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
, could y be
1? No, because that would give
, 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
is positive.
So, in one case, y could be 1, since
would then be
2 and would be positive. But in another case, call it
a made-up Case II, we could have
, because in such a case
, 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).
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