
With quantitative comparisons questions, frequently you don't need to finish your calculations or determine an exact answer. You just have to know enough information about the quantities to determine which one is greater.
The first and the most important thing to do about this question types is to memorize the four answer choices correctly. Don't remember choice A and choice B in the opposite way. Check the directions again if you are not absolutely sure during the test. It will be too bad if you know which quantity is greater, but select a wrong choice. Remember, if any TWO of the answers (A), (B), or (C) can be true for a particular question, then the correct answer to that question is (D).
Think of the columns as a balanced scale. You are trying to figure out which side of the scale is heavier, so eliminate any quantities that are the same on both sides of the scale. That means that anything that both sides have in common is irrelevant. For example:
First of all, we need to make the two columns look alike so that they can be compared. Apparently column A can be converted to resemble column B:
Both columns have x^{2} + y^{2} that can be eliminated. The result is:
Now we have no trouble to compare the two columns. Since x and y can be positive, negative or zero, the value of 2xy can be anything, you name it. Therefore, the correct choice is (D)  the relationship cannot be determined from the information given (there's no comparison!).
Another tip for quantitative comparisons questions is to plug in values for variables. Remember:
 Make sure you check above the columns for any information about what the values can be.
 When plugging in values, make sure you check the special cases: 0, 1, at least one number between 0 and 1, a number or numbers greater than 1, and negative numbers.
Remember: assume nothing! Quantitative comparisons are designed to test your ability to separate the given facts from the assumptions you might make. Your assumptions may or may not be correct. But your ability can be improved through practicing at this Web site!
Your work speed on quantitative comparisons questions should be one per minute. If you come across a question that requires lengthy calculation or seems too hard for you to solve, mark it, skip it and move on. Come back if you still have time. Using your guessing and eliminating skill if needed.
However, there's one special rule about guessing that applies only to quantitative comparisons. On about one third of quantitative comparisons questions, no unknown quantity is involved: there's no x or n, nor is there any geometric quantity (degree or length, etc.) that is unknowable. Whenever this is true, the answer cannot be (D). Even if you can't figure out which quantity is greater, it is theoretically possible to figure it out. So (D) cannot be the correct answer. For example:
Column A

Column B

 

$45 after a discount of 10%


The question doesn't contain any unknown quantity. So answer (D) can't be correctly.
If you want to start practicing now, click here to login "SAT Practice" section. We suggest that you come back to this page and read the content again after you have spent 2 weeks of practicing. You will definitely have a better understanding about the strategies!


