Here are some tips for handling GRE math questions in the Quantitative Comparison format (Quantitative Comparisons account for half the questions on a GRE Quantitative section):
1. Do only as much work as you need to do to make the comparison. All you have to do is determine which quantity is greater (or whether they're equal, or whether no comparison can be made). You don't have to determine how much greater one quantity is than the other.
2. Do the math if it's not difficult. Even if you're confident that your comparison is accurate, if a simple computation will confirm your analysis, by all means do it. There's no sense in analyzing a problem entirely in the abstract if it only takes a few seconds to scratch some numbers down on paper. Committing your mental process to paper helps you see if you're making a mistake along the way.
NOTE: You shouldn't have to do involved calculations to get to the answer in a Quantitative Comparison question. A few simple calculations may be required; but if you're doing a lot of number crunching, you've probably missed the mathematical principal the question is asking about.
3. Just as in Problem Solving, never make a comparison by visual estimation or measurement. Instead, make your comparison based on you knowledge of mathematics, along with non-graphical data provided in the question.
4. Never choose the last (fourth) answer choice (the relationship cannot be determined from the information given) if a comparison does not involve variables or figures. Why? If the comparison at hand involves numbers only, you'll always be able to calculate specific numerical values for both expressions (assuming you have time to do the math). You certainly don't need more information just to compare the relative size of two specific numbers, do you? So the last (fourth) answer choice cannot possibly be the correct one!
5. Consider all the possibilities when it comes to unknowns. When comparing expressions involving unknowns, unless the centered information restricts their value, 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 the last (fourth) answer choice.
6. If you're clueless as to how to analyze a particular problem, try manipulating one or both of the expressions — until they resemble each other more closely. You may be able to combine numbers or other terms, do some factoring, or restate in equation in a slightly different form. Get your pencil moving, and you'll soon see the light! (The next two tips are related to this one.)
7. 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 to 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.
8. You might be able to simplify one or both expressions by multiplying or dividing both by the same term. But don't multiply or divide across columns unless you know that the quantity you're using is positive! Multiplying or dividing two unequal terms by a negative value changes the inequality; the quantity that was the greater one becomes the smaller one. So think twice before performing either operation on both expressions. You can do so safely only if you use a specific positive number (not a variable that could be either positive or negative).
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