A sufficient assumption question! Let's get to the core:
Pizzerias only ones that get data (+ Pizzerias can easily ID customers with this data) --> Pizzerias utilize direct mail more effectively than other restaurants
We're looking for a sufficient assumption to completely fill the gap. So, what's the gap? There's a couple of fishy issues (anchovies?) about how pizzerias are the only ones that can get the data, but the argument doesn't say they're the only ones that can ID customers. Maybe other restaurants can ID customers through another means? Another gap I noticed is whether the pizzerias will actually use that data to ID customers (the stimulus says they can, but does it mean they do?). But both of those gaps are within the premise, we want a gap that includes the conclusion. And there is one: who says that the data (and gaining the ability to ID customers) helps make direct mailings more effective? There's a big jump there. With sufficient assumption questions, we can expect the answer to play on a large gap and fill it fully.
The answer, (E), addresses that final gap in such a way to ensure that pizzerias are more effective at direct mailings. If we assume that restaurants that collect the data regularly are always more effective, we know that pizzerias are more effective, since they're the only ones that regularly collect the data! (E) even seals up the issue about whether the restaurants actually will use the data because "they always utilize it more effectively.."
(A) is tempting! However, even if the other restaurants can't easily ID the customers, perhaps they CAN do it (but with some extra effort). And, more importantly, perhaps these other restaurants can still do effective direct mailings. This doesn't connect to the conclusion.
(B) is also tempting! It seems to say that direct mailings can only be done by pizzerias. But it doesn't say that. It says that direct mailings require some data - and perhaps those other restaurants have some data (they just don't routinely collect the data).
(C) is initially suspcious since it hinges on something "generally requiring," but it's definitely wrong since it connects data and IDing customers, and doesn't connect to the conclusion about direct mailings. We already know that the pizzerias can ID the customers easily with the data, and, while ruling out other ways of IDing customers would be good, (C) doesn't do it because it says that IDing customers generally requires something, (and even if (C) did establish that only pizzerias can ID customers, we still wouldn't know IDing would make direct mailing mroe effective).
(D) is out of scope. We're not concerned with whether the direct mailing is beneficial. We want to know if pizzerias can do them more effectively.
By the way, a more formal approach might be this:
pizza --> routine data
To draw the conclusion, we want this chain: pizza --> routine data --> more effective mail.
We're missing routine data --> better mail, which (E) provides.
This is tricky (I had several teachers debating this!), because the wording of the first sentence feels like it establishes data --> pizza, but it actually establishes that as well as pizza (most) --> data. This is an awkward question in this respect, because it seems the LSAT is interpreting "routinely" to mean that most pizzerias collect the data.
This allows this thinking:
P: MOST pizzerias record data, and no other restaurants do
A (E): those that record data are always more effective at mail
C: Pizzerias as a whole are better than other groups of restaurants at utilizing mail
This is why I try to stay clear of automatized interpretations of logical statements!