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Statement 1: z² < y No information about x, so statement 1 is NOT SUFFICIENT

Statement 2: x < z No information about y, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined NOTE: the error that many students will make is to assume that z < z², but this is not necessarily the case. For example, if z = 1/2, then z² = 1/4, in which case z² < z On the other hand, if z = 3, then z² = 3, in which case z < z² This feature will create conflicting answers to the target question. Here's what I mean: There are several values of x, y and z that satisfy BOTH statements. Here are two: Case a: x = 0.3, y = 0.4, and z = 0.5 (which also means z² = 0.25). Notice that z² < y and x < z, so both conditions are met. In this case x < y Case b: x = 0.4, y = 0.3, and z = 0.5 (which also means z² = 0.25). Notice that z² < y and x < z, so both conditions are met. In this case x > y Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Since we do not have any information regarding x, statement one is not sufficient to answer the question.

Statement Two Alone:

x < z

Since we do not have any information regarding y, statement two is not sufficient to answer the question.

Statements One and Two Together:

Using the information in statements one and two, we still cannot answer the question. For instance, if y = 10, z = 2, and x = 1, then x is less than y. However, if z = 1/2, x = 1/3, and y = 1/3, then x IS NOT less than y.

Answer: E
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