This one is a difficult question. Perhaps, it is a good idea to hear Experts.
My explanation is below. Initially I answered A, then realized that the answer must be C.

amysky_0205 wrote:Trans World Entertainment Corporation, which owns the Record Town and Saturday Matinee retail chains, announced that since sales of up to one-fourth of its stores are poor, they will be closed.

amysky_0205 wrote: A. that since sales of up to one-fourth of its stores are poor, they will be closed
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First of all, "announced" can be used without "that" so it's a fake split.

Secondly, "announced" requires the following statement to be in the past, so we have to use "future-in-the past" - would (not will).

Thirdly, for me it is not clear to which noun "they" refers to.
In fact, there are three options:
1) All stores
2) one-fourth => 25% of many, so it's plural one.
3) sales

amysky_0205 wrote: B. it is closing up to one-fourth of its stores, which accounted for its poor sales

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1) Again. Present after Past is wrong
2) "which accounted for its poor sales" means that sales of stores accounted for poor sales of the whole corporation.

amysky_0205 wrote: C. it was closing up to one fourth of its stores because of poor sales

>> This is a right answer. It becomes clear that the corporation closes only 25% of its stores, which have poor sales.

amysky_0205 wrote: D. to be closing, on account of poor sales, up to one-fourth of its stores

>> "Trans World Entertainment Corporation, .... , announced to be closing" means that the corporation has to be closed.

amysky_0205 wrote: E. having poor sales, such that up to one-fourth of its stores will be closed

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1) "announced having poor sales" means that during announcement, the corporation is having poor sales.
2) Again Future-in-the-past is required.
3) I doubt about construction "such that" but I can't explain.
I think that adjective+noun should be between "such" and "that"

SUCH
Such + adjective + noun + that
"¢It was such a good new that I couldn't wait to share it with my parents.
"¢Such changing conditions as seasonal and daily cycles or different planetary
"¢Such extraordinary fees

Such + noun + as to (noun=way, manner etc)
"¢Xue Mei spoke in such a way as to calm us down.
"¢The sales materials are presented in such a way as to encourage attendees to
purchase the products on the spot.
NOTE - such + noun + as to is much less common than so + adj/adv + as to