Explanation

How much Pat saved last week is described by two possibilities or cases: if she earned less than $1,000, she saved $100. If she had earnings E of more than $1,000, then she saved . Considering both possibilities, let's analyze the statements, separately first.

Statement (1) gives some information about Pat's earnings and her savings. Let's see how it fits with the two cases we discussed. If earnings did not exceed $1,000, then, by the question, her savings is $100. By this statement, she earned ten times her savings. That would mean she earned exactly $1,000. There is nothing contradictory there, so this case is one possible outcome: she earned $1,000. In the second case, she earned more than $1,000, and her savings is . Adding in the information of this statement, that would mean . That gives







That doesn't seem right! When you're working with algebra and you end up with 0=0, it often means that you were combining two pieces of information that you thought were different but were actually the same. Is Statement (1) the same as what we were already told? Almost, because she saves 10% on her first $1,000 and 10% on everything afterward. So Statement (1) actually just describes the condition of earning $1,000 or more, as we can see with this algebraic manipulation:







Considering the two cases together, we have learned only that Pat earned $1,000 or more, but aside from that, the earnings and therefore the savings could be any amount. Therefore this statement is insufficient.

Statement (2) tells us her earnings, so we will be able to calculate her savings. We are limited to the possibility that she earns more than $1,000, so analysis by cases is not relevant. Now that we have burned some cycles on Statement (1), we know it will be 10% of the total. Sufficient.

The correct answer is (B).