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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To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.

To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.

Here are the free GRE events we’re holding this week (All times local unless otherwise specified):

11/11/13– Online- Mondays with Jen– 7:00PM – 8:30PM (EDT)

11/17/13– Online- Free Trial Class- 2:00PM – 5:00PM

Looking for more free events? Check out our Free Events Listing Page.

To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.

We hope everyone had a happy Halloween! Yesterday we asked our friends on our Manhattan GRE Facebook page to attempt this Trick-or-Treat Halloween Challenge Problem. As promised, today we are sharing the answer and explanation to the problem:

Let’s use x for the number of bags produced by the original recipe, and y for the weight of each of the bags. Given those variables, our first equation is simply xy = 600. We also need to create an equation that represents the new recipe. Since the number of bags produced has increased by 30, and the weight of each bag has decreased by 1, the new equation is (x + 30)(y – 1) = 600. Remember, the total weight is still 600 ounces. Foiling this equation yields xy – x + 30y – 30 = 600.

We now have two equations with two variables. There are several different paths we can go down here, but all involve substitution of one of the variables, and all will yield a quadratic. The simplest path is to recognize that since xy = 600, we can substitute for xy in the second equation to get 600 – x + 30y – 30 = 600. Subtracting the 600 from both sides, and adding an x to each side gives us 30y – 30 = x. We can now substitute for x in the first equation.

 
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Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

Welcome to part 4 of the article series on analyzing your GRE practice tests. As we discussed in the first, second, and third parts of this series, we’re basing the discussion on the metrics that are given in Manhattan Prep tests, but you can extrapolate to other tests that give you similar performance data. If you haven’t already read those, do so before you continue with this final part. Read more

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

Welcome to part 3 of the article series on analyzing your GRE practice tests. As we discussed in the first and second parts of this series, we’re basing the discussion on the metrics that are given in Manhattan Prep tests, but you can extrapolate to other tests that give you similar performance data. If you haven’t already read those, do so before you continue with this third part. Read more

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

Welcome to part 2 of the process for analyzing your GRE practice tests. As we discussed in the first part of this series, we’re basing the discussion on the metrics that are given in Manhattan Prep tests, but you can extrapolate to other tests that give you similar performance data.

Last time, we discussed how to assess the data provided in the “question list”—the list that shows the questions you received and how you performed on each one. This week, we’re going to interpret the analysis given in the Assessment Reports. Read more

You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here.

The purpose of taking practice tests is two-fold:

(1) You’re testing yourself to see whether you’ve learned what you have been trying to learn.

(2) You’re diagnosing your strengths and weaknesses so that you can build a study plan going forward. Read more