Buyers are more likely to purchase clothing from companies that donate a portion of their profits to charity.
Many retailers will hold sample sales at a downtown event. Organizers plan to hand out flyers listing which of the retailers donate to charity

Aim of plan:
Increasing those companies’ sales at the event

We need to weaken

(A) The cost to the organizers of designing and printing the flyers is equivalent to half an average day’s worth of sample-sale profits for one of the retailers at the event.

The cost of the flyers is immaterial. The organisers are distributing the flyers to increase the sales of some retailers. Profitability of neither the organisers nor the retailers is in our scope. Even if the cost of flyers is more than the sales, note that it doesn't affect our plan. The aim of the plan is not higher profitability but higher sales for some particular retailers. We stick to our aim.

(B) Many of the retailers who donate profits to charity do so in order to garner tax breaks, rather than for purely altruistic reasons.

Irrelevant to our plan. The reason for donating to charity is out of scope.

(C) Among the retailers who will hold sample sales at next week’s event, those that donate a portion of their profits to charity far outnumber those that do not.

It doesn't matter how many of the participating retailers will be on the list in the flyer. The aim is to increase sales for those who donate to charity by advertising that they donate to charity. Whether it affects 10% of the retailers, 50% of the retailers or all the retailers, it doesn't matter to us. The competition is not between those that donate to charity vs those that do not donate. It is between the revenue that a relevant retailer gets without distributing the flyer vs the revenue he gets after distributing the flyer.

(D) Of the retailers at the event that donate a portion of their profits to charity, most have publicized those donations extensively in their advertising.

This weakens our plan. The retailers donating to charity have already publicised it extensively. The flyers will likely not give any new info to the customers. Hence the flyers will likely have no impact on the sales.

(E) Many of the retailers who donate a portion of their profits to charity vary that portion from season to season, allocating a greater portion of their profits to charity during peak sales seasons.

We just need to mark out the retailers who donate to charity - when percentage, when etc is irrelevant.

Answer (D)