Is y a positive number? (1) 33y > 44y (2) y + 1 is positive.

Official Explanation

Here we have a question about positive and negative numbers. We can use some combination of rules and cases to evaluate the situation. Starting with the data statements, separately: we'll examine Statement (1) by considering cases. If 33y > 44y, could y be 1? No, because that would give 33 > 44, which isn't the case. Any other positive number or zero runs into the same problem. So Statement (1) says that y is negative, which allows us to answer definitively the question that is asked (in the negative), so Statement (1) is sufficient. On to Statement (2), which we opt also to examine through cases. Statement (2), which we must accept as fact while we examine it, says that y + 1 is positive. So, in one case, y could be 1, since y + 1 would then be 2 and would be positive. But in another case, call it a made-up Case II, we could have y = -1/2, because in such a case y + 1/2 = 1/2, which is positive, so it's an allowed case. In the first case, y is positive, and in the second, y is negative. That means that we can't definitively answer the question. So Statement (2) is insufficient. The correct answer is (A).

Note that, in considering cases for Statement (2), there are a few different logical questions that we must keep organized. We have the question that is being asked; we have whether or not we are able to answer the question; we have what the statement is telling us; and, when we are considering cases, we have to confirm whether the case is permitted by the statement before deciding the significance of that case. One of the main reasons to practice Data Sufficiency questions is to feel completely at home in keeping all of these matters straight, as confusing them is one of the most common causes of error on these questions.

Again, the correct answer is (A).

Video Explanation