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.

Yes, the holidays have come and gone. Welcome to 2014! But having spent the last month listening to Christmas music non-stop, I have lots of these songs still stuck in my head. Whether or not you celebrate Christmas, these songs are around this time of year and tend to plant themselves in our minds. So if they’re stuck in your head too, there’s a good chance to learn a little vocab!

Here are seven examples of GRE words in holiday songs. If you find others, share them in the comments!

(1) Terrific. Here’s one of those words that the GRE likes to use for its less-conventional meaning. We usually think of terrific as “great”, but it really means “awesome” in the literal sense: big and awe-inducing, often in a bad or scary way. Like the word “terror”. To be honest, I can only think of one popular culture use of “terrific” in this way, and that’s in “Home for the Holidays,” which tells us, “…from Atlantic to Pacific, gee the traffic is terrific!”

(2) Conspire. In “Winter Wonderland,” the singer says, “Later on, we’ll conspire as we dream by the fire.” So picture the couple in the song, chatting away and planning for the new year. To conspire is to make secret plans together, although those plans are to do something bad… maybe that song is a bit naughtier than the sing-song tone would have us believe.

(3) Incarnate. “Incarnate” means given a body or shape, and it’s usually easiest to remember by thinking of the more-frequently-used “incarnation”. But you could also think of the lyrics to “Hark! The Herald Angels Sing”, which implore the listener to “hail the incarnate deity” when telling the story of the first Christmas.

(4) Cloven. The song “It Came upon a Midnight Clear” is full of great vocab, but one of the best words in “cloven”, which means “cut in two”. We mostly hear this word describing “cloven hooves” – or hooves that are split in the middle, such as those of a cow. The song speaks of angels coming to earth and says, “through the cloven skies they come”, describing the sky breaking in two.

(5) Traverse. “Traverse” means to move to travel across something. “We Three Kings” begins, “We three kinds of Orient are bearing gifts we traverse afar.” And if you’ve always sung that as “travel afar”, you’re already all set on this one.

(6) Lament. To lament is to grieve or be sorrowful, often in a way that involves crying or wailing. In “Good Kind Wenceslas”, the king and his page are traveling “though the rude wind’s wild lament and the bitter weather.” That wailing of the winter wind is a great way to remember the word “lament”.

(7) Laud. We mostly hear “laud” used as a verb meaning “to praise or glorify,” but it is also a noun for the praise or glory that is given. It’s used in this way in “What Child is This,” which says, “Haste, haste to bring Him laud, the Babe, the son of Mary.”

There’s a point here far beyond these seven words: GRE vocab is everywhere. When you hear or read a word that you don’t know, look it up! You might find that you start noticing GRE vocab everywhere. And who knows – learning it might be, dare we say it, sort of fun.

Below is an excerpt from Andrew Yang‘s new book, Smart People Should Build Things: How to Restore Our Culture of Achievement, Build a Path for Entrepreneurs, and Create New Jobs in America, which comes out in February 2014. Andrew was named Managing Director of Manhattan GMAT in 2006, Chief Executive Officer in 2007, and President in 2010. He left Manhattan GMAT in 2010 to start Venture for America, where he now serves as Founder and CEO.

#### The Prestige Pathways.

Let’s imagine a very large company. It is a leader in its industry and much admired by its peers. It invests a tremendous amount of money—literally billions of dollars a year—in identifying, screening, and training its many employees. Those employees who are considered to have high potential are sent to special training programs at substantial additional cost. Happily, these top training programs are considered to be among the best in the world. After these employees complete their training, the company encourages them to choose for themselves the division in which they’d like to work. Employee preferences are deemed to be the most efficient way of deciding who works where.

This seems like a good system, and it works well for a long time. However, perhaps predictably, many of its most highly rated employees eventually become drawn to the finance and legal divisions because these divisions have very effective recruitment arms, are more visible, pay better, and are thought of as providing a more intellectual level of work.  Over time, proportionally fewer of the top recruits go toward the management of the company or the company’s operations.  The company’s basic training division is considered a backwater, with low pay and low recognition. And only a relative handful of employees go toward research and development or the launching of any new products.

Take a second to think about the company described above. What do you think will happen to this company as time passes? And if you think that it’s not set on a path to success, what would you do to fix it? This company reflects, in essence, the economy of the United States of America.

If you are a smart college student and you want to become a lawyer and go to law school, what you must do has been well established. You must go to a good school, get good grades (already accomplished, for many), and take the LSAT (a four-hour skill test). There is no anxiety in divining the requirements, as they are clearly spelled out. Most undergrads, even those with little interest in law school, know what it takes to get in. The path location costs are low.

The same is true if you want to become a doctor. Becoming a doctor is hard, right? Sort of. It is arduous and time-consuming, but it is not hard if you have certain academic abilities. You must take a battery of college courses (organic chemistry being the most infamous and rigorous of them) and do well, study for the MCAT (an eight-hour exam), and spend a summer or even a year caddying for a researcher, doctor, or hospital. These are time-consuming hoop-jumping tasks, to be sure, but anyone with a very high level of academic aptitude can complete them.

If you attend an Ivy League university or similar national institution, legions of suit-wearing representatives from the big-name investment banks and consulting firms will show up at your campus and conduct first-round interviews to fill their ranks each year, even in a down period (as with the recent years following the financial crisis). They will spend millions of dollars enlisting interns and educating the market annually. Most freshmen have no idea what management consulting is, yet seniors can rattle off the distinctions of different firms with little difficulty. All undergraduates have friends in the classes above them who have gone through this process and gained analyst or associate positions at major investment banks and consulting firms.

Today wraps up our “Oh What Fun!” celebration! Manhattan Prep’s first-ever 12-day holiday celebration was a great success and we hope that everyone got the chance to enjoy all of our exclusive promos, contests, and free study materials.

If you’ve missed any of this year’s celebration, not to worry, we still have a few promotions going on. Our Black Friday Sale for \$150 off all December GMAT classes ends December 15, 2013, with code “BLACKFRIDAY150.” There are still some spots open in our two December online classes, which you can sign up for here and here. Located in NYC? Come join us in-person for our classes beginning on Dec. 14th and Dec. 15th.

We’re also still offering a free download to our 1-year access GRE Challenge Problem Archive. Remember to enter the code “OWFGRECHALLENGE“ at checkout.

To keep the giving going and the holiday spirit alive, we are very excited to share today’s final celebration! We will be collecting non-perishable food to be donated to New York’s City Harvest now through Dec. 20th. Our goal is to collect a minimum of 200 food items including but not limited to: canned goods, peanut butter, mac-n-cheese, cereal, soups, pastas, etc. We will also be collecting children’s toys to be donated to the Marine Toys for Tots Foundation. Our goal is to collect a minimum of 50 new/unwrapped toysto be distributed to needy children in NYC. Finally, we are also collecting warm clothing to be donated to New York Cares Coat Drive. Our goal is to collect a minimum of 50 new or gently used coats, sweaters and blankets to be distributed to New Yorkers in need. Donations may be made at 138 West 25th St, 7th Fl. New York, NY 10001. Let’s make this season brighter for our community and those in need.

Lastly, be sure to check our Facebook page tomorrow, where we will officially announce this year’s “Oh What Fun!” winners of the free GMAT course and the \$250 Amazon Gift Card.

A big thank you to everyone in our social community who participated in this year’s “Oh What Fun!” festivities! Enjoy the remainder of the holiday season and best of luck with your studies!

Each week, we post a new GRE Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.

If x and y are integers such that x < y and xy = 4, which of the following could be the value of 2x + 4y?