasure.

-Regards,
Payal

(PS: I hope I did not ramble too much here, its almost midnight here so I am not in my brightest of modes right now , but this question was intriguing enough that I could not keep myself from writing this. )