Let's look at the structure of the argument. We have the following premises: (1) Cafeteria does not wash its apples (2) Most fruit is sprayed with dangerous pesticides before its harvested and is dangerous until washed.
The argument then concludes that: Therefore, cafeteria is selling pesticide-covered fruit, endangering its patrons.
There is an obvious gap between the premises and the conclusion. The apples/ fruit are sprayed with pesticides before harvest -> ? -> cafeteria sells fruit as is without washing. We cannot conclude that cafeteria is selling pesticide covered fruit unless we know that the apples are in fact never washed between the time they are sprayed and delivered to the cafeteria. One way to identify a necessary assumption is to negate it and see if the argument falls apart. If we negate (A) -"the apples are washed after harvest but before being delivered to the cafeteria," then the argument no longer makes sense and we cannot conclude that the cafeteria clearly sells pesticide covered fruit.
The issue with (B) is that even if it is false - "most pesticides do not leave greasy residue on the fruit," the conclusion could still be true assuming the apples are never washed. The fact that the apples are greasy is irrelevant as the grease could be something other than pesticides, perhaps the greasiness is due to wax being applied after harvesting to preserve freshness. Since the argument could still follow logically without pesticides leaving greasy residue, we can conclude that it is not a necessary assumption.
Let me know this makes sense and if you have any further questions.
