A representative of the Women’s Bureau of the United States Department

A representative of the Women’s Bureau of the United States Department of Labor contends that employers who offer benefits which permit that employees can balance home and work responsibilities better, realizing gains in attendance, recruiting, and retention.
(A) which permit that employees can balance home and work responsibilities better, realizing
(B) which permit employees balancing home and work responsibilities better will realize
(C) that permit employees to balance the responsibilities of home and work better will realize
(D) that permit employees a better balance between the responsibilities of home and work, thus realizing
(E) such that employees are permitted a balance between home and work responsibilities, and they will realize

Pick C.
Here the part "permit employees to balance the responsibilities of home and work better" is a restrictive clause. So you need to use that. Since its the benefits that permitted the employees to do X which helped in Y.

Which is used in non-restrictive clauses, tells something incidental but does not define the subject of the sentence.

If you do care for which or that, then be sure about these simple rules. 1. Which can never be used without a comma before it and that is never used with a comma before it. Thus A and B are out. D is a fragment without a working verb for the sub-clause. E is also a fragment in this portion - employers who offer benefits such that employees are permitted a balance between home and work responsibilities – There is no verb to represent the action of the employers who offer benefits.

C, therefore, is the choice.

However, it is worthwhile to note GMAT’s thinking on this issue from the following topic.- (OG 12 SC Q 10)

Carnivorous mammals can endure what would
otherwise be lethal levels of body heat because they
have a heat-exchange network which kept the brain
from getting too hot.
(A) which kept
(B) that keeps
(C) which has kept
(D) that has been keeping
(E) having kept

Official explanation
Verb form; Rhetorical construction
Th e use of the past tense (kept) is incorrect
because a current situation is discussed; the
present tense (keeps) is consistent with the other
verbs in the sentence. In (A) and (C), which
introduces a restrictive clause. Some writers
follow the convention that which can only be used
for nonrestrictive clauses, but insistence on this
rule is controversial, and both (A) and (C) can be
rejected on other grounds

I do not think GMAT is fussy about the use of which or that and therefore look for other grounds in the sentences than getting stuck.

I second your opinion daagh but would like to make a point:

X accused Y over deals in which A profited.

i think this construction is correct hence "which " may have this usage also.

any thoughts..??

My observations were limited to the use of relative pronouns which and that. In which is rather different construction though.

A) which permit that employees can balance home and work responsibilities better, realizing
B) which permit employees balancing home and work responsibilities better will realize
C) that permit employees to balance the responsibilities of home and work better will realize
D) that permit employees a better balance between the responsibilities of home and work, thus realizing
E) such that employees are permitted a balance between home and work responsibilities, and they will realize

Ans C.

Bumping for review and further discussion*.

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A can be eliminated because of use of ‘contend’ as well as ‘can’.

B is awkward because of “employee balancing”.

D can be eliminated because of “thus realizing”.

E can be eliminated because of “and they will realize”.

Hence - Answer is C

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