The sociologist's argument doesn't involve any value judgments or "should" statements, it just talks about how things are. That's already a red flag for (A). We can confirm this using the negation test, which gives us: "news can serve its intended function (providing information) and also be entertaining. That doesn't cause any problems: the sociologist's claim is that primarily entertaining news doesn't give information, not that informative news can't be entertaining at all.

Because we can negate (A) without ruining the argument, it can't be a necessary assumption.

The sociologist is only concerned with whether news is able to serve its intended function of providing actionable information. Viewers’ preferences are irrelevant to this question—they're beyond the scope of the argument, which is doesn't deal with preferences at all. Because (B) doesn't directly relate to the substance of the argument, it can't be necessary to assume.

The argument is only concerned with news’s ability to serve its intended function, which we already know is is providing actionable information. It wouldn’t matter if (C) were negated and news also had other important functions, meaning (C) is not the necessary assumption.

In other words, if news is primarily entertaining, then it can't provide information (i.e. its intended purpose). This is exactly the necessary assumption we're looking for, because it fills in the missing premise about how news being entertaining relates to it being informative.

If we negate (D), we get: "primarily entertaining news can still give us information," then primarily entertaining news could serve its intended function. That would destroy the conclusion, which confirms that (D) is necessary to assume.

The sociologist already establishes in the context that news in a consumer society—i.e. the relevant domain—is primarily entertainment. Because we're confined to this particular domain, we don't need (E) to be true across all possible circumstances where the news industry wants to make a profit. (E) isn't necessary because it's outside the scope of the argument.