Quantitative Comparison Questions
Questions of this type ask you to compare two quantities — Quantity A and Quantity B — and then determine which of the following statements describes the comparison:
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Tips for Answering
- Become familiar with the answer choices. Quantitative Comparison questions always have the same answer choices, so get to know them, especially the last choice, "The relationship cannot be determined from the information given." Never select this last choice if it is clear that the values of the two quantities can be determined by computation. Also, if you determine that one quantity is greater than the other, make sure you carefully select the corresponding choice so as not to reverse the first two choices.
- Avoid unnecessary computations. Don't waste time performing needless computations in order to compare the two quantities. Simplify, transform or estimate one or both of the given quantities only as much as is necessary to compare them.
- Remember that geometric figures are not necessarily drawn to scale. If any aspect of a given geometric figure is not fully determined, try to redraw the figure, keeping those aspects that are completely determined by the given information fixed but changing the aspects of the figure that are not determined. Examine the results. What variations are possible in the relative lengths of line segments or measures of angles?
- Plug in numbers. If one or both of the quantities are algebraic expressions, you can substitute easy numbers for the variables and compare the resulting quantities in your analysis. Consider all kinds of appropriate numbers before you give an answer: e.g., zero, positive and negative numbers, small and large numbers, fractions and decimals. If you see that Quantity A is greater than Quantity B in one case and Quantity B is greater than Quantity A in another case, choose "The relationship cannot be determined from the information given."
Simplify the comparison. If both quantities are algebraic or arithmetic expressions and you cannot easily see a relationship between them, you can try to simplify the comparison. Try a step-by-step simplification that is similar to the steps involved when you solve the equation for x, or that is similar to the steps involved when you determine that the inequality is equivalent to the simpler inequality Begin by setting up a comparison involving the two quantities, as follows:
where is a "placeholder" that could represent the relationship greater than (>), less than (<) or equal to (=) or could represent the fact that the relationship cannot be determined from the information given. Then try to simplify the comparison, step-by-step, until you can determine a relationship between simplified quantities. For example, you may conclude after the last step that represents equal to (=). Based on this conclusion, you may be able to compare Quantities A and B. To understand this strategy more fully, see sample questions 6 to 9.
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