For many students, there’s an air of mystery surrounding the GMAT Integrated Reasoning section.  Designed to test real-world skills, the IR section can seem more complicated to study for than the other sections of the exam. In this guide, I’ll help you find the best tools for GMAT integrated reasoning practice.

First, I’ll talk about what the IR section tests and the types of questions you’ll see on it. Next, I’ll talk about what you need to prepare for the IR and what you should look for in your IR practice materials. Then, I’ll review both official and unofficial practice materials so that you have a good starting place to begin your practice. Finally, I’ll give you some tips for making the most out of your Integrated Reasoning GMAT practice.

What’s on the GMAT Integrated Reasoning Section?

The GMAT Integrated Reasoning section is non-adaptive (meaning the difficulty level of questions doesn’t vary depending on how you do), contains 12 questions, and lasts for 30 minutes. The IR section is scored from 1 to 8, in single-digit increments. Like the Analytical Writing Assessment, your IR score is separate from your Quantitative and Verbal scores and doesn’t factor into your total GMAT score.

IR questions a more open-ended than normal multiple choice questions. Instead of simply selecting the one right answer of five options, you may choose one, two, three, four, or even all five answers as correct. IR questions ask you to use both your Verbal and Quantitative skills together. You’ll have to analyze data in a number of forms (words, charts, tables, etc) and pull out insights from each.

There are four types of GMAT IR questions:

• Two-part analysis: these questions are often wordy and have small tables attached to them. You’ll be asked to choose two correct answers out of five or six options.

• Multi-source reasoning: these questions present information from, you guessed it, multiple sources. You’ll navigate through and analyze multiple sources of data.

• Graphic interpretation: these questions require you to analyze the information presented in a graph or a chart. You’ll have two questions, with answer choices presented in drop down menu format.

• Table analysis: data in these questions is presented in a sortable table along with three questions. To answer these questions correctly, you’ll need to differentiate between essential and nonessential information.

What Should I Look for in GMAT Integrated Reasoning Practice?

As a test-taker, it can be hard to figure out which GMAT integrated reasoning practice questions are right for you. Here are some questions to ask yourself when considering which materials to use.

#1: Do the Questions Have the Same Format as Real GMAT IR Questions?

GMAT IR questions have unique formats that are unfamiliar for most students and can be confusing. The only way to ensure you know how to approach the questions on test day is to practice with questions that look like those you’ll see on the real GMAT IR section until you’re comfortable with with their style. As such, it’s vital that your GMAT IR practice questions are the same four types and closely resemble those you’ll see on the test.

#2: Is the Resource Computerized?

You’ll take the GMAT on a computer, so it makes sense to practice on a computer as much as possible before test day. This is especially important for IR practice, since the questions require you manipulate data and interact with answers in ways that aren’t possible on paper.

#3: Does the Difficulty Level of the Practice Questions Match the Real GMAT?

While the Integrated Reasoning section isn’t adaptive, you will see questions at different difficulty levels (easy, medium, and hard). When practicing, you’ll want to make sure that your GMAT IR practice questions cover all difficulty levels so you’re prepared to solve whatever questions you see on test day.

You should also beware that unofficial questions can sometimes be much easier or harder than the questions you’ll actually see on the GMAT. If you notice that you’re doing much better or worse than usual on a specific set of practice questions, consider that they may not be very accurate.

#4: Are Practice Questions Grouped by Skill or Difficulty Level?

Targeted practice, when you focus your practice session on one specific skill or question type, is one of the most effective ways to prepare for the GMAT. If you decide to focus on solving only graphic interpretation questions for one hour-long session, you’ll learn more than if you break that same one-hour session into shorter, 15-minute sections for all four question types. You might also want target your practice by difficulty level, for instance working at solving easy questions in a shorter amount of time.

Resources that allow you to sort questions by difficulty level or skill are extremely valuable, since they make creating targeted practice sets much simpler.

Official GMAT Integrated Reasoning Practice

Using official GMAT integrated reasoning practice questions is a great way to ensure that you’re preparing with high-quality practice questions. The questions in GMAT official resources are actual, retired GMAT questions, written by the same people who write the real GMAT.

The Official Guide for GMAT Review 2017 ($28.89)

This print guide, written by GMAC, is an official study guide that covers all sections of the GMAT. The guide comes with a chapter dedicated to the Integrated Reasoning section, which reviews the question types and discusses strategies for solving problems. The guide also comes with access to an online Integrated Reasoning companion, which includes more information about the IR section as well as 50 online IR practice problems.

Overall, it’s a great place to start with your GMAT prep, including for IR.

GMATPrep (Free)

This online software gives you access to two full-length practice computer-based tests, with the option of purchasing up to six total CATs. Each of the practice tests includes one IR section, with 12 questions.

Beyond the CATs, GMATPrep includes an additional 15 free IR practice questions.

IR Prep Tool ($19.99)

This online software includes 48 IR questions, answer explanations, and customizable question sets. This resource is great because it lets you create your own sets of GMAT IR practice questions, sorting by question type and difficulty. It also lets you practice questions in either study mode (untimed) or exam mode (timed).

If you really want to focus on GMAT IR practice, this is one of the best tools available, but it’s fairly expensive for just a few dozen questions, especially compared to the full official guide.

Unofficial GMAT Integrated Reasoning Practice

Because the Integrated Reasoning section is the newest section on the GMAT, there are relatively few resources out there, especially if you compare the few GMAT Integrated Reasoning practice questions to the numerous Quant or Verbal questions. Even so, there are some high-quality GMAT IR practice materials out there that you can use to supplement the official resources in your prep.

Veritas Prep Integrated Reasoning Sample Questions

Veritas Prep has developed a number of Integrated Reasoning practice questions, and offers 14 of them free-of-charge on their website. Veritas Prep is known for having high-quality practice questions and this resource gives you realistic examples of all four types of questions that you’ll find on the IR section. The questions are also accompanied by in-depth explanations that explain why each answer is correct or incorrect.

GMAT Club’s E-Book Bundle

GMAT Club, an online forum that provides support and advice for GMAT test takers, has compiled a list of all free e-books and practice question sets that address the IR section. This resource is great for test takers who are looking for materials that include both instruction and practice questions. Note that these downloadable resources are available as PDFs, so you won’t be able to solve questions online.

GMAT Pill’s Integrated Reasoning Sample Questions

GMATPill has compiled nearly 200 IR sample questions that you can practice online. These questions are broken down into question type, with specific information on skills tested and solve rate, so you can see how hard each question is.

The online format is useful, because you’ll get used to solving the questions on a computer, but the web-based interface doesn’t look anything at all like the interface on the real GMAT. Keep that in mind as you’re practicing.

800score.com’s Integrated Reasoning Sample Questions

800score.com offers demos of the four question types in an online format that has a very similar interface to the actual GMAT. The site also offers instructional videos and other resources you can use in your prep.

Unfortunately, there are only four GMAT integrated reasoning practice questions here, but they’re of high quality and worthwhile for their similarity to actual GMAT IR questions.

4 Tips for Making the Most of Your GMAT Integrated Reasoning Practice

It’s important to make sure that you’re making the most out of your GMAT test prep by practicing smart. Here are some tips for how to make sure you’re making your GMAT IR prep valuable.

#1: Practice Your Pacing

The GMAT IR section is short – only 30 minutes to solve 12 complex, multi-step questions. It’s important to consider timing when you’re practicing. You’ll want to pay attention to how long it takes you to solve problems, particularly during practice tests, when you’ll be answering all 12 questions in one sitting. As you practice, place time limits on yourself and work to see how quickly you can solve problems.

#2: Put Away the Calculator

The IR section doesn’t let you use your own calculator, though you’ll have access to an online calculator with basic functions. Practice using the online calculator with your sample questions, or using a simple four-function calculator on your phone that mimics the simple calculator you’ll use on the test. By only using the resources you’ll actually have on the GMAT, you’ll ensure you’re comfortable and prepared on test day.

#3: Dedicate Time to IR Practice

Many test takers skip preparing for the IR section in favor of spending more time on the Quant and Verbal sections, since they’re considered more important. But as the IR section becomes more seasoned, business schools are considering IR scores more. Especially since the IR section is designed to simulate skills you’ll need in the real world, it’s important to make sure you do well on it!

While you’ll likely spend more time prepping for the Quant and Verbal sections, build in time to focus on IR. Make sure you take the IR section on every practice test you do and spend a few dedicated study sessions on IR questions.

#4: Familiarize Yourself With the Questions

The IR questions look different from every other question type on the GMAT. Spend time with the practice questions so that you familiarize yourself with the visual nature of these questions, as well as with the practice of choosing multiple right answers. Doing so will help you feel more confident on test day. It will also save you time, as you’ll be able to easily recognize question types and know what to when you take the actual exam.

What’s Next?

Learn more about the other sections of that GMAT by reading our guides on GMAT Quant and GMAT Verbal.

Is the GMAT Total score the only one that matters? Read our guide to find out how the total score is calculated and how business schools weight the different scores.

Take a look at our massive collection of GMAT sample questions to start your prep with a huge selection of practice questions for all four sections,

The post The Best GMAT IR Practice: 200+ Questions for Your Prep appeared first on Online GMAT Prep Blog by PrepScholar.

If you’re like me, you probably haven’t thought about remainders in over ten years, when you first learned about long division in elementary school. Remember those lessons on what we call the number that’s left over in a division problem? Yeah, that number’s called a remainder.

And guess what? Remainders show up a lot on the GMAT. Of course, the remainder problems you’ll encounter on the GMAT are much different than the ones you worked on when you were ten years old. GMAT remainder questions can often be quite tricky, but don’t worry! In this guide, I’ll give you a comprehensive overview of GMAT remainder problems so that you feel ready to solve them when you see them on test day.

First, I’ll walk you through a brief refresher course on remainders. Next, I’ll offer some tips for solving GMAT remainder questions. Finally, I’ll provide some sample GMAT remainder problems and explanations for you to study.

What Is A Remainder?

If you’re a bit fuzzy on what a remainder actually is, don’t sweat it. Many GMAT test takers haven’t worked with remainders in many years. Let’s start by going over the basics of what a remainder is and how you’ll see them tested on the GMAT.

Think back to that fourth grade math class you took a long time ago. Let’s review the specific terminology we use to talk about division:

• When you divide $x$ by $y$, it’s the same as the fraction “$x/y$.”
• If we were dividing 6 by 3 (or, $6/3$), 6, the term we’re dividing by something else, would be the “dividend.”
• 3, the number that’s doing the dividing, is the “divisor.”
• In the case of the simple division problem $6/3$, 2 is our answer, or our “quotient.”

But, as I’m sure you know, not all division problems are as nice and neat as $6/3$. That’s where remainders come in.

Simply put, the remainder is the fraction part (or what “remains”) when you divide two numbers that don’t result in a whole number quotient.

For instance, when you divide $8/3$, the remainder is 2. When you divide 8 by 3, you have two sets of 3, with 2 leftover.

An easy way to think about remainders is to think about them as mixed numbers. For instance, the fraction $8/3$ is the same thing as the mixed number $2 2/3$. $2/3$ represents our remainder. We express it as $2/3$ because we have 2 parts left out of the 3 parts we need to make a whole number. The denominator will always be the same as the divisor.

Now that we’ve reviewed the basics, let’s move on to some more complicated, GMAT-style remainder math. Let’s say that we’re dividing our dividend $a$ by our divisor $b$ to yield our whole number quotient $c$ and our remainder $d$. That translates into the following equation:

$$a/b=c+d/b$$

For instance, in the simple problem we worked through before:

• $a$: 8 (dividend)
• $b$: 3 (divisor)
• $c$: 2 (quotient)
• $d$: 2 (remainder)

It’s worth memorizing this basic remainder equation – it’ll come up fairly often on the GMAT.

Remember, remainders can also be expressed as decimals. For instance, the remainder $2/3$ could be represented as .66 (repeating). That’s what you’ll likely see when you’re using a calculator (e.g., $8/3=2.66666$).

GMAT remainder problems are obviously more complex than what we’ve gone over in this section. For the GMAT, you’ll be asked to apply your knowledge of the basic relationship between dividend, divisor, quotient, and remainder to solve moderate to advanced algebraic equations.

As with all GMAT quant questions, we’ll have to rely on more than just our basic remainders knowledge to get the right answer. In the next section, I’ll give you some tips on solving GMAT remainder questions and then walk you through solving four sample questions.

Tips for Solving GMAT Remainder Questions

While GMAT remainder problems can be quite complicated, there are some things you can to do to more easily solve the problems you encounter. Keep in mind these tips as you’re working on GMAT remainder problems.

#1: Memorize the Remainder Relationship Formula

In the previous section, I gave you the formula for finding the remainder of a division equation:

$a/b=c+d/b$, where $a$ = dividend; $b$ = divisor, $c$ = quotient, and $d$ = remainder.

Knowing this equation is the key to answering remainder questions on the GMAT. You should also be comfortable moving around the variables in the equation, so that you understand the other relationships this equation yields such as:

$$a=cb+d$$

Being able to quickly recall the remainder equation and manipulate it in different ways by moving the variables on either side of the equal sign will really help you on the GMAT. You’ll be able to correctly plug-in the different numbers and formulas the GMAT throws at you so that you can figure out exactly what you need to solve.

#2: Plug-In Numbers for Variables

A great way to work out tricky remainder questions is to plug-in numbers for variables into your GMAT remainders equation. While this strategy won’t work all the time, plugging in numbers can be helpful if you’re stuck and unsure how to get to an answer. Let’s look at a sample question to see how this works:

What is the remainder when $x$ is divided by $3$, if the sum of the digits of $x$ is 5?

E. 6

That means we can plug in a number for $x$ that has digits that add together to equal five. For instance, we can use the number 14, because $1 + 4 = 5$. If we divide $14/3$, we find out that the remainder is 2. Let’s keep testing this theory. If we plug in the number 50 for $x$ (because $5 + 0 = 5$), we get the equation $50/3$, which equals 16 remainder 2. We can test this one more time with $23$ ($2 + 3 = 5$). If we divide $23/3$, we get 7 remainder 2. That tells us that the answer is A: 2.

Plugging in numbers doesn’t always work, particularly if you’ve got a number of different unknown variables. However, if you’ve got a relatively small set of potential numbers (e.g., numbers whose digits add up to five), you can plug in numbers to test for the correct answer.

#3: Learn Remainder Shortcuts

There are several nifty remainder “shortcuts” that you should keep in mind when you’re working on GMAT remainder questions. These shortcuts will save you time so you don’t have to completely write out calculations.

The possible remainders when a number is divided by a divisor $b$ can range from 0 to one less than $b$. For example, if $b$ = 5, the possible remainders are then from 0 – 4 (which is one less than 5). If $b$ = 10, the possible remainders range from 0 – 9 (which is one less than 10).

If a number is divided by 10, its remainder is the last digit of that number. If you divide it by 100, its remainder is the last two digits of that number, and so on. For, example 49 divided by 10 equals 4 with a remainder of 9.

You can take the decimal portion of the quotient and multiply it by the divisor to get the remainder. For example, if we know $9/5=1.8$ we can multiply .8 by the divisor 5, which gives us the remainder, 4. Keep in mind that you won’t have a calculator on the GMAT, though, so this tip may or may not save you time.

GMAT Remainder Problem Examples

Now that we’ve learned some tips for solving remainder questions, let’s see them in action. In these GMAT remainder problems, I’ll walk you through how to solve each question using the equations, tips, and tricks we’ve discussed earlier in the article.

Problem Solving Remainder Sample Question

Let’s start with this question by plugging what we know into our remainder equation. In this case, we know the following:

$x$/$y$ = $q$ + 9, where $q$ is the quotient (which is unknown), $x$ is the dividend (unknown), and $y$ is the divisor (also unknown).

From the question, we also know that $x/y = 96.12$. Remember how we talked about decimals earlier? When we’re giving an answer to a division problem that has a decimal in it, the whole number (in this case, 96) is the quotient and the decimal is the remainder. So, in this case, we express our answer as 96 + 0.12, with 96 as the quotient and 0.12 is the remainder.

We can also express our remainder as $\remainder/\divisor$, which gives us the equation:

$$x/y = q + 9/y$$

Since we now have two values for $x/y$, we can set them equal to each other, which yields:

$$96 + 9/y = 96.12$$

We can solve this equation through by subtracting 96 from the left side of the equation so we get:

$$9/y = .12$$

That leaves us with $9/y = 0.12$, or $y = 75$.

Data Sufficiency Remainder Sample Question

When we approach data sufficiency questions, we always want to solve each statement alone before looking at them together. Keeping that in mind, let’s look at statement (1) first.

Remember, we’re trying to figure out if we can determine the tens digit of a positive integer.

Statement (1) tells us that, when our positive integer $x$ is divided by 100, it has a remainder of 30.

This statement is a good example of something that you can plug a number into. For this, I’m going to try dividing different numbers by 100. I’ll start with 100. When you divide 100 by 100, you don’t get a remainder. When you divide 110 by 100, you get a remainder of 10. When you divide 120 by 100, you get a remainder of 20. When you divide 130 by 100, you get a remainder of 30.

You can also use the remainder shortcut that, if any number is divided by 100, its remainder is the last two digits of that number. That tells us that tens digit of our number has to be 3. This statement is sufficient.

Now let’s try statement (2). Remember, we want to look at each statement by itself first.

We can try plugging in numbers for statement (2). Using the same method of plugging in every number from 100 to 300 counting by tens, I find that if I divide 140 by 110, my quotient is 1 remainder 30. However, if I divide 250 by 110, I get a quotient of 2 remainder 30.

In this case, I have two different numbers that both yield me a remainder of 30. That means statement (2) is not sufficient.

I can’t use statement (1) and statement (2) together because they are mutually exclusive. Therefore, my answer is A.

Review: GMAT Remainders

While remainders may seem like elementary math you haven’t touched in years and don’t need to remember, remainder questions will often appear on the GMAT.

The most important step in solving GMAT remainder problems is to memorize the remainders relationships equations. However, plugging-in numbers and recognizing patterns can also help you solve these tricky questions.

What’s Next?

Are you confident in solving remainders questions now? Looking to move onto a new GMAT quant challenge? We have in-depth guides on many of the math concepts you’ll see on the GMAT. Check out our guides to GMAT geometry and GMAT rate problems to boost your knowledge on two other commonly tested GMAT concepts.

If you’re looking for a more generalized overview of the GMAT quant section, our GMAT quant guide will give you a solid overview of the content of the GMAT quant section, while our GMAT quant practice guide will help you better understand how and what to practice to ace the quant section.

Looking to completely change it up? If you want to focus on verbal instead, our in-depth guide to the GMAT verbal section will give you a great overview of the GMAT verbal section, while also suggesting resources you can use to practice.

The post GMAT Remainder Problems: 3 Key Tips appeared first on Online GMAT Prep Blog by PrepScholar.

The quantitative section is probably the most notorious and daunting section of the GMAT exam. It can feel like you need to be a genius to get a good score, but really all you need is practice!

In this guide, I’ll explain what you need to prepare for the GMAT quant section and list the best resources for GMAT math practice. Last but not least, you’ll see my best study tips for the math section to help you achieve your goal score.

What’s Tested on the GMAT Quant Section?

Simply put, the GMAT Quant section tests your ability to analyze data and draw conclusions using reasoning skills. There are two types of questions on the GMAT quant: data sufficiency and problem solving.

The quant section tests your content and analytical knowledge of basic math concepts, such as arithmetic, algebra, and geometry. Contrary to popular belief, the GMAT quant section doesn’t test on advanced math concepts. Instead, you’ll be tested on how you apply your knowledge of basic math concepts.

What Do I Need to Prepare for GMAT Quant?

When you’re studying for GMAT quant, you’ll need a mix of practice and study materials, including GMAT-style practice questions, math content review, and full-length practice tests.

It’s also vital that you use high-quality GMAT math practice resources so you don’t waste precious studying time. Below, I’ve listed the qualities to look for in your study materials for GMAT quant.

#1: Use the Same Format as the Real GMAT

The GMAT is an unique test with often confusing question formats. The more time you spend answering questions that test the same content and look the same as the real test, the more comfortable you’ll be on test day. You won’t have to waste any time wondering “Where do I submit my answer?” or “Where are the directions for this question?”

#2: Test the Same Content as the Real GMAT

The GMAT quant section tests on the following concepts: algebraic equations and inequalities, arithmetic, decimals, percentages, ratios, exponents and square roots, geometry and coordinate geometry, integers, factors, multiples, number lines, and variable operations. You need to make sure that you’re practicing all of the content included on the GMAT quant, without adding in anything extraneous or missing any areas.

#3: Be Computerized, If Possible

The GMAT is a computer adaptive test (CAT). Practicing with online questions will help you be more comfortable reading and answering questions on a computer before test day.

#4: Cover a Variety of Content Areas and Difficulty Levels

The GMAT is an adaptive test, meaning that it gets harder or easier depending on how well you’re doing. You should practice easy, medium, and hard questions so that you’re prepared for whichever levels of questions you may face.

Your GMAT quant practice question sets should include questions organized by topic, so that you can drill specific skills (e.g., coordinate geometry) that you need to work on. Drilling specific skills helps you target your practice and focus on one skill per practice section, so that you can truly master it before moving on to the next skill.

Official GMAT Quant Practice Materials

Official GMAT practice questions are written by GMAC, the same company that writes the GMAT, and are often real questions that have been retired from the actual test. Practicing with official GMAT Quant practice questions is almost always the best option, since you know they’ll be accurate representations of what you’ll see on test day.

The Official Guide for GMAT Quant Review 2017

Price: $12.53

This guide, written by GMAC, provides official GMAT prep focused on the quant portion of the exam. It includes sections that review the fundamentals of the math section of the GMAT, including algebra, geometry, and arithmetic concepts, as well as word problems. The guide includes over 300 practice questions with full answers and explanations to test your understanding, as well as full-length practice CATs.

This guide is a great resource for official practice questions, especially since the online companion lets you build personalized practice sets to hone in on specific skills. However, it doesn’t go into that much depth in its review of skills and isn’t suitable for test-takers who need substantial quant review. It’s also insufficient for students who are looking to test themselves at higher skill levels, since it includes a limited number of hard questions.

GMATPrep

Price: Free!

This online software gives you access to two full-length practice CATs, with the option of purchasing more. The software also gives you access to 45 GMAT quant practice questions and lets you sort the questions into the sets so that you can practice specific skills. You can also purchase extra question packs for an added fee from MBA.com.

Like the official quant review book, this program is a solid resource for official practice questions. It also has the very useful “Exam Mode” which will familiarize you with the exact format of the CAT. Unfortunately, the basic software doesn’t have a wide range of questions, and some of the answer explanations can be convoluted and confusing.

Unofficial GMAT Quant Books

In addition to the Official Guide for GMAT Quant Review, there are tons of unofficial prep books out there. These tend to have more extensive content review, but lower quality practice questions. Here are a few books that are worth looking into for their overviews of the quant section.

Manhattan GMAT Math Guides

These single-focus guides, which range in price from $14 – $26 on Amazon, will help you take deep-dives into the specific content areas that you’re struggling with. For instance, you can be a guide that focuses specifically on fractions, decimals, and percents, or on algebra strategy. Each guide also comes with access to six online CATs and additional online question banks that focus on the specific skill you’re working on.

Manhattan Prep guides are great because they provide in-depth instruction, so you’re really mastering the content knowledge required to solve each of the questions. However, they don’t contain as many practice questions as most competitors’ books (you’ll only get access to 25 online questions per skill), so they’re most useful when used in conjunction with the GMAT official practice materials and questions.

Kaplan GMAT Math Workbook

This book, which costs $13.38, offers comprehensive review for every part of the GMAT quant section, building up your skills as you work through it. It’s mostly focused on building your knowledge, and includes a lot of skill drills, rather than GMAT-style questions. This book is a nice option if you want to buy one resource that’ll take you through the basics of GMAT math.

However, this book doesn’t include many difficult questions and skips a few important math topics, so it’s not a good choice for people who are looking for a high score.

Manhattan Prep’s GMAT Advanced Quant

This book, which costs $15.49, is great if you need more advanced GMAT math practice to help you knock your quant score out of the park. This guide reviews more advanced concepts and offers you the opportunity to work on mainly hard questions. I wouldn’t recommend it for beginners or people who need more foundational review.

Unofficial GMAT Math Practice Tests

Practice tests are an important way to measure your progress and build your stamina on all four sections, including the quant. Here are some full-length, free CATs that you can take to develop your skills. Lots of practice tests also offer answer explanations which will help you diagnose mistakes that you made and hone your GMAT math practice.

Veritas Prep

Veritas Prep offers one free GMAT practice test with explanations. If you’d like, you can purchase 6 more tests for $49. Veritas Prep tests have solid practice questions that are reflective of the actual GMAT and offer the option to take the test with the standard time constraints or with 50% or 100% extra time.

Manhattan Prep

Manhattan Prep offers free access to one full-length GMAT online, which includes rigorous and accurate GMAT-style questions. However, this practice test doesn’t come with answer explanations, which severely limits its utility.

Kaplan

Kaplan offers two types of free online GMAT practice tests: self-proctored and instructor-proctored. For the self-proctored test, you’ll receive your scores and answer explanations to peruse at your leisure. For the instructor-proctored exam, you’ll get your scores, and then work with an instructor in real-time online to get answer explanations.

Despite extensive answer explanation, this practice test isn’t a great option for most students. Kaplan practice questions are OK, but you’ll notice that some are either a little different in format or a little off from GMAT core content. This resource can be helpful if you’d really like someone to walk you through a few questions and you aren’t planning to hire a tutor, but otherwise you should focus on other resources.

Unofficial GMAT Math Practice Question Banks

The GMAT quant section is notoriously tricky, so there are a ton of question banks out there with hundreds of GMAT math practice questions.

Nova’s GMAT Prep Course

This book, which costs $39.95, isn’t a question bank, strictly speaking, but it might as well be. This book is simply a collection of math problems with clear answer explanations. It’s a great resource if you’re looking for more GMAT quantitative practice questions, especially at harder difficulty levels. However, it does include a fair number of typos and misprints, which can be frustrating.

Tagged Question Banks in GMAT Forums

Beat the GMAT and GMAT Club are great resources for GMAT knowledge and, if you need it, emotional support as you go through the business school application process. Many users have uploaded question banks that they used to practice during their own GMAT prep, and can often help explain tricky questions.

You can search for tags in the forums like “quant questions” to find downloadable materials. Check out this list of question banks to get started.

Other GMAT Quantitative Practice Question Resources

In addition to the books and software listed above, there are a number of other resources that you can use to boost your GMAT quantitative practice.

Flashcards

Flashcards are a quick and easy way to build your fluency with formulas and rules you’ll see on the test. They can help you drill important skills at any time, in any place!

Magoosh GMAT Flashcards

Magoosh offers free online flashcards to help you practice GMAT math topics. You can download these flashcards online or as an app for iPhone or Android. They aren’t full-length GMAT questions, but rather drills that can help build your foundational knowledge.

GMAT Club Flashcards

GMAT Club flashcards are great for honing in on specific topics for each of the parts of the GMAT quant section. You’ll cover all of the math concepts tested on the GMAT in concise and easy-to-use cards.

Apps

Like flashcards, GMAT apps are helpful for studying on the go, though they’re no substitute for full-length practice tests or drilling with official GMAT questions.

Veritas Prep GMAT Question Bank

This app by Veritas Prep lets you practice hundreds of realistic GMAT math practice questions and is 100% free. You can customize and create your own GMAT quizzes to work on skills that you’re struggling with. However, some users have complained about the confusing layout and frequency of crashes.

Prep4GMAT

Prep4GMAT (or Ready4 GMAT) is a free app that has over 1,000 verbal and quantitative questions and explanations, as well as hundreds of flashcards and practice tests. It’s great for traveling, because you can download it on your phone. The app can be a bit buggy and some users report that it crashes frequently.

Economist GMAT Tutor App

The Economist’s free app covers every section of the GMAT with lessons and practice questions, and offers the Ask-a-Tutor feature, which helps put you in touch with live GMAT coaches. Unfortunately, the app doesn’t let you customize your prep, so you have to follow the prescribed lessons and question sets in order.

4 Key GMAT Math Study Tips to Help You Prep

Although having high-quality GMAT math practice practice resources is an important place to start, you also need to know how to use them effectively for high-impact prep. Check out our top study tips below:

#1: Practice Without a Calculator

You don’t get a calculator on the GMAT quant section, meaning you’ll have to do all of the arithmetic in your head. You absolutely must get practice doing these calculations by hand, so you should never use a calculator for your GMAT math practice. I know it can be frustrating, especially at first, but it’s vital that you get comfortable without a calculator or you’ll really struggle on test day.

#2: Analyze Your Practice Test Results to Target Your Prep

You can be much more efficient with your prep is use your practice tests to inform your studying. Practice tests will tell you the areas you’re doing well on and the areas that need work. For example, you might look at a practice test and realize you missed half of the exponent questions but only one geometry question. In that case, you probably need to spend more time studying exponents that geometry!

You can (and should) use your analysis to figure out which areas you need to spend the most time on, but don’t forget to review every section of the test. Getting all of the algebra questions on one practice test right doesn’t guarantee you’ll have the same success on the test itself.

#3: Familiarize Yourself With the Format of GMAT Quant Questions

The GMAT quant section only has two types of questions: problem solving and data sufficiency. Both, but especially data sufficiency, have their own unique style and quirks that you need to be comfortable navigating if you want to excel on the exam.

To that end, it’s vital you spend time familiarizing yourself with the format, features, and directions for these sections. Learn exactly what to expect and how questions will be phrased. The more familiar you are with the style of the questions, the more quickly and easily you’ll be able to answer questions.

#4: Drill the Basics

Contrary to many myths surrounding the GMAT, the quant section only tests basic math concepts that you’ll have covered in high school: pre-algebra, algebra, and geometry. What makes the GMAT math section challenging is the tricky ways it test you on these relatively basic concepts.

As such, you really have to have the foundational skills mastered to ensure you can tackle harder questions. Even if you consider yourself good at math, take the time to drill basic GMAT math skills until you’re able to quickly, easily, and accurately identify and execute the math you need to answer questions correctly.

What’s Next?

Looking to make a study plan to get you ready for test day? Read our GMAT study plan to find out where to start.

Struggling with the Verbal section? Check out our guide to the GMAT Verbal section to brush up on your skills.

Want to learn more about the GMAT total score? Take a look at our guide breaking down what it is and what it means.

The post The Best GMAT Math Practice: 500+ Questions and Tests appeared first on Online GMAT Prep Blog by PrepScholar.

The GMAT quantitative section is probably the most notorious and daunting section of the exam. There are many myths surrounding the quant section of the GMAT, such as that it tests extremely advanced math concepts or that it’s impossible to achieve a perfect score. However, by building your understanding of the quant section through careful preparation, it’s more than possible to do well on this challenging part of the GMAT.

In this complete GMAT quantitative review, I’ll be giving you an in-depth look into the format of the section and what skills are tested on it. I’ll also take you through a detailed look at the two types of GMAT quant questions (data sufficiency and problem solving). Finally, I’ll give you tips that’ll help you achieve success in your test preparation and on test day.

GMAT Quantitative Overview

The GMAT quant section tests your ability to analyze data and draw conclusions using reasoning skills.  There are 31 multiple choice questions on this section that test your abilities in these areas, and you’ll have 62 minutes to complete the section. The quant section is the third section of the test, after the analytical writing assessment and integrated reasoning sections.

Like the two previous sections on the GMAT, you’ll take the quant section on a computer. However, unlike the integrated reasoning and analytical writing assessment, the quant section is adaptive. What that means is that the difficulty of the questions you get will be adjusted as you get questions right or wrong. If you’re struggling, you’ll receive easier questions. If you’re doing well, you’ll receive more difficult questions. Your score on the quant section is determined by three things: the number of questions you answer, the number of questions you answer correctly, and the difficulty of the questions you answer.

Quant scores technically range from 0 to 60, but the range in which people actually score is 6 to 51. Your quant score also contributes to your GMAT total score, which ranges from 200 to 800.

What’s Tested on the GMAT Quantitative Section?

The quant section tests your content and analytical knowledge of basic math concepts, such as arithmetic, algebra, and geometry. Contrary to popular belief, the GMAT quant section doesn’t test on advanced math concepts. In fact, you only need to know high-school-level math for the GMAT quant section. You’ll see the following concepts on the test:

• algebraic equations and inequalities
• arithmetic
• decimals
• percentages
• ratios
• exponents and square roots
• geometry and coordinate geometry
• integers
• factors
• multiples
• number lines
• variable operations

Rather than testing your knowledge of complex mathematical concepts, the GMAT wants to see how you apply your knowledge of basic math concepts on two types of questions: data sufficiency and problem solving. While both question types will require you to do the same kinds of math, they’re testing very different skills. The problem solving questions test how well you can figure out the answers to different kinds of numerical problems, such as knowing how much commission to give on the sale of a good. The data sufficiency questions test your ability to determine whether information is adequate enough to solve problems. We’ll talk more about these two types of questions in the next section.

The 2 Types of GMAT Quant Questions

There are two types of GMAT quantitative questions: data sufficiency and problem solving. In this section, I’ll go into more detail about the format of each question type and give you an example problem and solution for each.

If you’d like to get more in-depth information about strategies for either of these sections, check out our detailed data sufficiency and problem solving guides (coming soon).

Data Sufficiency

Data sufficiency questions are multiple choice questions that come with two statements of data. Your job is to figure out whether or not the statements provide sufficient data to answer the question. Then, you’ll have to decide whether one or both statements, by themselves or together, give you enough information to answer the problem. You’ll have the same five answer choices for every data sufficiency question:

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Let’s look at what a data sufficiency question looks like in practice.

Data Sufficiency Sample Question

Here’s an example of a data sufficiency sample question that’s retired from an actual GMAT.

First, let’s look at the features of this data sufficiency question. Notice how the question comes first (“Is the average (arithmetic mean) of x and y greater than 20?”). After that, the two statements are listed. Your job is to figure out whether each of those statements is enough to solve the question, either by themselves or together. Let’s look at the solution for that problem.

Data Sufficiency Sample Question Explanation

The first step for any question on the quant section is to understand what the question is asking you to find. This question is asking you to determine the mean of x and y. The mean (or average) can be expressed as the sum of both numbers divided by 2. So, you can express the mean of x and y in either of these equations:

(x + y)/2 > 20

x + y > 40

Now, you’ll want to turn your attention to each statement. Let’s look at statement 1 first. For this statement, you’ll need to express the statement as an equation and then simplify to solve for x + y. First, let’s figure out your equation. The statement says that the average of 2x and 2y is 48. That information yields this equation:

(2x + 2y)/2 = 48

Next, you can simplify to isolate x and y.

2x/2 + 2y/2 = 48

x + y = 48

Think back to the first inequalities. We said that we can express the mean of x and y as either (x + y)/2 > 20 or x + y > 40. In the math we just did for statement 1, we simplified the equation to show that x + y = 48. 48 is greater than 40, which satisfies the requirement that x + y > 40. That means that the information is sufficient.

Now, let’s look at our second statement. Whenever you’re solving a data sufficiency question, you want to first solve the statements by themselves before considering them together. We solved statement 1 by itself, now we’re solving statement 2 by itself.

Statement 2 says that x = 3y. That means that we can substitute for x in our original inequality.

x + y > 40

3y + y > 40

Remember, x = 3y. So, in my second equation I substituted in 3y for x. Now, I can combine like terms.

4y > 40

y > 10

So, solving this inequality shows us that y is greater than 10. But let’s think back to what the question is asking us. The question is asking us if x + y > 40. From solving this inequality, we don’t have enough information about y or about x to see if x + y > 40.

You can also solve statement 2 by substituting values for x and y that satisfy the condition x = 3y. For instance:

If y = 7 and x = 21 then (x + y)/2 = 14, which is NOT greater than 20.

If y = 40 and x = 120, then (x + y)/2 = 80, which IS greater than 20.

Because there’s the possibility to get an answer greater than OR less than 20 for statement 2, we’ll need more information to solve the problem.

The correct answer to this sample question is, then, is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Problem Solving

Problem solving questions are multiple-choice questions that test high school math skills. These questions are much more traditional and straight-forward than data sufficiency questions. For these questions, you’ll need to use basic math concepts from topics like arithmetic, algebra, and geometry to solve math problems. Let’s take a look at a problem solving sample equation.

Problem Solving Sample Question

Here’s an example of a problem solving sample question that’s retired from an actual GMAT.

Notice how the problem solving sample question looks much more like a question that you would see in your math class or on another standardized test. All problem solving questions have five multiple choice answers.

Problem Solving Sample Question Explanation

The first step to solving this problem is to figure out what it’s asking you and what it requires that you know. You’re trying to figure out the total cost of food for 7 adults on a 5-day trip. In order to do that, you need to figure out the cost of food per day for each adult. You can find that by looking at the costs of the 3-day trip.

In order to determine the food costs per person per day, divide the total food cost ($60) by the total number of adults (4), and then divide that by the number of days (3). Your equation should be: (60/4)/3 = x, when x is the food cost per person per day.

(60/4)/3 = x

(15)/3 = x

5 = x

The food cost per person per day is $5. Let’s plug that into an equation to determine the cost of food on the 7-day trip: $5 (food cost per person per day) * 7 (number of adults) * 5 (number of days) = y (total cost of food on a 7-day trip)

5 * 7 * 5 = y

5 * 7 * 5 = 175

Total food cost per day on a 7-day trip is $175. So the correct answer is B.

10 Tips for Mastering the GMAT Quantitative Section

In this section, I’ll give you some tips that’ll help you as you practice and get ready to take the GMAT and some tips that’ll help you succeed on test day.

Overall GMAT Quant Study Tips

In your GMAT quantitative review, keep in mind these overall tips that’ll help you build your speed, accuracy, and confidence in solving data sufficiency and problem solving questions.

Master the Fundamentals

The GMAT quant section only tests high school math concepts. That means that you’ll have likely seen every skill you need to master the test. The key, then, lies in mastering these fundamentals. You won’t be able to use a calculator on the GMAT, so you’ll have to be fast with your basic calculations. Practice multiplying and dividing decimals and fractions. Memorize the exponent rules. Memorize common roots and higher powers. These simple tips will build your confidence and save you time on test day.

Use What You Know

GMAT quant questions are designed to look very complex and intimidating. However, no matter how difficult the question may look, remember that you’ll only need to use high school level math to answer it. Start small on these questions by using what you know. If you break the problem down into small steps, beginning with what you know, you’ll be able to work towards an answer.

Plug-in Smart Numbers

Plugging-in numbers is a useful strategy for solving questions. If a question gives you only variables and doesn’t ask you to solve for a number, you can pick values for the variables to make them easier to work with or to test statements.

However, you want to make sure you’re using smart numbers. -1, 1, and 2 are good numbers to plug in if you don’t have any confines, because they’re easy and manageable. If the question asks you to use a specific type of number (e.g., a multiple of 3), make sure you’re using one that’ll be easy to do basic calculations with (e.g., use 6 instead of 54).

Data Sufficiency Tips

The data sufficiency section is different than any other math test section you’ve seen before. Here are some tips to keep in mind as you’re preparing for and taking the GMAT.

Evaluate the Statements Individually First

Evaluating each statement individually will help you answer data sufficiency questions quickly and more easily. Evaluate statement 1 first, then evaluate statement 2 by itself. When you do evaluate statement 2, you’ll need to forget everything you did for statement 1. Pretend that they’re two different questions. Once you’ve determined whether each statement is sufficient on its own, you’ll be able to put them together. This strategy will also save you time. For instance, if neither statement is sufficient on its own, you’ll be able to eliminate answers A, B, and E. If both statements are sufficient on their own, you’ll be able to eliminate A, B, C, and E right away.

Memorize the Five Answer Choices

Every single data sufficiency questions has the same 5 possible answers:

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

The 12TEN mnemonic can help you remember those answers and save you time:

• 1: only statement 1
• 2: only statement 2
• T: both statements together
• E: either statement
• N: neither statement

Know the Two Types of Questions

There are two basic kinds of data sufficiency questions: value questions and yes/no questions. By learning to identify which type a given question is, you can be sure you understand what it’s asking and how to answer it.

Value questions ask you to find a numerical value (e.g., what’s the value of 5x?). For value questions, if you’re able to find a specific value using the information in either statement, then that statement is sufficient.

Yes/no questions ask you whether or not something is true (e.g., is y an even number?). For yes/no questions, a definitive yes or a definitive no answer are both considered sufficient. An answer that is sometimes yes or sometimes no is not sufficient.

Remember: a definitive answer is always sufficient. An answer that may or may not be correct is not sufficient.

GMAT Quantitative Test Day Tips

Here are some tips that’ll help you ace the quant section on test day.

Spend time reviewing the information in graphs, charts, and tables

There will be a number of questions on the GMAT quant section that require you to interpret charts, graphs, and tables. Try to spend at least 30 seconds reviewing the information on these. It’s extremely important that you read the axis labels, the key, and the units of measurement so that you’re correctly interpreting the information contained in the graph, chart, or table and using the right information to make your calculations.

Read questions carefully

One of the most common mistakes you can make on the GMAT is to answer the wrong question. The people who write the GMAT will purposefully include questions that ask things like “Which of the following may not be true?” which can be commonly misread or misunderstood as “Which of the following may be true?” Make sure that you read every question carefully so you’re finding the correct answer to the correct question.

use your scrap paper

Even though the GMAT quant section test on high school math skills, use your scrap paper as much as possible. Writing down your calculations will help you see any mistakes and force you to make sure you’re thinking through every step of the question, especially since you can’t use a calculator on the GMAT quant section.

work backwards

If you’re not sure where to start on a question that asks you to solve for a specific value, remember that the test has already given you the right number — you just have to find it among the wrong ones. You can work backwards by plugging in the possible answers until you find one that works.

Moreover, the GMAT normally arranges answer choices in the ascending numerical value, so you can save time by starting with the middle answer. Then you can determine whether you need to go higher or lower with your answer and eliminate multiple incorrect answers at once.

GMAT Quantitative Review: What You Need to Know

The GMAT quant section can be daunting, but with careful preparation and attention-to-detail on test day, you’ll be able to master it. Spend time during your practice developing a deep familiarity with the two types of questions on the quant section (data sufficiency and problem solving) and mastering the basic math fundamentals tested on this section and you’ll be well on your way to achieving your goal score.

What’s Next?

If you think you’ve gotten a good handle on the quant section, check out our guide on mastering the three questions of the GMAT verbal section.

Still confused by data sufficiency? Check out our in-depth guide to learn more about this unique test question type.

Find out more about what makes up your GMAT total score and how business schools weight it against your quant score.

The post GMAT Quantitative: 10 Tips to Master the Math Section appeared first on Online GMAT Prep Blog by PrepScholar.

GMAT questions are complex, testing a lot of concepts at once, so you need to really know fundamentals like math formulas, idioms, and grammar rules. But what’s the best way to learn them? GMAT flashcards! They can help you practice these key quant and verbal concepts until they become second nature.

In this article, I’ll talk about why flashcards are useful, how you should study with flashcards, whether or not you should make your own flashcards (spoiler alert: you should), and review some of the best GMAT flashcards available.

Why Should I Study With GMAT Flashcards?

For many test-takers, studying for the GMAT can seem like a long, difficult affair that involves many hours hunched over an in-depth review guide. Are simple tools like flashcards, then, even worthwhile for GMAT prep?

In a word: yes.

Flashcards are an incredibly effective way to prepare for both the GMAT quant and verbal sections. You can use GMAT quant flashcards to build your fluency with the formulas and concepts you’ll see on the GMAT quant section. Verbal flashcards, on the other hand, are a great way to improve your mastery of the idiomatic language and grammar skills.

Here are three reasons why flashcards are a great tool to help your GMAT prep:

#1: Flashcards Help You Confront the Material

Flashcards require you to actively engage with the material. For instance, rather than just trying to memorize a list of many different formulas you’ll use on the quant section, you’ll engage with each formula one by one. You’ll be forced to ask yourself whether or not you really know how to use the formula in a quick, concise way.

#2: Flashcards Are An Effective Study Tool

According to a study by Time, flashcards are one of the best tools you can use to master material. Every time you use a flash card, you’re training your brain to quickly and accurately recall information. As you practice with flashcards, you’ll be able to strengthen your knowledge and build your memory.

#3: Flashcards Help You Master Quant Fundamentals

Questions on the GMAT quant section often ask you to use more than one skill to get the right answer. Flashcards, on the other hand, only ask you to use one skill. In some ways that’s a drawback, but practicing each skill in isolation will help you achieve mastery of the fundamentals you need to succeed on GMAT quant. Then, when faced with a complex question you’ll be able to confidently combine those skills.

What Can I Study With GMAT Flashcards?

As I mentioned before, flashcards are a great tool to help you study for the GMAT, but they don’t have long, GMAT-style questions on them. Instead, they have bitesize chunks of information on them, such as an idiom or a particular math equation. You’ll use flashcards to build your fluency with these fundamental concepts that you need to master the longer, harder GMAT questions.

Most GMAT quant flashcards ask you about simple math concepts such as: “What is a polygon” or “Factor this equation.” These bite-sized math chunks are basically the fundamental high school math skills you’ll need to answer the more complicated math questions on the GMAT quant section.

Most GMAT flash cards for the verbal section focus on either idioms or grammar terms. Idiom flashcards ask you to explain the meaning of common idioms that you’ll see on the GMAT verbal section, while grammar flashcards ask you about grammar concepts that come up on sentence correction questions, such as identifying where to correctly place a comma in a sentence.

Again, GMAT flashcards don’t focus on GMAT-style questions. Rather, they focus on building the fundamental skills you need to answer GMAT-style questions.

How to Study With GMAT Flashcards

As with any study method, there are good and bad ways to practice. In this section, I’ll teach you the best way to study with GMAT flashcards to maximize your studying time.

The best way to study GMAT flash cards is to use the waterfall method. In the waterfall method, you work through smaller and smaller subsets of flashcards as you learn the different topics, then work back up through the cards once you’ve learned them all.

Let’s see how that works. Take your pile of flashcards.

First, you’ll go through the cards individually. For each card that you can answer right easily, you’ll put it in the “Know it” pile on the left. For each card that you answer wrong or struggle with, you’ll put it in the “Struggled” pile on the right.

Once you’ve gone through all of your flashcards, pick up the “Struggled” pile. Go through this pile. For cards that you can answer, place them in a second “Know it” pile next to but not combined with the first “Know it” pile.

For cards that you can’t answer, make a new “Struggled” pile next to but not combined with the first “Struggled” pile. Repeat this process until your “Struggled” pile only has 4-5 cards. This process creates your “waterfall.”

After you’ve worked through all of your flashcards, you’re going to move back up the “waterfall.” Starting with the last “Struggled” pile, repeat these flashcards until you can answer every question in the pile.

Then, add the most recent (the rightmost) “Know it” pile. Go through these cards until you can get all of the answers right. If you miss any cards, shuffle the cards and start again. Continue this process with every stack of cards as you move back up the waterfall. Keep going until you can answer every card correctly.

The waterfall method works because you’re seeing the concepts that you struggle with the most often. You’ll study the cards you don’t understand more than you’ll study the concepts you’ve already mastered.

Eventually, you’ll have worked through your flashcards so often that you’ll know every concept.

Should I Make My Own GMAT Flashcards?

There are tons of free GMAT flash cards out there. Is it worthwhile to make your own?

Yes. The best flashcards are the flashcards you make yourself.

For one thing, writing down material is a great way to learn it. As you’re making your flashcards, you’ll be writing material, which will help you learn.

You can customize your flashcard set so that it contains more of the content you’re struggling with and less of the content you’ve already mastered. Building your flashcard deck with lots of cards on topics you struggle with will help you see those questions more often and lead to faster mastery.

When making your own flashcards, then, consider the topics you struggle with. Maybe you have trouble mastering the rules of probability. Maybe you really struggle with idioms. Build cards with those questions into your deck.

You’ll want to have two sides to each flashcard. On one side, you’ll give an example of a skill. For instance, you might want to write: “How do you find the area of a triangle?” On the second side, you’ll provide the correct answer to the question. You can also have a short question (such as, “Factor this equation”) on the first side, with the answer on the second side.

Ideally, you’ll make your flashcards on notecards so that you can use the waterfall method when you’re studying. You can purchase notecard decks or rings at any office supply store. You can also use an app to make your flashcards or create them in a program like Microsoft Word.

Keep your flashcards short and sweet. Flashcards aren’t the place to test your ability to solve long, multi-part questions. Each flashcard should only test one specific skill. Testing one specific skill means that you’ll have a targeted focus for each card and that you’ll be able to easily identify which skills you’re struggling with.

Best GMAT Flashcards Review

If you don’t want to make your own flashcards, or you’re looking to supplement your own flashcard deck with other flashcards to practice, there are a number of different options available around the web. There are free GMAT flashcards that you can download or use online, as well as flashcards you can purchase. In this section, I’ll review some of the best GMAT flashcards out there.

Beat the GMAT

• Cost: Free with login
• Format: PDF or app

Beat the GMAT’s downloadable flashcards cover all the major topics tested on the GMAT, as well as strategies for the verbal and quant sections. You can practice memorizing different formulas you’ll see on the quant section as well as applying the knowledge you’ve gained with short, one-step questions. These flashcards come in PDF form or through an app, so you can use them with the waterfall method or just pull out your phone if you don’t have a lot of space to work in.

GMAT Club

• Cost: Free with login
• Format: PDF

GMAT Club has an extensive array of flashcards that cover almost every concept you’ll see on the GMAT, from statistics to subject-verb agreement. This set is the most complete set of flashcards you’ll find on the GMAT. The questions are presented in easily digestible chunks which make the flashcards perfect for truly targeting your practice and mastering fundamentals one at a time. The PDF does have four different flash cards on one page, so you’ll have to spend some time with scissors getting them ready for use.

Magoosh

• Cost: Free
• Format: Online or in-app

Magoosh’s online GMAT flashcards are easy to use and get started with. You don’t have to have a login or download an app; you can simply visit the website to get started. The site breaks down flashcards by concept (e.g., algebra or number properties) and offers mixed concept review as well. The flashcards ask you questions about concepts more than they ask you to memorize formulas, such as “How do we add or subtract fractions?” If you’re looking for clear, quick answers, these cards might not be for you, as the explanations can be a bit wordy. Unfortunately, since you can only use these flashcards online, you can’t use the waterfall method with them.

Kaplan

• Cost: $12.70
• Format: Paper flashcards

Kaplan’s GMAT flashcards are better for building your knowledge of the GMAT than for testing the actual content on the test. While there are cards that review grammar, math formulas, and idioms, a large percentage of the flashcards focus on the GMAT itself, asking questions about the different sections of the test or how much time you have for each section. The breakdown of the flashcards is 260 cards for the quant section, 190 cards for the verbal section, and 50 cards on the test format itself. If you’re not concerned about the mechanics of taking the test, I’d skip these cards. You can get better flashcards for free from Beat the GMAT or GMAT Club.

Ready4 GMAT (Formerly Prep4 GMAT)

• Cost: Free with in-app purchases
• Format: iOS/Android app

Ready4 GMAT (formerly Prep4 GMAT) is a great app that has a number of features, including practice questions, in-depth answer explanations, and personalized coaching and feedback. The app also has hundreds of flashcards that review important GMAT skills, like idioms and formulas. The app also contains flashcards that review vocabulary words you may see on the GMAT verbal section. While you can access the vocabulary flashcards and some introductory flash cards for quant and verbal for free, you have to subscribe to the app to use all of the features. A subscription is a one-time fee of $19.99 (not including tutoring).

The app has a sleek design and is packed with content, but can be buggy and slow. If you’re already thinking about purchasing the app, the flashcards are a nice bonus feature. If not, I’d use one of the other resources before trying this one. Unfortunately, since you can only access these flashcards via an app, you can’t use the waterfall method with them.

What’s Next?

Are you filled with flashcard card and wondering how to build flashcards into your GMAT study plan? Well, you’re in luck! Check out our total guide to crafting a GMAT study plan and learn about how many hours you should devote to studying with flashcards every week.

Wondering what other GMAT resources you can use to supercharge your prep? Don’t worry, we’ve done all the research for you. We’ve compiled guides on the best GMAT books, as well as the Best Online GMAT Resources (link coming soon!). Check out these detailed guides to find the resources that’ll work for you.

Looking for even more ways to achieve your GMAT goal score? Our guide to the top 10 GMAT strategies offers tips and strategies to help you ace your practice and the GMAT itself on test day.

The post The Best GMAT Flashcards and How to Use Them appeared first on Online GMAT Prep Blog by PrepScholar.

The Quantitative section of the GMAT strikes fear into the hearts of many test takers who haven’t taken a math class in years. If you’re one of those test takers, you shouldn’t worry! You can totally handle the math in this section.

While the Quantitative section is challenging, it doesn’t test especially advanced concepts. This guide will show you what math is on the GMAT, along with key tips on how to prepare.

First, let’s discuss a general overview of GMAT math.

GMAT Math Section: An Overview

The GMAT Quantitative section is your third section on the GMAT. You’ll take it after the 30-minute Analytical Writing Assessment, 30-minute Integrated Reasoning section, and an optional eight-minute break.

The Quantitative section is the first adaptive section on the GMAT, meaning that the questions change to match your ability level. You’ll start out with some medium level GMAT math questions, and the problems will get easier or harder depending on how you’re doing.

The GMAT math section will continue to give you customized questions to get a more and more accurate measure of your skills. This adaptive format allows for comparable scores across different tests, plus it enhances security since no two tests look exactly the same.

You’ll get 31 GMAT math questions in 62 minutes, leaving you with approximately two minutes per question. Unlike the Integrated Reasoning section, you won’t have access to a calculator. You will get some note boards and markers to write out your work.

While you’ll need to know a variety of math concepts for this section, you’ll only see two question types. Read on to learn what they are.

GMAT Math Questions: 2 Types

There are just two types of Quantitative questions, and they’re interspersed throughout the section in random order. The two types are problem solving questions and data sufficiency questions.

Typically, about two-thirds of GMAT math questions will be problem solving and one-third will be data sufficiency. However, this proportion could change depending on how many experimental questions you get of each type.

Problem solving questions are just like any other typical question you’d get on a math test. They may ask you to solve an equation, figure out a word problem, or answer questions on a graph.

Each question has five answer choices, and there’s only one right answer for each. Where these questions do get tricky is when they require multiple steps or abstract thinking.

Here’s one example of a problem solving question on the Quantitative section of the GMAT.

 Answer: A

The second type of Quantitative question, data sufficiency problems, are more unusual. These questions present you with a math problem followed by two pieces of information. You don’t have to solve the problem, but rather indicate whether one or both statements give you “sufficient data.”

Here’s an example of a GMAT math data sufficiency problem.

The answer choices for data sufficiency questions are always the same as the ones you see above. You don’t need to solve the initial problem. You just need to know if you could solve the problem based on the given information.

While there are only two question types in the Quantitative section, there are quite a few more concepts that show up. Below, you’ll find an overview of the tested GMAT math concepts, along with sample problems for each one.

What Math Is on the GMAT Quantitative Section?

As you read above, the Quantitative section doesn’t require you to be a mathematician. Your GMAT math review won’t involve advanced calculus or trigonometry. In fact, the GMAT math topics don’t get much more advanced than high school-level algebra.

The main challenge for a lot of people, then, is reviewing concepts that they studied in the past but haven’t used in a long time. The main skills you need to answer both question types involve arithmetic, algebra, geometry, and word problems.

Let’s take a closer look at the topics within each of these skill areas as outlined by the official GMAT Prep Software, starting with arithmetic.

GMAT Math Topics in Arithmetic

You’ll get a variety of problems that require skills in arithmetic. You shouldn’t have to do particularly advanced calculations, since you won’t have use of a calculator, but the questions may require some strategic problem solving and complex thinking.

For arithmetic math in the Quantitative section, you should be familiar with

• Properties of integers
• Fractions
• Decimals
• Real numbers
• Ratio and proportion
• Percents
• Powers and roots of numbers
• Descriptive statistics
• Sets
• Counting methods
• Discrete probability

The problem below, for example, is a problem solving GMAT math question that involves fractions and percents. 

 Answer: A

This second sample problem is a data sufficiency question that calls on your arithmetic and logic skills.

GMAT Math Topics in Algebra

In addition to arithmetic, another major skill area is algebra. As part of your GMAT math review, you definitely want to get work with algebraic expressions and solve for variables. You should be comfortable with

• Variables and algebraic expressions
• Manipulating algebraic expressions
• Equations
• Solving linear equations with one unknown
• Solving two linear equations with two unknowns
• Solving equations by factoring
• Solving quadratic equations
• Exponents
• Inequalities
• Absolute value
• Functions

The sample question below is a typical problem solving question that involves an algebraic expression with two variables and an exponent.

 Answer: D

Data sufficiency questions may also call on your algebra skills, like in the practice question comparing two variables below.

GMAT Math Topics in Geometry

You won’t find quite as many questions on geometry as on arithmetic and algebra, but they definitely still come up. To prepare, you should study the following concepts:

• Lines and angles
• Polygons (convex)
• Triangles
• Quadrilaterals
• Circles
• Rectangular solids and cylinders
• Coordinate geometry

This problem solving question, for instance, asks about properties of triangles.

This data sufficiency question requires you to have some understanding of angles and how they relate to one another.

 Answer: C

GMAT Word Problems

Word problems may call on arithmetic, algebra, or geometry skills, plus they require careful reading to identify exactly what the problem is asking you to do.

You might be asked to calculate simple interest or compound interest, calculate rate, or measure profits. You also may have to work with data from a table, line chart, bar graph, scatter plot, or pie graph. Finally, a question may ask you to analyze sets, as presented in Venn diagrams, or analyze probability.

These are some typical concepts you need to understand to solve GMAT word problems.

• Rate
• Work (these questions typically show the rates at which a person and a machine work alone, and you’ll have to compute the rate at which they work together, or vice versa)
• Mixture (in these problems, substances with different characteristics are combined, and you’ll need to determine characteristics of the resulting mixture)
• Interest
• Discount
• Profit
• Sets
• Geometry
• Measurement
• Data interpretation

This problem solving practice question asks you to calculate how fast the Earth travels around the sun. You need to convert miles per second into miles per hour.

 Answer: D

This data sufficiency question is a word problem that calls on your arithmetic and logic skills.

 Answer: E

Knowing what math is on the GMAT is an important first step, but what else can you do to prepare for the Quantitative section? Read on for six key tips on getting ready for GMAT math.

How to Review Math for the GMAT: 6 Key Tips

How can you get ready for the problem solving and data sufficiency questions on the Quantitative section? What can you do to review concepts that you may not have seen since high school?

Read on for six tips to guide your GMAT math review.

#1: Review the Fundamentals

As you read above, GMAT math doesn’t involve particularly advanced concepts. You won’t need calculus, trigonometry, or any college-level mathematics.

Your first step in preparing, then, should be to review fundamental math concepts. You need to have a solid foundation of key concepts in arithmetic, algebra, and geometry, plus a firm grasp of logic and analysis that will help you solve word problems.

Make sure your study materials offer a thorough review of all tested concepts, and take time to work through the lessons.

#2: Drill With Realistic Practice Questions

As you review key concepts, you should reinforce your understanding with GMAT math practice problems. Even though the math in the Quantitative section isn’t particularly advanced, the questions are still challenging.

They often require complex thinking and multiple steps. Even if you know how to calculate the area of a right triangle or solve a quadratic equation, you need to make sure you can apply that knowledge to GMAT math questions.

By drilling with realistic practice questions, you’ll learn how to apply your math knowledge to the GMAT. The best practice questions come from the official test makers, as on the GMAT Prep Software. Third party test prep companies, like Kaplan and Manhattan Prep, also offer useful practice questions and tests.

As you answer the questions, take notes on anything that confuses or trips you up. Take time to read answer explanations and find the source of your confusion. By understanding your mistakes, you can take specific steps to fix them.

#3: Take Timed Practice Tests

After you’ve done initial concept review and tried out some practice problems, you should set aside time to take a timed GMAT practice test. Find a quiet place, take a practice test with a computer adaptive format, and give yourself 62 minutes to complete the section.

After you’ve finished the practice test, take time to review any questions that you got wrong or felt unsure about. Try to locate the source of your error.

Were you running out of time? Did you misunderstand what a question was asking you to do? Did you make an arithmetic mistake? Were you unfamiliar with a concept? Did you simply make a careless error?

By figuring out where you went wrong, you can take the right steps to fix it for next time. The practice test will not only help you figure out what concepts you need to review, but it will also give you feedback on your pacing. Doing well on the Quantitative section requires you to work quickly and efficiently, and taking practice tests will help you improve your test taking rhythm.

#4: Memorize Data Sufficiency Answer Choices

Data sufficiency questions are weird; there’s no doubt about it. You won’t really see questions like them anywhere but on the GMAT.

To minimize confusion, you should familiarize yourself with the answer choices before test day. You’ll always see the same five answer choices that ask whether statement 1, statement 2, both, or neither give you sufficient information to solve the problem.

Remember that you don’t need to solve these problems, but rather indicate whether you have enough information to solve them. Memorize the answer choices before test day so you know exactly what you’re looking for in each data sufficiency problem and don’t have to waste time reading through or trying to differentiate between the answer choices.

#5: Write Out Your Work

As goes the mantra of high school math teachers everywhere, make sure to show your work. You can’t use a calculator in the Quantitative section, and mental math will only get you so far.

You’ll get note boards and markers in the testing center to write out your work. You should definitely use them to work through the challenging, often multi-step problems.

Try to be neat and organized so you don’t run out of room or make a careless error. If your answer doesn’t match any of the answer choices, then you may need to comb through your work to find the calculation mistake. Try to keep everything legible to make things easier on yourself.

These note boards won’t be graded and are entirely for your own use. You can use them on any of the GMAT sections, but they’re especially helpful when solving math problems.

#6: Practice, Practice, and Practice Some More

As a skill like any other, GMAT math demands a lot of dedicated practice. Whether or not you consider yourself a “math person,” you should set aside time to review concepts, answer sample questions, and take practice tests.

Not only will you sharpen your math skills, but you’ll also become a more efficient test-taker who can handle answering 31 questions in 62 minutes. Don’t get discouraged, but know that you can improve with effort, time, and a customized study plan.

GMAT Math Questions: Final Points

To prepare for the Quantitative section of the GMAT, you should focus on fundamental concepts of arithmetic, algebra, and geometry, plus you need to prepare for word problems. You’ll answer two types of questions, the straightforward problem solving questions and the more unusual data sufficiency questions.

After months of GMAT math review, you can go into the test familiar with these question types. You can hone your time management skills by taking timed practice tests. You’ll also find that the math section gets more and more manageable as you answer lots of GMAT practice questions.

You don’t need to be a math person to do well on the GMAT Quantitative section, but you do need to spend time preparing. With enough effort, you can sharpen skills that you first developed in high school and get yourself ready to conquer GMAT math.

What’s Next?

Now you’re an expert in GMAT math, but do you know what the rest of the exam looks like? Check out our guide to the full GMAT structure and format, along with examples of each question type across the test.

Do you know how the GMAT is scored? Check out our complete guide to GMAT scoring, and then head to this article to see how section and total scores correspond to percentiles.

The GMAT is a daunting test, but how hard is it, really? This article tackles that complicated question to show you just how challenging you can expect the GMAT to be.

The post What Math Is on the GMAT? Topics, Questions, and Review appeared first on Online GMAT Prep Blog by PrepScholar.

For many GMAT test takers, Data Sufficiency questions are the most difficult questions on the GMAT. But what do the hardest GMAT Data Sufficiency questions look like? What skills and concepts do they test? What do they have in common? What Data Sufficiency strategies can we use to get these challenging GMAT Quantitative questions right?

In this article, I’ll go over the five hardest GMAT Data Sufficiency questions, what you’ll need to know to solve them, how to approach them on test day, and what we can learn from hard GMAT Quant questions about mastering Data Sufficiency.

How We Found These GMAT Data Sufficiency Questions

To gather the hardest GMAT questions, our GMAT experts took advantage of the computer adaptive algorithm used on the test. Over the course of the test, the difficulty levels of questions change based on how well you performed on previous questions. Get a few questions right, move up a difficulty level. Get a few questions wrong, move down a difficulty level. By the end of the test, every test taker should be presented with questions that perfectly match their ability.

Our GMAT experts took the practice tests on the GMATPrep software multiple times without missing a single question on the Quantitative section. We collected the questions they received into a master list of the hardest GMAT Quantitative questions. We then looked at activity on various online forums to determine which of these hard GMAT math questions test takers struggled with the most from each question type. This left us with the five hardest GMAT Data Sufficiency questions out there, ready for you to study!

GMAT Data Sufficiency Question 1

This particular problem gives us four different numbers on a number line ($A$, $B$, $C$, and $D$) and tells us the distance between two sets of points ($A$ ↔ $B$ and $C$ ↔ $D$). We should also note that these points are not necessarily in alphabetical order. Whenever we have GMAT Quant questions dealing with shapes, graphs, number lines, etc., it’s a really good call to draw out examples — this is the visual equivalent of plugging in numbers.) Applying this trick here, and remembering that the distance between $A$ and $B$ is longer than between $C$ and $D$, we see that our line could look like this:
this:
this:
and so on.

We need to find the distance between $B$ and $D$. This means that we need to gather information

1. about the order of the points
2. about how our first set of points ($A$ and $B$) relate to our second set of points ($C$ and $D$)

Statement 1

If $A$ and $B$ are two different points and are both the same distance from $C$, this means that the distance between $A$ and $C$ must also be 18 and that $C$ must be directly between the two points like so:
We also know that $D$ is only 8 away from $C$, so it is closer to $C$ than either $A$ or $B$. However, we still don’t know where $D$ is compared to these points. It could be between points $A$ and $C$, making it 26 away from $B$:
or between points $C$ and $B$, making it 10 away from $B$:
Since we don’t know whether the distance between $B$ and $D$ is 26 or 10, Statement 1 is insufficient.

Statement 2

Statement 2 tells us that $A$ is to the left of $D$. Well, $A$ is to the left of $D$ in both of the number lines above, and the distance between $B$ and $D$ is not the same in either. So this doesn’t tell us much. If the statement told us that $A$ was directly to the left of $D$, this might be a little more helpful … but it didn’t and it isn’t. Statement 2 is insufficient.

BOTH

Well, we already established that $A$ is to the left of $D$ (fulfilling Statement 2) in both of the number lines we created to fulfilling Statement 1, so even with the information from both statements, we don’t know whether the distance between $B$ and $D$ is 26 or 10. Since we still can’t solve for a single solution, the correct answer is E: Statements 1 and 2 TOGETHER are NOT sufficient to answer the question.

GMAT Data Sufficiency Question 2

Whenever we have a word problem, like this one, we want to translate the words into math. Scanning over the problem, we see the phrases “36 or fewer” and “more than 36” — these are classic signs that we’re dealing with inequalities. This particular problem gives us two scenarios for calculating how much Bob is paid based on how many total items he produces in a given week (one for 36 or fewer items, one for more than 36 items), so we want to create two equations: one for each scenario. Letting $i$ = the number of items Bob makes in a given week, we can translate our first scenario as

$\If i ≤ 36\, \then \total \pay=x×i$

Our second sentence is a little more complicated. If Bob produces more than Bob is paid $x$ for the first 36 items (or $36x$). Then for all of the items after 36 (or $i-36$), he is paid $1.5x$ (or $1.5x×(i-36)$). Putting that together,

$\If i > 36\, \then \total \pay=x×36 + 1.5x×(i-36)$

So we have two equations, each with three variables ($i$, $x$, and $\total \pay$) … which means we need a bunch of information to figure out an answer. To figure out a value for $i$, we need information about

• which of the two equations to use
• the value of $x$
• the total pay

Statement 1

This statement tells us how much Bob was paid last week, but it doesn’t tell us anything about the specific value of $x$ or which of the two equations we should use. So we could have:

$i=1 \and x=480 → 480=480×1$

or

$i=32 \and x=15 → 480=15×32$

or

$i=76\ \and x=5 → 480=5×36 + 1.5(5)×(40)$

and so on. Statement 1 is insufficient.

Statement 2

This one tells us how much Bob was paid this week, and it compares the number of items he produced this week to the number he produced last week. Well, we don’t know anything about how many items Bob produced last week, so the last piece of information doesn’t tell us much about $x$ — he could have produced 1 item last week and 3 this week or 100 items last week and 102 this week. And, like in Statement 1, we don’t know whether or not $i$ is greater than 36, so we don’t know which statement to use. So we could have:

$i=4 \and x=145 → 580=145×4$

or

$i=29 \and x=20 → 580=20×29$

or

$i=41\, \and x=13{1/3} → 580=13{1/3}×36 + 1.5(13{1/3})×(5)$

and so on. Statement 2 is insufficient.

BOTH

What if we put the two statements together? Well, now we know something: the additional two items Bob produced this week earned him \$30 more than he earned last week. This means that Bob earned an extra /$15 per item. But we’re still missing a key piece of information: which scenario are we dealing with?

1. Did Bob produce 36 or fewer items this week? If so, then both items were produced at a rate of $x$, so that $x=15$.
2. Did Bob produce at least 38 items this week? If so, then both items were produced at a rate of $1.5x$, so that $1.5x=15$ → $x=10$?
3. OR did Bob produce exactly 35 items last week and 37 items this week? If so, then the first item was produced at a rate of $x$ and the second item was produced at a rate of $1.5x$, so that $x+1.5x=30$ → $2.5x=30$ → $x=12$.

We’ve got a few options here, so let’s try each individually. Remember, we want to solve for the number of items Bob produced last week, so we’ll use that equation:

1. $x=15$, $480=15i$ → $i=32$
2. $x=10$, $480=36(10)+1.5(10)(36-i)$ → $480=360+15(36-i)$ → $120=15(i-36)$ → $8=i-36$ → $i=44$

We already have two possible solutions, so we don’t need to look at our third, more complicated option. We cannot determine whether Bob made 32 or 44 items last week, so we cannot solve the problem with both statements. The correct answer is E: Statements 1 and 2 TOGETHER are NOT sufficient to answer the question.

GMAT Data Sufficiency Question 3

Reading through the question, we see that we’re dealing with a group of houses where some have a swimming pool and some have a patio. Scanning over the statements, we see that some houses have only a pool, some houses have only a patio, some have neither, and some have both. Almost anytime we see the word “both” in GMAT Quant questions, we’re dealing with an overlapping sets problem — we are looking at two criteria (here, having a pool and having a patio) and where they overlap (here, having “both” a pool and a patio).

Overlapping sets problems have a lot of information, so it’s really easy to get lost in them. A good trick is to use a visual representation to keep track of what you know:

• For two overlapping criteria, use a table, where each axis represents one criterion.
• For three overlapping criteria, use a venn diagram, where each circle represents a criterion.

Here, we have two overlapping sets, so we’re going to use a table. We’ll go ahead and fill in only what was stated directly in the question. We want to find the total number of houses that have a Pool, so we’ll represent that in our table as $x$:

Because of the way we’ve set the table up, the two numbers in each row should add up to the total at the end of the row and the two numbers in each columns should add up to the total at the bottom of the column. This means that if we have at least two of the three values in each row or column, we should be able to solve for the third. Looking at our table, we see that our total row along the bottom has two values. If there are 75 houses in total and 48 of those houses have patios, 75 – 48 = 27 of those houses must not have patios. We can go ahead and fill that information in our table:

Doesn’t seem like we can get much more out of our table at this point, so we’ll move on to our Statements.

Statement 1

To start we’ll fill in the information directly given in the statement:

We see that our first column has two values, so we should be able to solve for the third. If there are 58 houses with patios and 38 of those houses do not have pools, 48 – 38 = 10 of those houses must have pools:

Looking at the row and the column that contain $x$, we see that we only have one number value for each, meaning that we can’t solve for $x$. Statement 1 is insufficient.

Statement 2

This statement doesn’t give us any concrete numbers to work with, but it does tell us that two of our values (houses with both pools and patios and houses with neither pools nor patios) are equal to each other. When we know that the same number shows up in two places, but we don’t know what that number is, it’s a good idea to represent that number with a variable — if we represent both values as, say, $n$, we know that they are the same number and can combine or eliminate them down the line:

Now we’re getting somewhere! We don’t have two number values in any row or column, but we can use both the top row and the second column to represent No Patio/Pool with variables: if there are $x$ total houses with pools and $n$ of those houses have patios, $x-n$ must not have patios, and if there are 27 total houses that do not have patios, and $n$ of those houses do not have pools, $27-n$ must have pools:

Since the number of houses with no patio and a pool equals both $x-n$ and $27-n$, we can set the two equal to each other to solve for $x$:

$x-n=27-n$

$x=27$

We were able to determine that 27 houses have pools, which means that Statement 2 is sufficient. The correct answer is B: Statement 2 alone is sufficient to answer the question.

GMAT Data Sufficiency Question 4

Right away, the word “ratio” tips us off that we’re dealing with ratios in this problem, and the word “greater” indicates that we’re dealing with inequalities. However, as we read through the rest of the problem, things start to get a little more confusing: one company, two divisions, full-time and part-time employees … this is a lot to process.

We do see the words “either” and “both” though, which should get some overlapping sets wheels turning in our minds. We see that, like the problem above, we have two criteria: employees can belong to Division X or Division Y and can be full-time or part-time. Since this problem doesn’t have any concrete numbers, it isn’t strictly necessary to make a table like we did in the problem above. However, it can still be helpful to define the relationships between our sets and build equations:

We know that the two numbers in each row should add up to the total at the end of the row and the two numbers in each columns should add up to the total at the bottom of the column. So we can now build 6 different equations:

1. $\Full\-\Time \@ \X + \Part\-\Time \@ \X = \Employees \@ \X$
2. $\Full\-\Time \@ \Y + \Part\-\Time \@ \Y = \Employees \@ \Y$
3. $\Full\-\Time \@ \Z + \Part\-\Time \@ \Z = \Employees \@ \Z$
4. $\Full\-\Time \@ \X + \Full\-\Time \@ \Y = \Full\-\Time \@ \Z$
5. $\Part\-\Time \@ \X + \Part\-\Time \@ \Y = \Part\-\Time \@ \Z$
6. $\Employees \@ \X + \Employees \@ \Y = \Employees \@ \Z$

Now that we have this set up, let’s figure out what the question is asking for. Like with all word problems, we want to translate words into math. Whenever we’re dealing with ratios, we should remember that ratios can (and should) be expressed as fractions:

Is ${\full\-\time \@ \X}/{\part\-\time \@ \X} > {\full\-\time \@ \Z}/{\part\-\time \@ \Z}$?

or in other words, are there more full-time employees for every part-time employee at Division X than at the entire company?

Statement 1

This Statement gives us information about the ratio of full-time employees to part-time employees at Division Y compared to Company Z:

${\full\-\time \@ \Y}/{\part\-\time \@ \Y} < {\full\-\time \@ \Z}/{\part\-\time \@ \Z}$

Now, before we rule this statement out because it doesn’t tell us anything about Company X, let’s see how we can use our equations to substitute X back into the inequality. Looking at equations 4 and 5, we see that we can rearrange the equations to give:

4. $\Full\-\Time \@ \Y = \Full\-\Time \@ \Z – \Full\-\Time \@ \X$
5. $\Part\-\Time \@ \Y = \Part\-\Time \@ \Z – \Part\-\Time \@ \X$

Subbing those into our inequality gives us:

${\full\-\time \@ \Z – \full\-\time \@ \X}/{\part\-\time \@ \Z – \part\-\time \@ \X} < {\full\-\time \@ \Z}/{\part\-\time \@ \Z}$

Let’s think about what we know about fractions. To make a fraction smaller, we need to either

1. decrease the numerator relative to the denominator
2. increase the denominator relative to the numerator

We know that we are decreasing both the numerator and denominator, so we must be decreasing the numerator by a greater percentage than we are decreasing the denominator. This means that the number of full-time employees at Division X is larger relative to the number of part-time employees at Division X than the number of full-time employees at Company Z to the number of part-time employees at Company Z. In other words, the ratio of the number of full-time employees to the number of part-time employees is greater for Division X than for Company Z. Statement 1 is sufficient.

Statement 2

Like with Statement 1, let’s translate this into math:

$\full\-\time \@ \X > {1/2}\full\-\time \@ \Z$

$\part\-\time \@ \Y > {1/2}\part\-\time \@ \Z$

Given equation 5, the second half of our statement also tells us that

$\part\-\time \@ \X < {1/2}\part\-\time \@ \Z$

This means we can write the ratio of full-time employees at Division X as

${>{1/2}\full\-\time \@ \Z}/{<{1/2}\part\-\time \@ \Z}$

or, cancelling the {1/2} in both the numerator and denominator,

${>\full\-\time \@ \Z}/{<\part\-\time \@ \Z}$

To make a fraction larger, we need to either:

1. increase the numerator relative to the denominator
2. decrease the denominator relative to the numerator

Here, we’re doing both: full-time employees at Division X is greater than full-time employees at Company Z and part-time employees at Division X is less than part-time employees at Company Z. This means that

${\full\-\time \@ \X}/{\part\-\time \@ \X} > {\full\-\time \@ \Z}/{\part\-\time \@ \Z}$

which is exactly what we’re trying to solve for. Statement 2 is sufficient.

Since both statements are sufficient to solve the problem individually, the correct answer is D.

GMAT Data Sufficiency Question 5

The word “remainder” tells us that we’re dealing with, what else, a remainder problem. Remainder problems scare a lot of students because they don’t involve an easy to use/memorize formula. However, this means that we have a great opportunity to plug in numbers.

Even though this isn’t technically a “word problem”, we still need to translate the words into math to build an equation:

${(n-1)(n+1)}/24 = \? \| \R\: r$

Let’s make a note that $n$ must be a positive integer and move on to our statements.

Statement I

This statement tells us that $n$ is not divisible by two — in other words, it’s telling us that $n$ is odd. Let’s try plugging in numbers. When we select numbers to plug in, our goal is to prove that the statement is insufficient: in other words, we want to pick numbers that will give us different results. We also want to pick numbers that are easy to work with to save time.

We see that one of the values in our numerator is (n-1), which means that picking 1 will give us a zero in our numerator. That seems like it’ll give us an interesting result, so we’ll give it a shot:

${(1-1)(1+1)}/24$

${(0)(2)}/24$

$0/24$

$0 | \R\: 0$

So when $n=1$, $r=0$. Let’s try our next odd number up, $3$ — based on the size of the denominator, it seems like our numerator will be smaller than the denominator, giving a solution of 0 with positive remainder:

${(3-1)(3+1)}/24$

${(2)(4)}/24$

$8/24$

$0 | \R\: 8$

So when $n=3$, $r=8$. This means that $r$ can be either 0 or 8 given Statement 1. Since we can’t find a single value for $r$, Statement 1 is insufficient.

Statement II

This statement tells us that $n$ is not divisible by three. That knocks $n=3$ out of the running. $n=1$ still works, however, so we know that $r=0$ is still a possibility given Statement 2.

Since we tried only odd numbers last time, let’s try an even number this time to see if that changes things up: we’ll do 2 to keep our numbers easy to work with:

${(2-1)(2+1)}/24$

${(1)(3)}/24$

$3/24$

$0 | \R\: 3$

So when $n=2$, $r=3$. This means that $r$ can be either 0 or 3 given Statement 2. Like before, since we can’t find a single value for $r$, Statement 2 is insufficient.

BOTH

Putting these two statements together, we know that $n$ must be odd and cannot be divisible by 3: so we have 1, 5, 7, 11, etc. These numbers are going to get pretty big pretty fast, so let’s try them from smallest to greatest. We already know that $r=0$ when $n=1$, so we want to find a positive value for $r$ to prove that both statements are insufficient:

${(5-1)(5+1)}/24$

${(4)(6)}/24$

$24/24$

$1 | \R\: 0$

So when $n=5$, $r=0$. That’s the same as when $n=1$. Let’s try the next number up, 7:

${(7-1)(7+1)}/24$

${(6)(8)}/24$

$48/24$

$2 | \R\: 0$

So when $n=7$, $r=0$. We’re starting to see the hints of a pattern here. Let’s try one more, 11, to be sure:

${(11-1)(11+1)}/24$

${(10)(12)}/24$

$120/24$

$5 | \R\: 0$

So when $n=7$, $r=0$. Once we’ve tried at least 4 numbers in a series and confirmed that we’ve done a reasonable job picking numbers that would give us different results, we can usually determine that we have a pattern. Here, we can say confidently that given Statement 1 and Statement 2, $r$ will always be 0. This means that the correct answer is C: BOTH statements together are sufficient.

Key Takeaways: Learning From The Hardest Data Sufficiency Questions

So what can the hardest GMAT Quantitative questions teach us about GMAT Data Sufficiency questions in general?

1. Visuals — drawings, tables, Venn diagrams, graphs, what have you — are our friends, and not only on Geometry questions. On the GMAT, advanced quant questions are hard to conceptualize, and drawing things out keeps us from having to keep track of a lot of complicated relationships in our heads.
2. Whenever we have words, we need to translate them into math. Like visuals, building equations helps us take hard GMAT math questions and distill them into something we can work with. Use math-y keywords, like “greater than”, “equal to”, “divided by”, etc. to break sentences down into their component parts.
3. The hardest GMAT Data Sufficiency questions often involve more logic than simple math, especially around number sense concepts. Being comfortable making inferences based on what we know can save us a lot of time compared to slogging through a bunch of proofs.
4. That said, picking numbers to plug in is a great Data Sufficiency strategy that can help us avoid overthinking a problem or confirm our logic. Always pick numbers that you think will yield two different solutions, making the statement insufficient.

What’s Next?

What are the math concepts tested on the GMAT? The best GMAT math tricks and shortcuts? The most important Data Sufficiency tips? These articles expand on the concepts used in these five problems, explaining what you need to know about GMAT Data Sufficiency before test day.

Looking to improve your Quant score? This article explains what exactly a good GMAT Quantitative score is.

If you’d like similar analyses of the hardest questions from other GMAT question types, check out our post on the five hardest Sentence Correction questions.

The post The 5 Hardest GMAT Data Sufficiency Questions appeared first on Online GMAT Prep Blog by PrepScholar.

Luckily, we’ve done the hard work of distilling everything you need to know about GMAT exponents! In this post, we’ll cover all the relevant rules, properties, formulas, and shortcuts. We’ll also walk you through an example of every main kind of exponent question that you’ll encounter on the test, so you can see these formulas in action. By the end, you really will be an exponent expert!

What Are Exponents? Definitions and Terminology

Below are the basic definitions and terms that you need to know for GMAT exponents. Most of this is probably very familiar to you, but make sure you understand everything before moving on.

Definition of Exponents

Let’s start with the basics. An exponent indicates how many times a given number should be multiplied by itself. The number itself is called the base number, and for any base number $k$, the exponent $n$ says how many times to use that number in a multiplication. The exponent is written in superscript to the right of the base number:

$$k^n$$

We’re most familiar with the “square,” which is what it’s called when the exponent is 2.

$$k^2 = k × k$$

But an exponent can be any number. Here are some basic examples:

$$2^2 = 2 × 2 = 4$$
$$3^2 = 3 × 3 = 9$$
$$4^2 = 4 × 4 = 16$$
$$5^2 = 5 × 5 = 25$$

$$2^3 = 2 × 2 × 2 = 8$$
$$3^3 = 3 × 3 × 3 = 27$$
$$4^3 = 4 × 4 × 4 = 64$$

$$2^4 = 2 × 2 × 2 × 2 = 16$$
$$3^4 = 3 × 3 × 3 × 3 = 81$$
$$4^4 = 4 × 4 × 4 × 4 = 256$$
$$5^4 = 5 × 5 × 5 × 5 = 625$$

Another common term for exponents is “powers.” We can refer to $k^n$ as “the $n$th power of $k$,” or “$k$ to the power of $n$.” Raising any number to the power of 2 is called squaring that number, and raising the number to the power of 3 is called cubing the number.

Definition of Roots

The square root of any number $y$ is a number that, when squared, equals $y$. (If $y = k^2$, then $k$ is the square root of $y$.)

The same goes for the cube root: the cube root of any number $y$ is a number that, when cubed, equals $y$.

And so on for every exponent.

The square root of any number is represented by this symbol, called a “radical”:

$$√4 = 2$$
$$√25 = 5$$

Any root beyond a square root (cube roots and up) is represented by a little number in superscript to the left of the radical that indicates the power. Below are examples of cube roots:

$$√^3{8} = 2$$
$$√^3{125} = 5$$

Properties of Exponents

Now that we’ve reviewed the definitions, let’s get into the properties of exponents that you need to know for the GMAT.

Property of the Exponent 1

Any number to the power of 1 is just itself, which is why you don’t really see numbers with exponents of 1 next to them, as it just isn’t necessary.

$$2^1 = 2$$
$$8^1 = 8$$
$$5093^1 = 5093$$

Property of the Exponent 0

Any number to the power of 0 is 1:

$$2^0 = 1$$
$$5^0 = 1$$
$$217^0 = 1$$
$$509395934234^0 = 1$$

Squaring a Number Between 0 and 1

As you can see from the examples above, when you square (or raise to any higher power than 2) a base number that is greater than 1, the result will be a larger number.

When you square (or raise to any higher power than 2) a base number that is between 0 and 1, the result will be a smaller number. Here’s an example:

$$(1/2)^2 =1/4$$
$$1/4 < 1/2$$

Positive and Negative Powers

Positive and negative powers and their roots have particular properties.

Every Positive Number Has Two Square Roots

Every positive number has two square roots: the positive square root, and the negative square root. This is because a negative multiplied by a negative is a positive. Here’s an example:

$$√4 = 2  (-2)$$
$$2 × 2 = 4$$
$$(-2) × (-2) = 4$$

Cubes and Other Odd Powers Have Only One Real Root

Cubes, on the other hand, have only one real root, because a negative times a negative times a negative equals a negative, and a positive times a positive times a positive equals a positive.

$$√^3{8} = 2$$
$$2^3 = 8$$
$$√^3{-8} = -2$$
$$(-2)^3 = -8$$

Odd powers will always have the same sign as their roots.

Negative Squares

The square root of a negative number is not a real number.

$√(-9)$ = not a real number

This applies to all even powers ($x^2$, $x^4$, $x^6$…and so on)

Negative Exponents

Any base number to a negative power equals 1 divided by the base number to the positive version of the exponent:

x^-r = 1/x^r  , where $r$ is any positive integer and $x$ is any positive number.

$$5^(-2) = 1/(5^2) = 1/25$$

Fractional Exponents

Fractional exponents look tricky at first. Here are all the equivalencies ($x$ is any positive number and $r$ and $s$ are any positive integers):

$$x^{r/s} = (x^{1/s})^r = (x^r)^{1/s} = √^s{r}$$

The two middle steps here simply illustrate the ‘exponent to the power of another exponent’ rule; the most important thing to remember is that x^r/s = ^s√(x^r). Let’s see this in action:

$$27^{2/3} = (27^{1/3})^2 = (27^2)^{1/3} =√^3{27^2} = √^3{729} = 9$$

$$8^{1/3} =√^3{8} = 2$$

$$9^{1/2} = √9 = 3$$

So any number to the power of $(1/2)$ is just the square root of that number, and any number to the power of $1/3$ is just the cube root, and so on.

The Cyclicity Property

Successive powers have what’s called a “cyclicity” that manifests in the units digit. Take 3, for example:

$$3^1 = 3$$
$$3^2 = 9$$
$$3^3 = 27$$
$$3^4 = 81$$
$$3^5 = 243$$
$$3^6 = 729$$

Pay attention to the units digits. Notice a pattern? The last digit repeats itself after a cycle of 4, and the cycle is 3, 9, 7, 1.

This repetition of numbers after a particular stage is called the cyclicity of numbers. This comes in handy when you need to find the unit digit of a given number to a certain power on a GMAT question, as you just need to find the number on which the cycle stops.

Rules for Manipulating Exponents

Below are the rules for doing algebra and arithmetic with exponents that you’ll need to know for GMAT exponent questions.

Multiplying and Dividing With Exponents

Below are the rules for multiplying and dividing with exponents. Note: You can’t combine bases or exponents when adding or subtracting terms—the algebraic equivalents are much more complex. Which is why we’re jumping first into multiplication and division!

Multiplying and Dividing with Same Base, Different Exponents

If you have to multiply two values together that have the same base number but different exponents, you can simply add the exponents together. Here’s an example:

$$3^2 × 3^5 = 3^(2+5) = 3^7 = 2187$$

Algebraically, this rule is represented as follows:

$$x^r × x^s = x^(r+s)$$

where $x$ is any positive number and $r$ and $s$ are any real numbers.

This division rule is the opposite of the rule above. If you have to divide two values together that have the same base number but different exponents, you can simply subtract the exponent of the denominator from the exponent of the numerator:

$${x^r}/{x^s} = x^(r-s)$$

where $x$ is any positive number and $r$ and $s$ are any real numbers. Here’s an example:

$$4^5/4^2 = 4^(5-2) = 4^3 = 64$$

Multiplying and Dividing with Different Bases, Same Exponent

If you have to multiply numbers with the different base numbers but the same exponent, you simply multiply the base numbers and keep the exponent as it is:

$$x^r × y^r = (xy)^r$$

where $x$ and $y$ are any positive numbers and $r$ is any real number. Here’s an example

$$3^2 × 5^2 = (3 × 5)^2 = 15^2 = 225$$

For division, the opposite rule applies. A fraction to any positive power equals the numerator to that power divided by the denominator to that power:

$$(x/y)^r = {x^r}/{y^r}$$

where $x$ and $y$ are any positive numbers and $r$ is a real number.

$$(3/4)^2 = {3^2}/{4^2} = 9/16$$

Exponents Raised to Another Power

Exponents can be layered, like in this example:

$$(4^2)^3$$

When you have a value with an exponent raised to the power of another exponent like this, you simply multiply the two exponents:

$$(4^2)^3 = 4^(2×3) = 4^6 = 4096$$

In general terms, we can write the rule as such:

$$(x^r)^s = x^{rs}$$

where $x$ is a positive number and $r$ and $s$ are real numbers.

Simplifying Exponents and Base Numbers With Factors

Base numbers that are already squares, cubes, etc of other numbers can be simplified. To use the square root as a base number, you multiply the exponent by 2 to get an equivalent expression. Here’s an example:

$$4^14 = (2^2)^14 = 2^28$$

For the cube root, you’d multiply the exponent by 3:

$$8^7 = 2^21$$

And so on for all the powers.

GMAT Exponent Practice Problems

Below are examples of the key kinds of GMAT exponent questions you will encounter on the exam, including data sufficiency and problem solving varieties.

GMAT Exponent Question 1: Exponents and Cyclicity

This question is simpler than it looks! We just need to find the cyclicity of powers of 4 and powers of 9. One thing you can do is plug in number values for $a$ and $b$, starting with 1 for each. Let’s do $a$ first:

If $a$ = 1, $x$ = 4¹ = 4
If $a$ = 2, $x$ = 4² = 16
If $a$ = 3, $x$ = 4³ = 64
If $a$ = 4, $x$ = 4⁴ = 256

…Notice a pattern yet? There is a cycle of 2: the units digits for powers of 4 is either 6 or 4.

Now let’s do $b$:

If $b$ = 1, $y$ = 9¹ = 9
If $b$ = 2, $y$ = 9² = 81
If $b$ = 3, $y$ = 9³ = 729
If $b$ = 4, $y$ = 9⁴ = 6561

The units digits for powers of 9 is either 9 or 1, so there’s also a cyclicity of 2.

Now, let’s multiply the possibilities of units digits for $x$ with the possibility of units digits for $y$. A cycle of 2 possibilities times a cycle of 2 other possibilities = 4 possible combinations: (4×9), (4×1), (6×9), and (6×1)

$$4 × 9 = 36$$
$$4 × 1 = 4$$
$$6 × 9 = 54$$
$$6 × 1 = 6$$

So we’re looking for either 6 or 4. (B) is the answer.

GMAT Exponent Question 2: Exponents, Cyclicity and Remainders

Cyclicity is a concept that comes up a lot on the more challenging GMAT exponent questions, so we’ve included another example. Unlike the last question, this one doesn’t ask directly about units digits, which makes it even tougher!

We’re given that $n$ is a positive integer, so the cyclicity rule applies here. First, let’s find the cyclicity of 3, so we can determine the units digit of 3⁽⁸ⁿ⁺³⁾ :

3¹ → the units digit is 3
3² → the units digit is 9
3³ → the units digit is 7
3⁴ → the units digit is 1
3⁵ → the units digit is 3 again

… and so on

So, the units digit of 3 in positive integer power has a cyclicity of 4 for the units digit (3, 9, 7, 1).

3⁽⁸ⁿ⁺³⁾ will have the same units digit as 3³, which is 7, which we can see when we plug in values for $n$ in 3⁽⁸ⁿ⁺³⁾:

$n$ = 1 → 3¹¹, units digit is 7
$n$ = 2 → 3¹⁹, units digit is 7
$n$ = 3 → 3²⁷, units digit is 7

Thus, the units digit of 3⁽⁸ⁿ⁺³⁾ + 2 = 7+2 = 9.

Lastly, we have to divide by 5. Any positive integer with the units digit of 9 divided by 5 gives the remainder of 4. The answer is (E).

You could also just plug in an easy number for $n$ from the start and do some heavy multiplication and long division, but this will take much longer, since the calculations are very unwieldy.

GMAT Exponent Question 3: Factors and Simplifying

First, let’s simplify 4¹⁷ to get to the same base number:

4¹⁷ = 2³⁴, so we have 2³⁴ – 2²⁸

Remember, this is a subtraction equation with exponents, which means we can’t do the same simple swapping that we can with division: 2³⁴ – 2²⁸ does NOT equal 2⁶. Instead, let’s do a factoring and utilize the distributive property. A common factor of 2³⁴ and 2²⁸ is actually 2²⁸:

$$2^34 – 2^28 = 2^28 × (2^6 – 1) = 2^28 × (64 – 1) = 2^28 × 63$$

Suddenly, this problem is a lot easier. 2²⁸ is made up of all only 2’s, so the greatest prime factor is just going to be 2. What about the prime factors of 63?

$$63 = 9 × 7 = 3 × 3 × 7$$

So the prime factors of 2²⁸ × 63 are 2, 3, and 7. Hence, the largest prime factor is 7, and (D) is the answer.

GMAT Exponent Question 4: Negative Exponents

Remember: odd powers have the same sign as their roots, so given that $-37 = x^5$, then $x$ must also be negative.

The next thing to acknowledge is that, since we don’t have a calculator, we’re not going to be able to find the 5th root of -37. And the GMAT wouldn’t want us to: they want us to use our understanding of exponent rules and properties to get to the right answer.

So first, let’s try to find a known number whose value when raised to the fifth is in the ballpark of -37, so we can establish a baseline. $x = -2$ fits the bill:

$$(-2)^5 = -32$$

That’s pretty close. What happens when we try $x = -3$?

$$(-3)^5 = -243$$

That’s way off. So $x$ must be a teeny tiny bit less -2 (remember, we’re in the negatives here, so less means a tiny bit closer to -3 on the number line). Something around (-2.1). Even though that sounds vague, that’s all we need to know to estimate our way to the right answer.

We can easily eliminate (B), since we’ve already shown that $x$ must be less than -2.

We can also eliminate (C), since $(-2)^2 = 4$, and $x$ is actually a little more like (-2.1), so it’s definitely not going to be less than 4.

We can also get rid of (A). $√-x$ is about equal to $√-(-2.1)$, and the double negative cancels out, leaving $√2.1$. There’s no way the $√2.1$ is greater than 2.

$x^4$ would be $(-2.1)^4$, or 16.something, so it’s definitely not greater than 32.

That leaves us with (D). Let’s check it:

$$x^3 ≈ (−2.1)^3 ≈ −8.something.$$

-8.something, no matter what that “something” is, is definitely less than −8.nothing, so option (D) must be true.

GMAT Exponent Question 5: Exponents and Consecutive Integers

Some GMAT questions combine exponents with the concept of consecutive integers. Here’s an example:

Let’s solve this one by picking numbers.

Let $r$ = 1, $s$ = 2, and $t$ = 3:

$$3^r + 3^s + 3^t = 3 + 3^2 + 3^3 = 3 + 9 + 27 = 39$$

The greatest prime factor of 39 is 13 (13 × 3 = 39).

Does this work for every consecutive integer set? Let’s pick another and see. Let $r$ = 2, $s$ = 3, and $t$ = 4:

$$3^r + 3^s + 3^t = 3^2 + 3^3 + 3^4 = 9 + 27 + 81 = 117$$

The greatest prime factor of 117 is 13 (13 × 3 × 3 = 117).

We can now see that this will work for every consecutive integer set. (E) is the answer.

GMAT Exponent Question 6: Data Sufficiency and Exponents

Here is a typical data sufficiency exponents question:

Rather than jumping right to the statements, let’s first simplify the question stem. The rule for dividing with the same base, different exponents tells us that $x^(r-s) = x^r/x^s$. So:

$$5^(−k) < 5^(1−2k)$$
$$= 5^(−k) < 5^1/5^2k$$
$$= 5^(k) < 5$$

Now, onto statement 1. Let’s rearrange it slightly:

$$2 < 1 – k$$
$$2+k < 1$$
$$k < -1$$

If $k$ is less than -1, then $5^k$ will always be less than 5, as $5^k$ would equal $1/5^(+ version of k)$. So statement 1 is sufficient.

Onto statement 2.

$$2k<3$$
$$= k < 3/2$$

If $k$ is less than 3/2 or 1.5, $k$ could still be some value like 1.4, and 5^1.4 is greater than 5. So statement 2 is insufficient.

The answer is B.

4 Key Tips for GMAT Exponents

GMAT exponent practice problems can be challenging. Here are our top tips for nailing them.

#1: Memorize the Exponent Rules and Properties Above

The key to GMAT exponent questions is to know the above exponent rules and properties cold. Many exponent questions will not explicitly say so, but they’ll require you to spot the applicability of one of the rules for multiplying, dividing, cyclicity, etc. Implementing these rules with ease will help you simplify equations that seem more complex than they really are.

#2: Memorize Squares of 2-15 and Units Digits Cycles Through 12

Just like you drilled your multiplication tables as a kid, you should drill all the squares of 2 – 15. Also, for those pesky digit and remainder questions, it’s helpful to memorize the units digits exponent cycles for 2-12.

For the lower numbers (like 2 – 5), you may even want to memorize up to the fifth power.

This instantaneous knowledge comes in very handy, like on GMAT Exponent Question 4 above, in which it was extremely helpful to know offhand that 2⁵ = 32.

Here are all the squares of 2-15:

2² =4
3² =9
4² =16
5² =25
6² = 36
7² =49
8² = 64
9² = 81
10² =100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225

For cyclicity questions, here is an ordered list of units digit cycles for 2-12 powers:

2 = 2, 4, 8, 6
3 = 3, 9, 7, 1
4 = 4, 6
5 = 5
6 = 6
7 = 7, 9, 3, 1
8 = 8, 4, 2, 6
9 = 9, 1
10 = 0
11 = 1
12 = 2, 4, 8, 6

#3: Pick Numbers Strategically

Many GMAT exponent practice problems don’t require you to solve all of the equations within them. Sometimes picking a simple number and substituting it for the unknown variable works even better—and makes the problem simpler and easier—than actually solving a complex algebraic equation. Just like in example question 5 above, picking a value to stand in for the unknown can save time and make it much easier to visualize and solve the problem.

#4: Estimate When Given Irrational Roots

Some GMAT questions will give you values they know you can’t find without a calculator, like the fifth root of 37 in one of the examples above. In these kinds of questions, you really are supposed to estimate! Use the value that gets you the closest to approximate, and eliminate answer options that can’t possibly work. By that point, there will be only one left.

What’s Next?

Looking for more GMAT exponents practice? We’ve got you covered.

Alternatively, maybe you’d like to move on to everything you need to know about GMAT integers.

We also have some more general GMAT Quant tips and tricks to help you develop strategies to master the Quant section.

Happy studying!

The post GMAT Exponents: Rules, Tips, and Practice appeared first on Online GMAT Prep Blog by PrepScholar.

Never fear! In this post, we’ll tell you everything you need to know about fractions and decimals for the GMAT. We’ll give you a refresher on all the relevant rules and formulas, tips and tricks for every question you’ll see on them on the GMAT, and some example questions with thorough explanations so you can see these strategies in action.

GMAT Fractions: Rules to Know

Below are all the rules that you need to know about fractions for the GMAT.

Definition of a Fraction

A fraction is a visual representation of a number divided by another number. The top number of a fraction is called the numerator, and it’s the number being divided. The bottom number is called the denominator, and it’s the number that the top number is divided by. 

In the fraction $n/d$, $n$ is the numerator (the top number) and $d$ is the denominator (the bottom number). The fraction 1/2, for example, is 1 divided by 2 or one-half.

0 can’t be the denominator in a fraction, because dividing by 0 is undefined.

Two fractions are equivalent when they represent the same number. For example: 2/8 and 4/16 are equivalent, because they both equal 0.25.

When both the numerator and the denominator can be be divided evenly by the same number, the fraction can be simplified into its lowest terms (the smallest equivalent fraction). The largest number that both the numerator and the denominator can be divided by is called the greatest common factor (GCF) or greatest common divisor (GCD). Dividing both by the GCD simplifies the fraction into its lowest form.

For example, 2 is the greatest common factor of both 2 and 8. For the fraction 2/8, when you divide the numerator and the denominator by 2, you get 1/4—the lowest or most simplified form of the fraction. When dealing with fractions in equations, you almost always want them to be in their simplest forms, so that they’re easier to do calculations with.

Multiplying and Dividing With Fractions

Multiplying with fractions is easy: you just multiply the numerators and multiply the denominators.

For example:

$7/10 × 4/9 = 28/90$ or  $14/45$

To divide with fractions, “flip” the fraction after the division sign (called the divisor) so that the denominator becomes the numerator and vice versa, and then multiply with that number.

Example:

$${7/10} ÷ {4/9} = 7/10 × 9/4 = 63/40$$

This “flipped” version of a fraction is called its reciprocal or inversion. The reciprocal or inversion of any fraction $n$/$d$ is $d$/$n$ (where $n$ and $d$ ≠ 0).

Adding and Subtracting With Fractions

Two fractions with the same denominator can be added or subtracted easily. You simply add or subtract the numerators, and leave the denominators the same.

$$3/8 – 2/8 = 1/8$$
$$5/9 – 1/9 = 4/9$$

If you need to add or subtract with fractions that don’t have the same denominator, then you can do the opposite of simplifying and express them as equivalent fractions with the same denominator. As long as you multiply or divide the numerator and the denominator of a fraction by the same number, it will remain equivalent:

$$3/8 × 9/9 = 27/72$$
$$2/8 = 27/72$$

This gives us an always true rule, which is helpful in algebraic expressions:

$${x + y}/z = x/z + y/z$$

When adding or subtracting fractions with different denominators, multiplying the fractions so that the denominators represent the least common multiple (the lowest number that both denominators factor into) is usually the simplest way to go and makes doing calculations easier than working with larger numbers.

Example:

$$1/3 + 3/4$$
$$LCM = 12$$
$$1/3 × 4/4 = 4/12$$
$$3/4 × 3/3 = 9/12$$

$$1/3 + 3/4 = 4/12 + 9/12 = 13/12=1 1/12$$

By multiplying 3 and 4, we see that the LCM is 12. We then convert both fractions so that they both have a denominator of 12. Then it’s easy to add them together!

Mixed Numbers

A number made up of a whole number and a fraction (like 1 and 1/12 above) is called a mixed number. To change a mixed number into a fraction, multiply the whole number by the denominator and then add the result to the numerator. This then becomes the new numerator.

$$6 4/9 = {(6 × 9)+ 4}/9 = {54 + 4}/9 = 58/9$$

GMAT Decimals: Rules to Know

Below are all the rules you need to know about decimals for the GMAT.

Definition of a Decimal

Decimals and fractions are both ways of representing number values in between integers or whole numbers.

In the decimal system, the distance from the decimal point represents the place value of each number. For example, the number 412.735, has 4 in the “hundreds” place, 1 in the “tens” place, and 2 in the “ones” or “units” place; and then after the decimal, 7 in the “tenths” place, 2 in the “hundredths” place, and then five in the “thousandths” place. Here’s a table illustrating this information:

The Zero Rule

After you pass the decimal point, you can add an infinite number of zeros to the end of a number:

$$1.435 = 1.4350 = 1.4350000000000000000 = 1.43500000000000000000000000000000000000000$$

This rule only applies to after the end of the number after the decimal point:

$$1435 ≠ 14350$$
$$1435 = 1435.0 = 1435.0000000000000000000000000$$

Adding and Subtracting With Decimals

To add or subtract two decimals, the decimal places of each need to line up. You can use the zeros rule above if one number has fewer digits to the after decimal place than the other:

7.872 + 6.30285 =

    7.87200
+  6.30285
= 14.17485

Multiplying and Dividing With Decimals

When multiplying decimals, do not line up the decimal point: the decimal gets inserted afterward. Instead, multiply the two numbers as if they were whole numbers. Once you have the product, it’s time to put the decimal back in.

But how do you figure out where the decimal place goes? The rule is that you add up the amount of numbers after the decimal of each number you multiplied, and that sum is the number of decimal places that should be in the product: 

1.56 (two numbers after the decimal)
× 2.3 (one number after the decimal)
= 3.588 (three decimals—sum of one and two above)

To divide any number (a dividend) by a decimal (the divisor) using long division, move the decimal point of the divisor to the right however many places it takes to get to a whole number, and then move the decimal point in the dividend over by that many places as well. If there’s still a decimal left in the dividend after this, make sure you place it directly above the dividend in the answer.

Finally, do the division as you normally would. For example,

90.625 ÷ 12.5 becomes 906.25 ÷ 125

Then you do the long division with 906.25 as the dividend and 125 as the divisor, making sure to place the decimal in the answer directly above its place in the dividend.

Converting Decimals to Fractions

Every decimal can be expressed as a fraction with these steps:

1. Move the decimal point over however many places to the right until it becomes a whole number
2. Use that as the numerator
3. Place in the denominator the power of 10 that corresponds to however many places you moved the decimal over:

$$0.5 = 5/10$$
$$0.05 = 5/100$$
0.005 = 5/1000 or  1/200

Another way to think of it is that the number of places you move the decimal to the right to make the numerator a whole number is the number of 0’s you’ll add after 1 in the denominator.

Numbers less than -1 or greater than +1 with decimals can be expressed as fractions using the above rule in combination with the mixed number rule:

$$7.5 = 7 5/10$$
$$= {(7 × 10) + 5}/10$$
$$= [70 + 5]/10 = 75/10$$

And this can be simplified:

$$75/10 = 15/2$$
$$7.5 = 15/2$$

Converting Fractions to Decimals

When you plug in a fraction as a division problem into a calculator, it automatically gives you the decimal equivalent. Unfortunately, we don’t have access to a calculator on the GMAT Quant section, but the manual conversion isn’t too hard.

You can always find the decimal equivalent of a fraction with long division, by using the numerator as the dividend and the denominator as the divisor. But there’s an alternative method that can be handy as well.

First, find a number you can multiply the denominator of the fraction by to make it 10, or 100, or 1000, or any 1 followed by 0s. Next, multiply both numerator and denominator by that number to get its equivalent expression. Finally, write down just the top number, putting the decimal point in the corresponding place: one space from the right hand side for every zero in the bottom number.

Here’s an example using the fraction 3/4:

$$3/4 = ?/100$$
$$4 × 25 = 100$$
$${3 × 25}/{4 × 25} = 75/100$$
$$= 0.75$$

Scientific Notation of Decimals

“Moving over” decimal places with powers of 10 is a useful concept. Sometimes, numbers are expressed as the product of a number multiplied by 10 to a certain power. The power represents how many places you need to “move” the decimal point to get to its decimal expression. The sign of the exponent indicates which direction: a positive exponent moves the decimal over to the right, and a negative exponent moves it to the left.

Examples:

$$0.0489 = 4.89 × 10^{-2}$$
$$60235 = 6.0235 × 10^4$$
$$540 = 5.4 × 10^2$$
$$29 = 2.9 × 10^1 = 2.9 × 10$$

Terminating and Recurring Decimals

Terminating decimal GMAT questions sound scary if you don’t know what a terminating decimal is, but it’s actually deceptively simple.

All of the decimals in the examples above have an end. They are called terminating decimals because there aren’t an infinite amount of numbers after the decimal point. Any terminating decimal is can be represented as a fraction with a power of ten in the denominator. For example, 0.0462 = 462/10000 = 231/5000.

It’s possible to have an infinite amount of numbers after the decimal point. 1/3 is an example of a recurring decimal, as we can see when we convert it with long division:

$$1/3 = 0.333333333… = 0.\ov 3$$

The above are equivalent expressions: Both the ellipses and the line above the three indicate that the threes after the decimal point go on forever.

Recurring decimals are tough to work with. Knowing which fractions have infinite decimal expressions, like 1/3 and 1/9, helps significantly in deciding whether to convert it into a decimal or leave it as a fraction in solving problems.

The Key Rule for Fractions That Are Terminating Decimals

If the prime factorization of the denominator of a fraction has only 2 and/or 5, then it can be written as something over a power of ten, which means its decimal expression terminates.

If the denominator doesn’t have only 2 and/or 5 as factors, then the decimal expression is recurring. Here are some examples:

1/24 is recurring (24 = 2³ × 3, so 24 has a prime factor of 3 in addition to 2)

1/25 is terminating (25 = 5²)

1/28 is recurring (28 = 2² x 7, so there’s a prime factor of 7 in addition to 2)

1/40 is terminating (40 = 2³ x 5)

1/64 is terminating (64 = 2⁶)

Importantly, this rule only applies for fractions in their simplest forms. For example, 9/12 terminates, even though 12 has 3 as a prime factor, because 9/12 is really just 3/4, which is 3/2²

One key way to express this rule is that that the denominator must be some value equivalent to 2^m5ⁿ, where $m$ and $n$ are integers. So any fraction that can be expressed as $x$/2^m5ⁿ will terminate, and any other fraction won’t.

Note that the number 1 as a denominator satisfies those requirements, as any number to a power of 0 equals 1, and 0 is an integer, so it can be the value of $m$ and $n$:

1 = 2⁰5⁰

If you need a refresher on what prime factorization is, head to our guide to integer properties for the GMAT, which includes an entire section devoted to explaining prime factorization.

GMAT Fractions Questions

Below are the key kinds of GMAT fraction questions. Note that fractions as a concept overlap with some of the other types of questions, such as rate questions and average questions. The line is often blurry between fractions and decimals as well, and sometimes actually converting the given value to decimals from fractions or vice-versa can make the problem clearer. We’ll see an example of that below.

Example GMAT Fractions Question 1: Problem Solving and Averages

Here’s a GMAT averages problem involving fractions:

This is a fraction question baked into an averages question with algebra. As you may know, the formula for averages is simply to add all the numbers together and then divide by the total number of numbers, which is 4 in this case. This gives us the below fraction:

$${(n+2) + (2n-3) + (4n+1) + (7n+4)}/4$$

We also know from the question that the average is 15, so that equation is equal to 15:

$${(n+2) + (2n-3) + (4n+1) + (7n+4)}/4 = 15$$

To simplify this equation, let’s get rid of the fraction by multiplying both sides by 4 (the denominator):

$${{(n+2) + (2n-3) + (4n+1) + (7n+4)}/4} × 4 = 15 × 4$$
$$(n+2) + (2n-3) + (4n+1) + (7n+4) = 60$$

Since the right side of this equation is all addition and subtraction now, we don’t need the parentheses. Let’s simplify and solve:

$$14n + 4 = 60$$
$$14n = 56$$
$$n = 56/14$$
$$n = 4$$

(B) is the answer.

Example GMAT Fractions Question 2: Problem Solving and Rates

Here is a fraction problem in the context of a GMAT rate problem:

First, let’s make sure we understand what the numerator and the denominator represent in these fractions. The rate is per hour, so we’re talking about tanks (the numerator) per hour (the denominator).

So the rate of the small pump is 1/2 tank/hour, and the rate of the larger pump is 2 tank/hour, or 2/1 (in fraction expression). Together, the combined rate of the two pumps is:

$$1/2 + 2/1$$

You probably know this off the top of your head, but just to illustrate the addition of fractions, I’ll show you how to do it out. We need the lowest common multiple of the denominators so that we can render them both as expressions with the same denominator.

The LCM is 2, so:

$$2/1 + 2/1 = 1/2 + 4/2 = 5/2 \tanks \per \hour$$

To get to the time it takes to fill the tank, we need to divide the job (filling 1 tank) over their collective rate (5/2 tanks per hour).

Hence together they will fill the tank in $1/(5/2)$. Let’s use the rule about fraction division—that it’s simply multiplication with the numerator and denominator flipped—to simplify this:
$$1/(5/2) = 1 × 2/5$$
$$= 2/5 \hours$$

The answer is (C).

Example GMAT Fractions Question 3: Problem Solving and Probability

A basic knowledge of fractions is required for GMAT probability problems as well. Here’s an example:

As with many questions on the GMAT, this problem is simpler than the lengthy wording makes it sound.

We can think of the first 2 cards as cards that have already been turned “face up” and are therefore out of the pile. So the probability of picking a stock card goes from 8/48 to 8/46. Let’s simplify:

$$8/48 = 4/23$$

(E) is the answer.

Example GMAT Fractions Question 4: Problem Solving With Algebra

Sometimes it will be useful to come up with your own algebraic equation to solve a GMAT fractions question. Here’s an example:

Let the price of basic computer be $c$, and the price of the printer be $p$.

What do we know? We know that $c$+$p$=2500. We also know that the price of the enhanced computer will be $c$+500, since the question stem tells us that it’s 500 dollars more than the basic computer. So the total price of the enhanced computer and the printer is 500 dollars more than 2500, or 3000 dollars.

Now, we are told that the price of the printer is 1/5 of that new total $3000 price. Let’s figure that out:

$$p = 1/5 × $3000$$
$$= $3000/5$$
$$= $600$$

Now that we know how much $p$ (the printer) is, we can plug this value in the first equation to solve for $c$ (the basic computer):

$$c + $600 = $2500$$
$$c = $2500 – $600$$
$$c = $1900$$

The answer is (D).

Example GMAT Fractions Question 5: Data Sufficiency

Here is a relatively simple data sufficiency fraction problem:

So all we know from the prompt is that 4 servings of Malik’s dish require 1 and 1/2 or in decimal expression 1.5 cups of pasta.

Statement 1 is insufficient because it just says: “Malik will make half as many servings as he did the last time he prepared the dish.” However, we have no idea how many servings Malik prepared last time. Since we don’t know the servings, we can’t find how much pasta is required. Hence, insufficient. Eliminate (A) and (D).

Statement 2 says Malik used 6 cups of pasta the last time he prepared this dish. Just looking at this statement by itself (without statement 1), it doesn’t really indicate anything: if 6 cups of pasta was the last time, we clearly can’t say how many cups of pasta Malik will use the next time. Hence, insufficient. Eliminate (B).

Now, let’s combine statements 1 and 2. We know that Malik used 6 cups of pasta the last time and that he will make half as many servings as he did the last time. That being the case, Malik will clearly require 3 cups of pasta next time (1/2 of 6 = 3). Sufficient.

Thus, (C) is the answer.

Example GMAT Fractions Question 6: Data Sufficiency With Algebra

Here’s a slightly more advanced data sufficiency question with fractions, involving algebra:

This question is basically asking us if $x$ is a fraction/decimal between 0 and 1. Let’s work methodically through the statements.

Statement 1 is insufficient because there are many values not between 0 and 1 that satisfy the condition of being between -1/2 and 3/2. If that’s not obvious, you might want to convert the statement into decimals. In decimal form, all statement 1 is telling us is that $x$ is between -0.5 and 1.5. So if $x$ was 1.1, 1.2, 1.3, -0.4, etc., it would be between -0.5 and 1.5 but not between 0 and 1. Hence, statement 1 is insufficient. Eliminate (A) and (D).

Now let’s test statement 2. Statement 2 is just an overcomplicated way of saying that:

$$x = 3/4 – 1/4$$

So we solve for $x$ very easily:

$$x = 3/4 – 1/4 = 1/2$$

1/2 is between 0 and 1, so statement 2 is sufficient and the answer is (B).

GMAT Decimal Questions

Below are the key kinds of GMAT decimal questions. Like fractions, decimals questions overlap with other kinds of questions, and often come with a fraction aspect as well. The GMAT particularly loves to test you on the concept of terminating versus recurring decimals, so we’ve included several examples of that below.

Example GMAT Decimal Question 1: Problem Solving With Terminating and Recurring Decimals

This question tests you on both fractions and decimals. One key rule to remember for this question is that a fraction in its simplest form with a denominator that has only 2 and/or 5 its prime factors will convert to a terminating decimal:

x/2^m5ⁿ = terminating decimal

Head back to the section on terminating and recurring decimals above if you need more of a refresher.

Now, onto the question.

First, let’s rephrase it algebraically. Let $p$ = the prime integer that’s greater than 100, which = the sum of all the deposits up to and including the day. Let $d$ be the number of days, up to and including the chosen one ($d$ = 1 would be June 1, $d$ = 30 would be June 30).

The average daily deposit up to and including the chosen day will be the sum of the deposit divided by the number of days, or $p$/$d$.

So the question becomes: What is the probability that $p$/$d$ will have less than 5 decimal places?

Now that we know what we’re being asked, the next step is to hone in on only the days that would have a terminating decimal, since those that yield a recurring decimal will by definition have more than 5 decimal places.

As stated above, to be a terminating decimal, $p$/$d$ must = x/2^m5ⁿ, so $d$ must = 2^m5ⁿ. And luckily, because the numerator $p$ is a prime number, all the possible values of $p$/$d$ will be in their simplest forms, so we can test the denominator without worrying that the terminating decimal fraction rule might not apply. .

The days in June (values for $d$) that can be expressed as 2^m5ⁿ and are thus not recurring are day 1, 2, 4, 5, 8, 10, 16, 20, and 25. You can figure this out by doing a prime factorization of each of the 30 days in June, but as long as you’re still know your multiplication tables, you should be able to look at a number between 1 and 30 and realize almost right away if it has a prime factor other than 2 and/or 5.

So now, of days 1, 2, 4, 5, 8, 10, 16, 20, and 25, we have to check if any of them have more than 5 decimal places, which is possible even though they do terminate. We can do this using the rule for converting fractions to decimals. 5 decimals is the ten thousandths place, so to have 5 decimal places or less, $p$/$d$ × 10,000 must yield an integer:

p/d × 10000 = an integer (nothing after the decimal point)

For this to work, $d$ will have to be a factor of 10,000. As it happens, all of these numbers go into 10,000 (10,000 is divisible by 1, 2, 4, 5, 8, 10, 16, 20, and 25), so for all 9 of these $d$’s, $p$/$d$ = a number with less than 5 decimals.

Thus, out of all of the days of June, there are 9 values for $d$ for which $p$/$d$ has less than 5 decimal places, so the probability is 9/30 = 3/10.

(D) is the answer.

Example GMAT Decimal Question 2: Problem Solving and Scientific Notation Format

Here’s an example of a GMAT terminating decimals question in which knowledge of scientific notation comes in handy.

First, let’s multiply both the numerator and the denominator by 2⁴, so that we can get the exponents of both the base numbers in the denominator to be the same:

$$1/{2^3×5^7} × 2^4/2^4 = 2^4/{2^7 × 5^7}$$

Now we can multiply the bases together, and put the exponent 7 with the result:

$$2^4/{2^7 × 5^7} = 2^4/10^7 = 16/10^7$$

16/10⁷ is the same as 16 × 10^-7

16 × 10^-7 is just the scientific notation for the decimal 0.0000016 (you move the decimal to the left 7 times). Thus, $d$ will have two non-zero digits, 16, when expressed as a decimal. The answer is (B).

Example GMAT Decimal Question 3: Problem Solving and Estimation

This is a great example of a GMAT decimal question in which you should use your powers of estimation instead of solving it:

We don’t want those plus signs in this fraction—let’s do the additions and see what the resulting fraction looks like:

$$1+0.0001/{0.04+10} = 1.0001/10.04$$

Now we can see that these tiny little decimals are negligible: basically, the numerator is 1 and the denominator is 10. So this fraction is virtually 1/10, which equals 0.1. (C) is the answer.

Example GMAT Decimal Question 4: Data Sufficiency and Terminating Decimals

Lots of GMAT data sufficiency decimal questions will ask you if a certain equation or variable is a terminating decimal. Here’s an example:

Statement 1 indicates that $x$, the numerator, is a multiple of 2, which has nothing to do with the terminating or recurring property of decimals—that’s based on the denominator.

We can test this by plugging in multiple-of-2 values for $x$: 2/4 is a terminating decimal, but 4/6 is a recurring decimal. So, statement 1 is not sufficient. Eliminate (A) and (D).

Statement 2 says that y is a multiple of 3. You might be tempted to say that this violates the denominator = 2^m5ⁿ rule, but be careful! Statement 2 gives no information about whether or not $x$ and $y$ have common factors. For instance, 12 is a multiple of 3, but 9/12 is terminating, since it simplifies into 3/4. But 8/12 is recurring, as it simplifies 2/3. into So statement 2 is also not sufficient. Eliminate (B).

Now, let’s plug in numbers to test statement 1 and 2 together. 4/9 satisfies both the statements and it’s recurring, but 18/24 also satisfies both requirements and it’s terminating. So even together the statements are not sufficient and the answer is (E).

Tips for GMAT Fractions and Decimals Questions

Below are the key tips for mastering fraction and decimal questions on the GMAT.

#1: Memorize the Decimal Conversion for All Single-Digit Fractions

When it comes to fractions, being able to convert them to and from decimals with ease will help you get the correct answer faster on many different kinds of GMAT questions. Just because a question is ostensibly asking about medians or areas or probability doesn’t mean that you won’t need to work with fractions at some point to solve the question.

Here’s the conversion for 1/2 through 1/9:

1/2: 0.500
1/3: 0.333
1/4: 0.250
1/5: 0.200
1/6: 0.167 (half of 1/3)
1/7: 0.143 (just need to know this one)
1/8: 0.125 (half of 1/4)
1/9: 0.111

#2: Memorize the Terminating Decimal Rule for Fractions

In addition to the basic conversion, take some time to memorize the rules and properties sections above—especially the x/2^m5ⁿ rule for terminating decimals.

#3: Convert Freely Between Fractions and Decimals as Needed

By the time you take the GMAT, you should be able to fluently convert fractions to decimals or vice versa, depending on what will make a given problem easier. As you do more and more practice questions, you’ll become better at detecting which expression will be the easiest to use to solve the question. The GMAT will often give you the format that is harder to work with to start, as they are testing both your fluency with fractions and decimals and your ability to come up with the best route for solving the problem on your own.

For example, if you’re trying to determine where a variable x falls on the number line, it’s probably easier to work in decimals than in fractions. On the other hand, if you’re given a number like 0.111111111111111 and you have to do algebra with it, it’s probably easier to use 1/9—especially since the answer options will likely be spaced far enough apart that .000000001 of a difference isn’t going to leave you stuck between options.

Remember, you don’t have a calculator for the Quant section, so if you encounter a question on the GMAT that seems impossible to solve without one, there’s almost always a rule, property, or different form of expression that you can use to make it easier. Keep an eye out for strange wording that’s obscuring a very basic principle, and try converting the given fractions to decimals or vice versa if you’re stuck.

#4: Look at the Answer Options Before Solving

In the terminating decimal GMAT question about what the fraction with those tiny decimal points was closest in value to, you may have been tempted to solve for the exact value. But a quick glance at the answer options, which are all spaced out by a power of ten, tells you that all you have to do is get the location of the decimal point correct—not the exact value. That’s a pretty wide margin.

You should always look at the answer choices before even beginning to solve a problem—they’ll clue you in to the right approach.

Whenever you see tricky-looking decimals with widely varying answer choices, as in the terminating decimal GMAT question above, that best approach might be simply to estimate.

#5: Don’t Solve Further Than You Need To

Speaking of approaches, as with the first terminating decimal GMAT question, in the example of Malik’s serving dish you may have been immediately tempted to find how many cups of pasta are needed per serving. 4 servings of the dish required 1.5 cups, so the amount of cups per serving is 1.5/4, or 15/40 when we multiply both numerator and denominator by ten to get rid of the decimal in the fraction. This simplifies to 3/8 a cup of pasta per serving.

But this information is actually useless for finding sufficiency, as the two statements gave us everything we needed to solve the problem of how many cups of pasta Malik will use the next time he makes the dish.

Bottom line: Glance at the answer choices first, and then focus on solving only what you need to solve to get to one answer choice.

What’s Next?

Another key topic to become familiar with for the GMAT Quant section is integers.

For more general advice, check out our 10 tips to master the Quant section.

If you’re looking for more tips, here’s our list of the best tips and shortcuts for doing well on the Quant section.

Happy studying!

The post GMAT Fractions and Decimals: Everything You Need to Know appeared first on Online GMAT Prep Blog by PrepScholar.

Have you ever heard of Dave Hopla? He’s a basketball coach. Well, more specifically, he’s a basketball shooting coach. Throughout his career, he’s made 98 percent of the shots he’s taken. And, he trains players to do the same. How? By mastering the fundamentals.

You might be wondering why I’m beginning an article about the GMAT by talking about a basketball coach. Well, in this article, I’m going to be talking about the importance of mastering GMAT math formulas. Mastering GMAT math formulas is like practicing your free throw if you’re a basketball player. It’s a way to build up your fundamental skills so that, on test day, you’re able to achieve your goal score.

In this article, I’ll talk about why GMAT quant formulas are important, break down the most important formulas to know by subject, and give you some tips for how to incorporate formulas into your prep. I’ll also give you access to a downloadable PDF that you can use to practice offline.

Why Do You Need to Know Math Formulas for the GMAT?

Spending time learning and memorizing GMAT formulas may seem like an overly simple task in light of the complex questions you’ll face on the GMAT quant section, but studying these formulas is an important part of reaching your goal score.

Despite the notoriety of the GMAT quant section, the questions on this section actually test basic math concepts that are presented in complex ways. Mastering fundamentals, like formulas, will help you solve these questions because you’ll be able to figure out the answers to each individual part of the problem, leading to your final answer.

The GMAT quant section only tests math concepts that you would’ve learned in high school. So, learning basic formulas will go a long way in ensuring you understand how to solve different questions.

Learning formulas is also a big time-saver. You only have a limited amount of time for the GMAT quant section, so you’ll need to work quickly and efficiently to answer every question, which is important to do so that you maximize your score.

By learning these formulas, you’ll be able to easily recall what you should do to answer each question. You’ll save time by using the most efficient methods for solving a question.

The GMAT quant section doesn’t allow you to use a calculator. So, you won’t be able to easily do long, complex calculations. Learning formulas will help you because you’ll have tools at your disposal to figure out different measurements or calculations without technology.

While learning formulas is an important part of studying for the GMAT, it’s not all you should do to prepare for the quant section. As I mentioned before, while the actual math on the GMAT is relatively simple, the questions are presented in a complex way. You’ll need to spend time applying your formula knowledge by practicing the different styles of questions on the GMAT. Studying in this way will help you feel prepared for the questions you’ll see on test day.

GMAT Quant Formulas

In this section, I’ll break down the most important formulas for you to know for the GMAT. I’ve broken them down by math topic so that they’re easier to sort through.

GMAT Geometry Formulas

Geometry questions make up about 20% of the questions test on the GMAT quant section. Use these formulas to master the content covered on those questions.

AREA & PERIMETER FORMULAS

Square:

• Area = $\length^2$
• Perimeter = 4*length

Rectangle:

• Area = length*width
• Perimeter = 2(length) + 2(width)

Parallelogram:

• Area = base*height
• Perimeter = 2(base) + 2(height)

Circles:

• Area = $πr^2$
• Circumference = $2πr$

Triangle:

• Area = $(\base*\height)/2$
• Pythagorean Theorem: $a^2 + b^2 = c^2$

Trapezoid:

• Area = $(1/2)*(a+b)/h$, where a and b are the length of the parallel sides

CIRCLE FORMULAS

Central angle = 2(inscribed angle)

Area of a sector = $(x/360)*πr^2$, where $x $is the measurement of the central angle of the circle portion in degrees

VOLUME FORMULAS

Cube: $(\length)^3$

Rectangular prism: length*width*height

Cylinder: $πr^2*h$

Cone: $1/3πr^2*h$

Pyramid: $1/3(\base \length*\base \width*\height)$

Sphere: $4/3πr^3$

GMAT Arithmetic Formulas

Arithmetic concepts are one of the most heavily tested content areas on the GMAT quant section, making up nearly 50% of GMAT quant question types. These GMAT quant formulas address the majority of concepts covered on the GMAT.

ORDER OF OPERATIONS

Parentheses – Exponents – Multiplication – Division – Addition – Subtraction (PEMDAS)

NUMBER PROPERTIES

(Positive Number) * (Positive Number) = (Positive Number)

(Positive Number) * (Negative Number) = (Negative Number)

(Negative Number) * (Negative Number) = (Positive Number)

(Positive Number) / (Positive Number) = (Positive Number)

(Positive Number) / (Negative Number) = (Negative Number)

(Negative Number) / (Negative Number) = (Positive Number)

(Odd Number) + (Odd Number) = (Even Number)

(Odd Number) – (Odd Number) = (Even Number)

(Odd Number) + (Even Number) = (Odd Number)

(Odd Number) – (Even Number) = (Odd Number)

(Even Number) + (Even Number) = (Even Number)

(Even Number) – (Even Number) = (Even Number)

(Odd Number) * (Odd Number) = (Odd Number)

(Odd Number) * (Even Number) = (Even Number)

(Even Number) * (Even Number) = (Even Number)

PERMUTATIONS AND COMBINATIONS

Permutation formula: $nPr = n!/(n-r)!$

Combination formula: $nCr = n!/((r!)(n-r)!)$

PROBABILITY

Probability = (Number of favorable outcomes) / (Number of all possible outcomes)

Probability of events A & B happening = (Probability of A) * (Probability of B)

Probability of either event A or B happening = (Probability of A) + (Probability of B)

GMAT Algebra Formulas

Algebra questions make up about 20% of the question types you’ll see on the GMAT quant section.

ABSOLUTE VALUE

|x| depicts absolute value.

|x| = x

|-x| = x

|x| = |-x|

|x| ≥ 0

|x| + |y| ≥ |x+y|

EXPONENT Rules

In the expression $x^n$, ‘x’ is the base and ‘n’ is the exponent. The way to interpret is that the base ‘x’ gets multiplied ‘n’ times. For example, $2^3=2*2*2$.

Some key rules and formulas for exponents:

$0^n = 0$

$1^n = 1$

$x^0 = 1$

$x^1 = x$

$(x)^-n = 1/x^n$

$x^m*x^n = x^(m+n)$

$x^m/x^n = x^(m-n)$

$(x/y)^n = (x^n)/(y^n)$

$(x^m)^n = x^(m*n)$

QUADRATIC EQUATIONS

$ax^2 + bx + c = 0$

$x = (-b ∓ √[b^2 – 4ac]) / 2a$

INTEREST

All interest formulas use the following variables: P = starting principle; r = annual interest rate; t = number of years.

Simple Interest = P*r*t

Annual Compound Interest = $P(1+r)t$

Compound Interest = P(1 + r/x)^(xt); x = number of times the interest compounds over the year

OTHER Algebra Formulas

Distance = Speed * Time

Wage = Rate * Time

PrepScholar GMAT Formula Sheet

Download our GMAT formula sheet to help you study your GMAT formulas.

How to Incorporate GMAT Formulas in Your Prep

As I mentioned before, simply memorizing the formulas I gave you above isn’t a good way to prepare for the GMAT quant section. In order to ensure your formula prep really helps your score, you’ll need to apply your formula mastery. Follow these tips to make your formula knowledge work for you.

#1: Use Flashcards

Flashcards are a great tool for memorizing GMAT math formulas because they’re easy to use and effective. You can quickly review flashcards on your commute or before you go to bed at night or while you’re scarfing down breakfast on the way to class… really, you can review flashcards any time, any place! By spending time memorizing formulas with flashcards, you’ll be able to quickly recall what you’ll need to do to solve a problem.

Flashcards require you to actively engage with the material. For instance, rather than just trying to memorize a list of many different formulas you’ll use on the quant section, you’ll engage with each formula one by one. You’ll be forced to ask yourself whether or not you really know how to use the formula in a quick, concise way.

#2: Understand the Underlying Concepts

While memorizing formulas is great, understanding the underlying concepts of each formula is better. Don’t just know what the formulas are – know how they work and, better yet, how to apply them. Understanding the underlying concepts means that you’ve reached a deeper level of learning beyond simply memorizing. If you’re able to understand something, you’ll be able to apply it to solve a question much more easily.

Take the formula for area of a sector of a circle: (x/360) * πr2

If you know that a sector is part of a circle that has its own interior angle measurement and you know that the area of a circle is πr2, it makes sense that you can find the area of a sector by multiplying that interior angle by the overall area of the circle.

#3: Apply GMAT Math Formulas by Practicing Real GMAT Questions

Memorizing formulas won’t help you if you don’t apply your knowledge. The GMAT quant section tests basic concepts in complex ways. You’ll need to spend time familiarizing yourself with the ways that the GMAT asks questions. It won’t simply ask you to find the area of triangle; you might need to find the area of a triangle on your way to discovering how much it costs to put fencing around a triangle-shaped yard.

Spend time learning the style of both problem solving and data sufficiency questions, so that you’ll be able to use your GMAT math formulas to easily get to the correct answer. The best way to practice for the GMAT is to use real retired GMAT questions, which you can find in the official GMAT guides or in the GMATPrep Software. Real, retired GMAT questions best emulate the style and content of what you’ll see on test day.

What’s Next?

Looking for a more in-depth review of the quant section? There’s a lot you need to know to be able to reach your GMAT goal score. Our guide to the GMAT quant section teaches you the ten essential tips you need to know to master the most notorious section of the GMAT.

We also offer more specific guides that break down the data sufficiency and problem solving question types on the GMAT. Learn about the types of content covered on the problem solving questions and the trick to mastering the difficult data sufficiency questions, while also learning how to solve sample questions.

Want to focus on a different part of the GMAT? We also offer in-depth guides to the verbal section, as well as tips for how to do well on the analytical writing assessment (link coming soon!). Check out those guides to boost your all-around GMAT scores and get into the business program of your dreams.

The post All 64 GMAT Math Formulas You Need + How to Use Them appeared first on Online GMAT Prep Blog by PrepScholar.