The GRE is Not a Math Test Part II: Making Quick Work of Percentages

A couple of months ago, my fellow blogger Boris wrote an entry entitled “A Math Test: What the GRE Quantitative Section Isn’t”. In it, he explains that the GRE is test of your logic skills, not your ability to do complicated math. There are lots of math shortcuts that will get you points while saving you time and energy on the GRE quant section. Here are the key shortcuts to know when working with percentages, on which students tend to do far more calculations than necessary:

- If you’re comparing percentages from the same total value, you can just compare the percentages without calculating the real values. Consider this problem:

Yes, you could set up an equation to find the value of c, and then take 47% of that. But since we’re comparing two percentages that are taken from the same total, we can save time. We know that the value of 21% of c is 840, and we’re looking for the value of 47% of c.

47 is a little more than twice 21, so the correct answer must be a little more than twice 840. 840*2 = 1,680, and only one choice is larger than that: Choice (E), 1,880. Problem solved with one calculation.

- x% of y = y% of x. This is true because of the commutative property of multiplication – thank me when you now have something to talk about at your office holiday party. Here’s how it can help you on the GRE:

Based on the commutative property, we can tell that these two quantities are equal without making a single note or doing a single calculation. Since you have an average of 1.5 minutes per quantitative comparison, you just banked approximately 1 minute and 20 seconds to spend on a tougher problem. This concept pops up in more convoluted questions as well; be on the lookout to use it whenever possible.

- If you decrease a number by a certain percentage, and increase the result by that same percentage, you will not get your starting number as a result. Let’s look at a problem to explain exactly what this means:

We need to use the centered information to find the values of x and y to get a value for Quantity A. We know that after a 25% discount, the sweater cost $36. So can we take 25% of 36, add that to 36, and get our answer? No, because of the principle stated above – decreasing something by 25% is not the same thing as increasing that result by 25%. Instead, think of it this way: Since we decreased x by 25%, the remaining $36 represents 75% of the pre-discount cost. So 75% of x = 36, and we can solve for x this way.

I’m going to leave the rest of this problem for you to do on your own – let me know what answer you get in the comments! Keep these percentages tricks in mind, and you’ll save precious time on test day.