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.

Do you remember, when you took exams in high school or college, being allowed to bring a one-page ‘cheat sheet’? I always spent days putting those cheat sheets together in my tiniest handwriting, summarizing an entire semester’s notes on a single page. The funny thing is, by the time I took the exam, I almost never needed to look at the cheat sheet I’d created. After spending all of that time creating it, I had practically memorized my notes. So, even if you can’t bring a GRE Quant Cheat Sheet to the test, you can still benefit from creating one. Synthesizing your notes and thoughts on a single page will give you the ‘big picture’ view of a topic—and will teach you what you do and don’t know. 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.

“When I See This, I Will Do This”: A GRE Study Tool

“I know all of the rules, but I’m nowhere close to my goal score.”

“When I study, I understand everything right away. But when I took the actual GRE, I couldn’t make it happen.”

“I never know what to do when I see a Quant problem for the first time. If somebody tells me how to set the problem up, I can do it perfectly, but I can’t get started on my own.”

“I get overwhelmed by Verbal questions. I’ll think that my answer makes sense, but then I’ll review the problem and realize that there were a dozen different things I didn’t notice.” 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.

When you take the test, you need a strategy for GRE percentage problems that works every time. Here’s that strategy, in four easy steps.
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GRE high-scorers might not be smarter than everyone else, but they do think about the test differently. One key difference is in how high-scorers do algebra. They make far fewer algebraic mistakes, because, either consciously or subconsciously, they use mathematical rules to check their work as they simplify. Here’s how to develop that habit yourself. Read more

Imagine that you asked a friend of yours what she got on the Quant section of the GRE. Instead of answering you directly, she said “let’s just say that 4 times my score is a multiple of 44, and 3 times my score is a multiple of 45.”

Could you tell what score she got? If not… you may need to work on your GRE translation skills!  Read more

In one of my recent classes, I told the students “You’ll never know how to answer a geometry question.”  The reaction was fairly predictable: “Why would you say that?!?  That’s so discouraging!!”

Of course, I certainly was NOT trying to discourage them.  I used that statement to illustrate that geometry questions are often a type of quantitative question that can feel immensely frustrating!  You know what shape you have, you know what quantity the question wants, but you have no idea how to solve for that quantity.

This is what I meant when I said you’ll never know how to answer these questions. That “leap” to the correct answer is impossible.  You can’t get to the answer in one step, but that’s all right: you’re not supposed to!

(An important aside: if you’ve read my post regarding calculation v. principle on the GRE, you should be aware that I am discussing the calculation heavy geometry questions in this post.)

The efficient, effective approach to a calculation-based geometry question is NOT to try and jump to the final answer, but instead to simply move to the next “piece”.  For example, let’s say a geometry question gives me an isosceles triangle with two angles equaling x.  I don’t know what x is, and I don’t know how to use it to find the answer to the question.  But I DO know that the third angle is 180-2x.

That’s the game.  Find the next little piece.  And the piece after that.  And the piece after that.  Let’s see an example.

The correct response to this problem is “Bu-whah???  I know nothing about the large circle!”

But you do know the area of the smaller circle.  What piece will that give you?  Ok, you say, area gives me the radius.  A = pi*r^2, so pi = pi*r^2, so r^2 = 1, so r = 1.  Done, and let’s put that in the diagram.
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I know that for people who’ve been away from math for a while, the GRE requires a lot of refreshment on topics and skills. Even for those of us who’ve been around math all along, there may be topics we haven’t seen since high school on the exam.

Most of getting good at GRE math is practicing your skills, learning to recognize clues and patterns on the exam, and knowing what material is being tested and how it is tested. One key step is knowing the definition of math words, because those definitions often come with important restrictions.

For example, when a question starts by specifying that x is an integer, that restriction will probably be a key to the problem. There is an infinite amount of numbers that are not integers, including fractions and radicals. It’s also important to remember that integers don’t have to be positive – there are negative integers, and zero is in integer as well.

My suggestion is that you clarify the definitions, but not simply memorize them. Let’s say that I realize knowing the definition of “integer” is important, so I decide to make a flashcard that says “integer” on one side and “a member of the set of whole numbers” on the other.

Great. That’s true, and if the test were going to ask me to define the word “integer”, that would be a great thing to know. But remember: for the most part, the quant section of the GRE is a skill test, not a knowledge test. It tests your ability to notice patterns and details, perform math tasks, plan an efficient road to a solution, and reason with numbers. So the definition of “integer” that I want to know is something that will help me.

I am not the biggest fan of flashcards for the quant portion of the GRE, but if I were going to make one for “integer”, I’d want to make sure the back of the card included:

• My own definition in my own words,
• Key trouble issues to watch out for, and
• How the concept tends to show up on the exam.

As I did additional problems, I might add information to the back of the card, so that eventually it would look something like this:

• not decimals or fractions
• Includes zero and negatives!
• When they say “non-negative integer”, think “positive OR zero”
• When they say “number,” think about fractions
• When the exponent is a positive integer, the value usually gets bigger. UNLESS that positive integer is one – value stays the same.

The key is that your definition should include all the things that tripped you up, written in your own language, and written in a way that tells you what to do, not what not to do. (Notice my card doesn’t say anything like, “don’t test only positive numbers”, because generally it’s much harder for us to remember directions given in the negative.) It’s less of a definition and more of a collection of key points that help you clarify how this topic is applied on the exam. In this way, you become a better issue-spotter and avoid common mistakes.

Thinking of definitions in this way can help you to realize their importance while also learning them in a way that’s directly applicable to the exam. The next paragraph is a big, long list of terms for which you might find a definition card useful. All these terms are covered in ETS’s math review for the GRE. You certainly don’t need to make definition cards for each of these words, but if you think it would help you, go for it!

You might find it helpful to make definition cards for the following terms: integer, even, odd, positive, negative, divisible, factor, multiple, greatest common factor, least common multiple, remainder, prime number, prime factor, composite number, zero, one, rational number, reciprocal, square root, terminating decimal, real number, less than, greater than, absolute value, ratio, proportion, percent, percent increase, percent decrease, domain, compound interest, slope, y-intercept, reflection, symmetric, x-intercept, parallel, perpendicular, line of symmetry, parabola, vertex, circle, stretched, shrunk, shifted, line segment, congruent, midpoint, bisect, perpendicular bisector, opposite angles, verticle angles, right angle, acute, obtuse, polygon, triangle, quadrilateral, pentagon, hexagon, octagon, regular polygon, perimeter, area, equilateral triangle, right triangle, hypotenuse, legs, square, rectangle, parallelogram, trapezoid, chord, circumference, radius, diameter, arc, measure of an arc, length of an arc, sector, tangent, point of tangency, inscribed, circumscribed, rectangular solid, face, cube, volume, surface area, circular cylinder, lateral surface, axis, right circular cylinder, frequency, count, frequency distribution, relative frequency, relative frequency distribution, univariate, bivariate, central tendency, mean, median, mode, weighted mean, quartiles, percentiles, dispersion, range, outliers, interquartile range, standard deviation, sample standard deviation, population standard deviation, standardization, finite set, infinite set, nonempty set, empty set, subset, list, intersection, union, disjoint, mutually exclusive, universal set, factorial, probability, permutation, combination, and normal distribution.

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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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