There are many ways in which you can attack a quantitative comparison question, when confronted on one on the GRE exam. To get a feel for the types of questions that you should expect, practice on as many practice questions as you can. A few tactics are given here.
If there are equations or variables in either of the columns, then you can try and substitute numbers for the variables to see if you can come up with a relationship that answers the question. For example, consider the following, shown previously in this tutorial: Plug in values x = 0 and x = 1, and in one case you'll get that Columns A and B are equal, and when x = 1, then you'll get that Columns A and B are not equal. In that case, the answer HAS to be 'cannot be determined'.
x is a non-negative integer
Plug in values x = 0 and x = 1, and in one case you'll get that Columns A and B are equal, and when x = 1, then you'll get that Columns A and B are not equal. In that case, the answer HAS to be 'cannot be determined'.
You can also try to break the relationship or try to determine if the values in both columns must necessarily be equal or not. For example:
Two sides of a triangle T are 3 and 4
In order to solve this question, you have to recall a few things about triangles. Namely, that the length of a side of a triangle cannot be larger than the sum of the two other sides of the triangle. Here, sides one and two are 3 and 4, for a total of 7, and so the third side CANNOT be larger than 7. Right away, then, you know that the value in Column B is larger.
Finally, as is the case with most of the math questions on the GRE, if you get stuck with doing overly long calculations, then STOP! Remember, the GRE is not a test of you calculation skills; instead, the math section is meant to gauge you math skills. If you find yourself doing long calculations, then stop and take a closer look at the question. Most likely, there is a shortcut that you didn't see and which the GRE test makers are trying to determine if you can figure out. For example:
Don't do the calculations, but instead notice that the values in Column B can be rewritten to be the same as in Column A. (1216)(2) = 2432, and (800-32) = 768, so Column B = (2432)(768).