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There are many different approaches to tackling GRE Quantitative Comparisons problems. One of my favorites is something that, in my opinion, generally doesn’t get talked about enough. This method is for people who feel very comfortable with the basics of quantitative comparisons, and have a decent handle on mental math. When executed properly, it can save you a great amount of time on the test, thus giving you the opportunity to solve other problems. It also can help avoid making silly errors by reducing the number of paper-and-pencil calculations you have to do. This method is called the Equal-Different, or E-D, method. Read more

When it comes to quantitative comparison questions, zero is a pretty important number, because it’s a weird number. It reacts differently from other numbers when placed in some of the situations. And zero isn’t the only weirdo out there.

Most of us equate “number” with “positive integer”, and for good reason. Most of the numbers we think about and use in daily life are positive integers. Most of our math rules were learned, at least at first, with positive integers.

The GRE knows this, and takes advantage of our assumption. That’s why it’s important to remember all the “other” numbers out there. In particular, when testing numbers to determine the possible values of a variable, there are a few categories of numbers you want to keep in mind.

If I’m going to think about picking numbers, I want to pick numbers that are as different as possible. I try to choose my numbers from a mixture of seven categories, which can be remembered with the word FROZEN:

FR: fractions (both positive and negative)
O: one and negative none
ZE: zero
N: negatives

So we’ve got positive and negative integers (the bigger the absolute value, the better), positive and negative one, positive and negative fractions, and zero. Don’t forget, zero is an integer too!

There are other categories of numbers to think about, particularly if they are mentioned in the problem: odd versus even, prime versus non-prime, etc. But the seven groups listed above account for most of the different ways that numbers behave when you “do math” to them. Because of that fact, picking numbers from different categories can be a fast way to understand the limits of a problem.

To illustrate my point, let’s think about the value of x raised to the power of y. What happens to the value of that expression as y gets bigger? Let’s simplify our lives even further by stipulating that y is a positive integer.

What first comes to mind is the idea that as we increase the value of the exponent, we increase the value of the expression. Well, if x is a positive integer, that’s true: the expression gets exponentially bigger as y increases. Unless x is the positive integer 1, in which case the expression stays the same size, regardless of the value of y. The same is true if x is equal to 0. If x is a positive proper fraction, the expression gets smaller as the value of y increases.
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Our latest book, the 5 lb. Book of GRE Practice Problems, just hit the shelves! The book contains more than 1,100 pages of practice problems (and solutions), so you can drill on anything and everything that might be giving you trouble.

We’ve already tried out a regular math problem. This time, we’re going to try out one of the weird Quantitative Comparison problems. If the question type looks unfamiliar, or if you just haven’t had much practice with QC yet, you might want to check out this introductory article first.

Alright, are you ready to try one? Give yourself about 1 minute and 15 seconds to do this problem. (Remember that these times are averages, not limits “ you can choose to take a bit longer, but don’t go beyond about 30 seconds longer than the average. At that point, all the extra time is telling you that you don’t really know how to do this one.)

0 < a <  < 9

Quantity A                                                   Quantity B

9 “ a                                                             b/2 – a 

© ManhattanPrep, 2013

 

Yuck. That inequality thing at the top doesn’t look fun. It might have been fine if it said 0 < a < b < 9, but I'm not really sure how to think about that b/2 piece.

Let’s see. So a itself is between 0 and 9. What about b/2? Here’s a cool little trick: when we have a multi-part inequality (an inequality with 3 or more pieces), we can just chop out two parts as long as we keep the correct relationship. So let’s look just at the last two parts: b/2 < 9. Read more