- The quantity in Column A is greater
- The quantity in Column B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given
Many people dread choosing answer choice (D) on Quantitative Comparison (QC) Some feel it may be conceding defeat. Others think that the GRE is trying to trick them by making them pick (D). After all, they think, there must be some pattern that I’m not getting.
The truth is answer (D) comes up often. And to determine whether an answer cannot be determined is actually not too difficult.
#1 Determine a relationship
Say you find an instance, in which the answer is (A) the information in column A is greater. If that is the case, then the next step is to disprove that.
#2 Disprove that relationship
Meaning, see if you can come up with an instance, either through plugging in different variables, manipulating algebra, or manipulating a geometric figure, in which the answer is not (A). As soon you do that, you can stop. The answer is (D).
If you can’t disprove your answer, then it must be correct: it must be (A), (B) or (C).
1. \(-100 < x < 0\)
| Column A | Column B |
|---|---|
| \(x^{-4}\) | \(x^{-3}\) |
- The quantity in Column A is greater
- The quantity in Column B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given
Explanations:
Question #1
After choosing a few numbers you should note something: that Column A will always be greater than Column B.
Why? Will, whenever, you have an even exponent, positive or negative, that exponent will always yield a positive number.
Odd exponents, on the other hand, give you a negative output if the base (the number below the exponent) is negative. Remember x has to be negative. So no matter what number you plug in Column A will always be positive, Column B negative. This is a definite not (D). The answer is (A).
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