Comparing Inequalities

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If and , is ?

(1)

(2)

Review: Comparing Inequalities




Explanation

We have got a zillion variables flying around here. We doubt that we are going to get definitions for all of them. Rather, the key is whether the first inequality and the second inequality can be related through a piece of information that allows us to answer the question. Let's look at the data statements, separately first.

Statement (1): this is insufficient. In one allowed case, . In other words, the second inequality is tacked on to the end of the first one, and in that case, . But this statement would also allow a case in which the second inequality isn't tacked into the first one, but slipped between the terms of the first one, so that . In that case, we get the opposite answer. Insufficient.

Statement (2): this information improves upon Statement (1). Namely, it says that the first case is the only case--the second inequality is tacked onto the end of the first, so that all the variables are lined up in order. We have sufficient information to answer the question of whether . Sufficient.

The correct answer is (B).


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