GRE Quantitative Comparison - Tricky?

GRE Quantitative comparison questions can be quite tricky. Although you may be able to think of a situation when the value in Column A is greater that the value in Column B, if there is at least one scenario when Column B is greater than Column A or when the two values in the Columns are equal, then the answer must be that the relationship cannot be determined.

For example, consider the following practice question:

x is a non-negative integer
Column A Column B
x 2x

You might jump to the conclusion that the value in Column B is always greater than the value in Column A because regardless of what positive integer you substitute for x, Column B seems greater. However, you are told only that x is non-negative, so it can be 0, in which case Column A = Column B, because (2)(0) = 0. Therefore, because you can come up with a relationship when Columns A and B are equal and when Column B is greater than the value in Column A, then the relationship cannot be determined without additional information, so the answer is, "cannot be determined."

Another example is the following:

x is a number
greater than 0
Column A Column B
x2 x3

You might be tempted to jump to the conclusion that any value cubed is always greater than that same value, squared. That's exactly the kind of quick, shabby reasoning that will get you into trouble on the GRE exam. Notice that you are ONLY told that x is a number greater than 0. But, how much greater? If x = 3, then yes, x2 is less than x3. However, if x = 0.5, then x3 = 0.125, and x2 = 0.25, in which case x2 is greater than x3. So, in the above example, the correct answer would be, "cannot be determined."