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Arithmetic Operations Review

Let’s review basic number properties and arithmetic operations – an absolutely must for GRE quant success!

PEMDAS – An acronym for the order of operations, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Always start with what is inside the parentheses then address any exponents to simplify an expression. Next, move left to right, doing all division and multiplication. Finally, again moving from left to right, do any addition or subtraction.

Number Types

Integers: All numbers that are multiples of 1 with no fractional or decimal parts.

Real numbers: All numbers on the number line.

Imaginary numbers: i is the most common. i = √-1, so i2 = -1.

Rational numbers: All numbers that can be expressed as a ratio of two integers. Decimals and fractions are rational numbers if they have a terminating or repeating decimal. For example, 1/3 is rational, as it repeats to .33333, but π is not.

A few operations to keep in mind:

Subtracting negative numbers: When you subtract a negative number, you will add the terms. Example: 5 – (-2) = 5 + 2 = 7

Zero: Dividing by zero is undefined. The denominator of a fraction cannot be zero. This concept is commonly tested on the GRE. 1/0 = undefined.

Recpirocals: The reciprocal of a number is 1 divided by the number. For a fraction, the reciprocal can be determined by flipping the numerator and the denominator. A number times its reciprocal = 1.

Squaring Fractions: If you square a number between 0 and 1, the number gets smaller. For example, (1/2)2 =1/4.

Multiplying & dividing negatives: The product or quotient of two numbers with the same sign is positive, even if both numbers are negative. (-4) x (-2) = 8.

Taking the GRE While Still in College

While some graduate school applicants have been out of school for a while, the best time to take the GRE is definitely while you are still in college. GRE scores are good for five years so it’s easier to take it now, while you’re still in the habit of studying and taking exams, rather than when you’re working a 9-5 job and haven’t studied for anything in three years.

Here are some FAQs about taking the GRE as an undergraduate. Happy studying!

When should I take the exam?

Since the GRE is a computer adaptive test, it is offered virtually every day of the year, unlike many other graduate school exams. Use this flexibility to your benefit and plan around your academic calendar when scheduling your exam. Avoid scheduling your GRE for the middle or end of the semester/quarter when you will be stressed with midterms and finals. Also, be sure to check your extracurricular activities to make sure that your group doesn’t have a performance, event or gathering scheduled the week of your exam.

The most common time to take the GRE is at the end of your junior year or beginning of senior year. If you take it at the end of junior year, study during the year but schedule the exam a few weeks after finals so that you will have some time to unwind. If you have the option of taking it during the beginning of senior year, make sure you schedule it early in the term before your other campus responsibilities start becoming serious.

Lastly, some test centers offer testing times at both 8 am and noon. Since college students tend to be night owls, consider which time slot you would prefer to take your exam. Sign up early if you want to get one of the noon times, as they tend to fill up very quickly.

What are my options for GRE prep?

Whether it’s an online course, in-person class or simply buying books and practicing on your own, there are myriad options for GRE prep. Go to the www.ets.org/gre and download their free Powerprep® Software to access practice tests so you can get a gauge of your raw performance. Compare this with your target GRE score to help you decide what type of help you need. Visit Grockit to join an interactive game and check out the Grockit forums and connect with other GRE test-takers.

Keep your study habits in mind. If you’re an active learner, preferring to discuss methods and terms with others, an online or in-person class might be best for you. If you’re the type that studies better by yourself, you might be better served by buying some of the many prep books on the market.

How do I balance GRE preparation with my regular course load?

Plan ahead.

With extracurricular activities, intramural sports, and part-time campus jobs on top of academic classes, college students are always busy. But preparing for the GRE, whether on your own or with professional help, is like taking an extra class. You need to set aside time regularly, just as you would for any other class, to practice problems and take practice exams so you can work on your pacing.

If you’re taking the exam during the academic year, examine your schedule for the last few weeks leading up to your GRE. If you have a lengthy paper due three days before your exam, try to finish that assignment early so that you can keep your focus on the GRE. It’s normal to be nervous and stressed out as your test date approaches, help your sanity by planning ahead and minimizing other stresses as much as possible.

GRE Combinations and Permutations

Let’s go over a few definitions before we go over the different types of combination and permutation questions.  The first thing to know is what ! means.  In general, you need to remember the formula for combination and permutation which involves the ! sign.  Calculators have combination and permuation functions built in but you won’t be able to use them on your GRE

“!” is read aloud as “factorial”.  For any integer n, n! = n*(n–1 )*(n–2)*…*3*2*1.

For example, 6! = 6*5*4*3*2*1

Combinations

Combinations are used when the order of the objects doesn’t matter.  The keyword that lets you know to use the combination formula is the word choose.  When you choose something, it doesn’t matter what order you choose them in.

The general formula for choose r objects out of n objects (where r is obviously less than or equal to n)

is n! / (n – r)! r!

For example, if I am trying to create a custom striped tie and I need to pick two colors for it out of 7, then how many color combinations can I have.  The answer is to choose 2 colors out of 7.  So in this case, n = 7, r = 2 and the answer is 7! / (5! * 2!) = 21

Combinations of combinations

What if the question tells you that you have a number of choices for one thing, and another number of choices for another, how many combinations can you have of the two things?

For example, any buyer of a new sports car has to pick between 2 of 5 options for seat colors and 3 of 4 options for dashboard accessories.  How many different combinations of colors and dashboard options are available to this buyer?

We look at seat colors first.  Choosing 2 out of 5 and applying the formula, we get 10.  Then choosing 3 accessories out of 4, we get 4 combinations.  So in total, we have 10*4 seat color-accessories combinations, because for every seat color combination, there are 4 accessory combinations that we could match with it.  With 10 seat-color combinations, we thus have 40 accessory combinations to match with it.

Permutations

With permutations, order matters.  For example, if we have 5 people and five seats on a plane, there are 120 ways of seating these 5 people.  If all the seats are empty and I want to fill the first seat, I have 5 people to choose from to fill the seat.  Then for the second seat, I have 4 people to choose from (because one person has already sat down).  And for the third seat, I have 3 people and so on.  So the answer is 5!

If I have 7 people and five seats, the same concept applies – 7 * 6 * 5 * 4 * 3 where each number represents the number of people I can choose from to put in each seat starting from the left.

Permutations in a circle

What if you need to sit people around a circular table? Since there is no longer a left end and a right end, the first person you seat is just a point of reference.  So if you are seating 5 people in 5 seats around a circular table, instead of having 120 seating arrangements like before, you have 24 arrangements.

In general, when arranging n people in a circle, there are (n-1)! Number of ways.

Permutations with repeated terms

This type of question usually asks, how many different words can you form from the letters of word.  And more often than not, the word will have repeated letters in it.

For example, how many 7-letter words can you form from the word APPEASE.  There are 7 letters so there are 7! ways of arranging these letters in order.  But P is repeated twice, and since one P looks the same as the other P, you have to divide 7! by 2!.  A and E are also repeated twice so you have to divide by 2! twice more.

The final answer is

Mnemonic Vocabulary

Studying reams of vocabulary words can be a mind-numbing process. When faced with the task of memorizing 1000+ unfamiliar (and sometimes useless) words, most of us will either behave like a lost child or a disaffected teenager; that is, we’ll either cower in fear or reject the whole endeavor completely. Believe it or not, the ETS has a reason for this. Chances are, a career in public administration will not require you to know the proper definition of peregrinate, but the prodigious task of learning these daunting words is analogous to the rigors of graduate school (even if the analogy is a bit of stretch).

Luckily, our brains are a built for more complicated and efficient processes than rote memorization; we can actually use creativity to improve the efficiency of learning vocabulary words. If you’ve made it through college, you’ve heard of mnemonic devices. To refresh your memory (I wonder if there’s a mnemonic to remember the definition of mnemonic?), a mnemonic is a linguistic device, often a rhyme, acronym, or anecdote, that aids recall. This is one of my favorites from AP Biology that helped me remember the order of taxonomic classifications: Kingdom, Phylum, Class, Order, Family, Genus, Species = King Philip, come on for God sakes! You likely may have heard a different version of this, but the best part is, they all will help you memorize this specific information.

Now, you may be thinking that such information lends itself well to a mnemonic, but obscure words may not. Indeed, that is partly true. But, many words do happen to conduce corresponding mnemonics–it’s all a matter of using your creativity and finding that customized mnemonic that works for you. Let’s look at a few examples.

  1. Nostrum: 1. Hypothetical remedy for all ills or diseases; once sought by the alchemists 2.Patent medicine whose efficacy is questionable 

Nostrum is a pretty rare word but a surprisingly useful one since one of its definitions is pretty unique. The first definition is basically the same definition as the more familiar word panacea–a cure-all, a hypothetical remedy for all ills.

The second definition, though, is best encapsulated by the idiomatic expression “snake oil,” which is defined as “a worthless preparation fraudulently peddled as a cure for many ills.” In essence, the English word for “snake oil” is “nostrum.”

Because I find this definition more interesting and useful, I will think of a mnemonic for that definition.

The Mnemonic: Put rum in your nostrils (or nose) to cure a cold.

Indeed, this mnemonic as not as catchy as some others you’ve heard, but I find it pretty effective. Putting rum in your nostrils sounds like those many specious home remedies for preventing colds that you may have heard about (most of which have been debunked by scientists).

  1. Abrogate: 1. Revoke formally

Abrogate is not a notoriously complicated word, but it has special relevance for me. I remember having a difficult time remembering the word when I was studying for my GRE. I would recognize the word, I would know that it had a simple definition, but I could never recall it. Then, it dawned on me. Abrogate means almost the same thing as Abolish, and, of course, both those words begin with “ab.”

The Mnemonic: Abrogate= Abolish

This is an example of the simplest kind of mnemonic you can imagine. There is no fancy anecdote, rhyme, or acronym here, just an easy way to remember a close synonym. Sometimes, that’s all you need.

Remember, if the mnemonic works for you, then use it. If it doesn’t, drop it. There’s no use in struggling to remember the mnemonic device on top of remembering these words.

For an impressively comprehensive list of vocabulary mnemonics, visit mnemonicdictionary.com. It’s a brilliant site that exploits the power of online collaboration (not unlike Grockit) to enhance education.

GRE Questions Tailored for YOU!

Here at Grockit, our philosophy is that students learn best when challenged with problems of appropriate difficulty. Each GRE student has a unique toolkit of complex reasoning, quantitative and English language skills, and Grockit’s analytical software provides that student with feedback on their performance, their progress, and their strengths and weaknesses. This feedback enables Grockit students to tailor their practice and allocate their study time more efficiently.

Grockit’s ever-growing bank of unique GRE questions has been written and reviewed by expert instructors and seasoned content writers. We design our questions using ETS® released questions from previous GRE exams along with other selected resources. This allows us to best model actual questions that you will see on the GRE on your test day. Each question is characterized by its difficulty level and the specific skills that it tests, and we use that information to provide you with fine-grained feedback on your performance and learning. When combined with the data that we’ve collected from your recent performance, this meta-data helps us provide Challenges custom-built for you.

500+ and 750+ students alike will benefit from Grockit’s algorithms. We aim to challenge you with test-true practice questions to help prepare you for your test day. Good luck with your studies!

Study for the GRE, track your progress and target specific skills

Grockit GRE is open to the public and people are busy studying for the GRE.

Grockit GRE

When you study for the GRE with Grockit you can practice questions whenever you want, for as long or as short a time as you like. Once you’ve practiced for a while, you can see a visualization of your accuracy across the skills tested on the GRE. Use your performance data to customize reviews and then orient your practice by customizing games to target weaknesses.

For example, your performance data may indicate that you are fairing well on Sentence Completion, but still need to improve your vocabulary skills overall. You may instantly create a custom review to see previously answered vocabulary questions with expert explanation and advice.

Track GRE Skills

Furthermore, you may practice more vocabulary questions, by creating a custom game that only targets vocabulary questions.

Target GRE Skills

In addition to the power of being able to track your performance and target specific skills when you study, Grockit offers you a way to collaborate with other GRE students and to get valuable instruction from tutors through the Group Study and Lessons tab in the Grockit lobby.

Start studying for the GRE on Grockit!