GRE Quant is school mathematics asked in ways designed to reward reasoning over calculation. Two techniques exploit that directly, and between them they cover a surprising amount of the section.
Plugging in your own numbers. When a question is about variables and the answers are in terms of those variables, choose your own convenient values, compute the answer as a number, then see which option produces it.
Rules that keep it safe: avoid 0 and 1, avoid numbers already in the question, and pick values that make the arithmetic easy (percentages love 100, fractions love the common denominator). If two options give the same result, change your numbers and test only those two.
Working backwards from the options. When the question asks for a specific value and the options are numbers, test them instead of solving. Start with the middle option: if it is too big you have eliminated three at once. On word problems with awkward set-ups this is routinely faster than the equation.
Quantitative comparison deserves its own habit. You are asked whether A is bigger, B is bigger, they are equal, or it cannot be determined. Try to make the comparison come out BOTH ways: test a positive, a negative, a fraction between 0 and 1, and zero where it is allowed. If two different tests give two different relationships, the answer is "cannot be determined" — and students choose that far less often than it is true.
Do not use the calculator as a first move. It is there, and reaching for it is usually the signal that you have missed the structure. Estimation beats it: if the answers are far apart, round hard and eliminate.
Read what is asked, twice. The most expensive errors in this section are not mathematical. The question asks for the perimeter and you found the area; it asks for the increase and you found the new value; it says "which of the following could be" and you looked for "must be".