Bunuel wrote:
Is x < y ?
(1) z² < y
(2) x < z
Target question: Is x < y ? 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 < yCase 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 > ySince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E