Look for Similarities
The first tip is to look for similarities. Most times the quantities are given in such a way that you don't have to work out the whole problem before providing your answer, so when you are working the problem, do only as much work as you need to figure out which is bigger. In some problems, you will see a pattern to the quantities. Once you figure out the pattern you will see that one is bigger or not at all. For example, the two quantities 5(10) + 20 and 5(15) + 5(3) has a pattern where both quantities have a factor of five. We can rewrite the first quantity as 5(10)+5(4). Now our quantities are beginning to look similar. To finish our problem we can simplify it a bit further. We can rewrite the first quantity as 5(10+4) and the second quantity as 5(15+3). Adding the numbers in the parenthesis gives us 5(14) and 5(18). Do we need to finish the problem? No. We can see that both numbers have five outside the parenthesis. Which number has the bigger quantity inside the parenthesis? The second one. So, our answer is B.
Dealing with Numbers
Another tip when you see two numbers as quantities, your answer will never be the fourth one, D. Why? Because if your quantities are both numbers, then you will be able to figure out which is bigger. In our last example, we had two numbers and, as you saw, we were able to figure out which one is bigger. So if you see two numbers, even if there are math operators involved, you can immediately scratch off answer D from your possible choices.
Working with Variables
The third tip is best for when you are working with variables. The tip here is to test the expression using zero, positive numbers, as well as negative numbers. You don't want to assume that your variables are positive numbers. Also, don't forget to use fractional numbers as well. If you find that your expression changes depending on what kind of number you use, then your answer is D. For example, take the quantities x^2 and x^3. At first glance you might assume that the second quantity is larger. You would be wrong, though. If we put zero for x, we would get 0 and 0. Our two quantities are equal. If we put in 2 we would get 4 and 8, now the second quantity is larger. If we put in a fraction, such as 1/2, we would get 1/4 and 1/8. Isn't that interesting? Our first quantity is now larger. As you can see, these two expressions depend on the number that is being used for the variable and you see that you get different answers depending on what kind of number you choose. Since the two quantities fluctuate like that, the answer is D. We could have stopped our testing after the 2, since at that point we already saw that these two quantities do not provide a consistent answer of which is larger.