Hey Skywalker,
I love this question because it rewards strategic thinking...a critical component of Data Sufficiency questions. Essentially, DS questions force you to determine "will I always get the same answer" given a piece of information. Accordingly, your job is to prove that you either will or you won't, which lends itself to thinking strategically.
Here, we're constrained by the fact that Friday is the second-highest number, and we want to know whether that number must be greater than 11.
Strategically, that allows us to have either a very high Saturday (the highest) and low values for the rest, or a low Saturday and maximize the rest. The higher Saturday, the lower Friday.
With Statement 1, we're allowed to have a freakishly high Saturday...it's not capped at all. If we want to prove that we could have fewer than 11 books sold on Friday, let's say that:
Thursday (8) is the third-highest
Friday (9) is the second highest
The others are 7, 6, 5, and 4.
That leaves us with 39, and we can fill in the rest (51) with Saturday, allowing us to have fewer than 11 sold on Friday.
Strategically, it shouldn't be too hard to prove that we can get more than 11 sold on Friday now - just reduce the number on Saturday and move them to Friday and we'll keep all the rules intact (e.g. make Saturday 41 and Friday 19).
With Statement 2:
If 38 are sold on Saturday, one of our big assets toward "11 or fewer" is now gone - we've capped that "sell as many as possible on Saturday" logic that helped us keep the other numbers down in the first statement. Therefore, it's going to be harder to keep Friday down to 11 or fewer.
Strategically, in order to do that, we want to maximize the other days to keep Friday down as low as possible. If we can't get it down to 11, then it's sufficient.
38 on Saturday leaves us with 52 books for the other 6 days, and Friday has to be the second most. If we call Friday 11 - the highest number that will give us a "no" since we know that getting that "no" is going to be tough - then the other days could be 10, 9, 8, 7, and 6. Those add up to 40, and the 11 books that we'd then sell on Friday would only bring us to 51. Accordingly, we need Friday to be greater than 11 in order to sell 90 books, and statement 2 is sufficient.
When you are faced with DS problems like this that would involve extensive algebra or calculation, keep in mind that your goal is to try to get two different answers to the main question, and act strategically. Often that can come from maximizing or minimizing the value of the other variables to see if you can get a certain value out of the one in question. That's how you can keep the time down (and learn to enjoy these...like this one, the "harder" of the two answers to get, in this case "no", is often only 1 away from being possible...they're really well-written).
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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