Tips for Handling GRE Quantitative Comparison Questions
Following is a list of tips for mastering the GRE Quantitative Comparison format — one of four basic question formats you'll encounter during each of the exam's Quantitative Reasoning sections.
Do only as much work as you need in order to make the comparison. Remember: your task is to determine only which quantity (if either) is greater — not how much greater one quantity is than the other.
Focus on concepts more than on numbers. Quantitative Comparison questions are not designed to require involved calculations. Although a bit of pencil work may help confirm your analysis, if you're doing a lot of number crunching you're probably overlooking whatever math concept is at the heart of the question.
Don't rely on your eye. If a question is based on a geometry figure or other visual aid, do not compare quantities by visual estimation or measurement. Compare them instead based on you knowledge of mathematics and on the non-graphical data provided. You cannot assume that a figure is drawn to scale unless it is accompanied by a "Note" indicating otherwise. (This holds true for all Quantitative Reasoning questions.)
Never select the fourth answer choice if the comparison involves only numbers (no variables). Why not? If you know you can calculate a specific number value for each quantity, then even if you haven't determined which is greater you at least know that they can be compared.
Consider all the possibilities when when comparing expressions involving variables. Unless the centered information restricts the value of all variables (such as x or y), consider positive and negative values, as well as fractions and the numbers zero (0) and 1. Comparisons often depend on which sort of number is used. In these cases, the correct answer is often the last (fourth) answer choice.
Rework one expression to more closely resemble the other. If you don't know how to compare the two quantities, try manipulating one or both expressions until they more closely resemble each other. You may be able to combine numbers or other terms, do some factoring, or restate an equation in a slightly different form. (The next two tips are related to this one.)
Simplify by canceling across quantities. If both expressions include the same term, you can safely "cancel" that term from each one — by either adding or subtracting it from both quantities. This technique may help simplify one or both of the expressions, thereby revealing the comparison. Remember: you don't change the relative value of two expressions merely by adding or subtracting the same terms from each one.
Be careful when multiplying or dividing across quantities. You might be able to simplify one or both expressions by multiplying or dividing both by the same term. But don't do so unless you know that the quantity you're using is positive. Multiplying or dividing two unequal terms by a negative value reverses the inequality.