B and C use "recently", which changes the meaning of the sentence. In the original, "the recent extended sales slump" means that the entire slump occurred recently, whereas "the recently extended sales slump" means that the slump was recently extended.

D and E use the plural pronoun "their" to refer to "retailer", which is singular. Thus, we are left with A.

We need past perfect because we have a simple past ("retailer said...") in the second half of the sentence. Since the problem occurred before that, we have to use past perfect.

GmatKiss wrote:Please take some time to underline the question and edit it before just pasting it from a source!!

Reporting that one of its many problems had been the recent extended sales slump in women's apparel, the seven-store retailer said it would start a three-month liquidation sale in all of its stores.

(A) its many problems had been the recent
(B) its many problems has been the recently
(C) its many problems is the recently
(D) their many problems is the recent
(E) their many problems had been the recent

IMO: A