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.

Like we discussed in our Online Lesson: Introduction to Data Sufficiency video, picking numbers should not be our go-to strategy for most questions on the GMAT Math section. Most problem types aren’t easily solved by plugging in numbers. Then, even on the problems where number picking is a viable strategy, most test takers approach it incorrectly, which causes them to waste time and confuse themselves. So when is this strategy actually useful? And how can we use it to improve our GMAT Math score?

In “How to Plug in ‘Smart’ Numbers on GMAT Math Problems: 4 Tips”, we’ll teach you how apply one of the most misused GMAT Math strategies successfully on test day with four GMAT Math tips.

While number picking shouldn’t be our first resort on any GMAT Math problem, some questions lend themselves more to number picking than others. Our first tip explores how we can identify questions that are good candidates for number picking.

In our second tip, we delve into our goals for number picking. One of the reasons that number picking is not always an effective strategy is that test takers often plug numbers in randomly without considering how the result will impact which answer choice they’ll pick. We look at how we should have different objectives for different GMAT Math question types, and how these goals will impact the types of numbers (as well as how many numbers) we pick.

Our third and fourth GMAT Math tips explore how to pick “smart” numbers to meet these goals. First, we look at how thinking about categories of numbers can give us a window into which numbers “work” in our problem and which numbers don’t. Then, we consider how to pick specific numbers within these categories for quick math without a calculator.

Watch the video to learn more!

To stay updated on our latest GMAT videos, you can subscribe to our new PrepScholar GMAT YouTube channel — we’ll have three new free videos every month.

Happy GMAT Math studies!

The post How to Plug in “Smart” Numbers on GMAT Math: 4 Tips [Video] 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 rate problems are a constant on the Quantitative section. Many students dread rate problems because they aren’t quick or easy — they often require a series of steps to get to the answer. To make matters worse, this series of steps is usually not immediately obvious because there are so many elements to the problem and because these elements are usually presented as part of a difficult-to-interpret word problem scenario. This means that seeing a clear path to the finish line is difficult with many GMAT rate problems.

So what should we do when we run into a rate problem that we just can’t see how to solve? In “How to Conquer GMAT Rate Problems”, we discuss one of the most valuable GMAT math strategies — taking complex problems step-by-step.

GMAT rate problems give us limited information that we can use in limited ways. At any given step, we are only able to do one or two things with the information we have. Because our options at each step are so limited, we can usually make our way to the answer by figuring out only the next step we are able to take now given the information we have, then repeating the process with the information we learn at each step until we reach our answer. While working out a full, multi-step game plan up top can be overwhelming, simply answering “What can I do with this information?” at each step is more manageable and will eventually lead us to our answer.

In the case of GMAT rate problems, the next step we are able to take is usually doing the next possible conversion — converting the value we have into any another value we can using rates from the problem. We walk through exactly what this means by solving one of the real GMAT rate problems from the GMATPrep software.

Watch the video to see how it’s done!

With this strategy, you’re ready for any multi-step rate problems GMAT test writers can throw at you. However, this isn’t all — taking problems one step at a time when the solution isn’t immediately clear is one of the broader GMAT math strategies, as we can apply it to a variety of multi-step problems. Not sure what to do with a bunch of terms with exponents? See how you can combine two or three of them, then see if it simplifies further with your new term. Have a complicated geometric figure? See which angle or side you can solve for now, then see if you can solve for more with the new information.

As a final note, this strategy applies best to distance rate problems, but it can also be used on certain work rate and interest rate questions. If you’d like more detailed information on how to solve each of these specific types of rate problem, check out our rundown of the three types of GMAT rate problems.

To stay updated on our latest GMAT videos, you can subscribe to our new PrepScholar GMAT YouTube channel — we’ll have three new free videos every month.

Happy GMAT studies!

The post How to Conquer GMAT Rate Problems [Video] appeared first on Online GMAT Prep Blog by PrepScholar.

Overlapping sets make for particularly hard GMAT math questions. While they technically fall into the category of arithmetic — a type of math most people feel comfortable with — the complexity and presentation of overlapping sets problems throw many test takers for a loop.

So how can test takers make sense of all of the complicated information in these questions? And how can we get overlapping sets GMAT problems right every time? In the new video “How to Beat Overlapping Sets GMAT Problems”, we discuss the number one strategy to conquer these deceptively difficult GMAT questions.

We start off by defining overlapping sets GMAT problems so you can recognize them on test day: they are word problems that deal with one large group that is being evaluated for multiple traits. This in essence breaks our larger group into many smaller groups with different combinations of traits.

We then delve onto our key strategy for overlapping sets GMAT problems: making a diagram. This allows us to

1. organize information from the problem.
2. clarify relationships between our smaller groups.
3. build equations we can then use to solve.

On overlapping sets GMAT problems where our larger group is being evaluated for two traits, we use a specific type of diagram called a “double matrix”, which we explain how to create on your scratch paper. We also use a real overlapping sets GMAT question to illustrate how to set up our double matrix diagram and then use it to solve. Finally, we talk about how to set up a diagram for the really hard GMAT math questions in which our overlapping sets involve evaluating for three or more traits.

Watch the video to see how it’s done!

To stay updated on our latest GMAT videos, you can subscribe to our new PrepScholar GMAT YouTube channel — we’ll have three new free videos every month.

Happy GMAT studies!

The post How to Beat Overlapping Sets GMAT Problems [Video] appeared first on Online GMAT Prep Blog by PrepScholar.

Many students think that Data Sufficiency is one of the hardest question types on the GMAT. Data Sufficiency is unlike anything they’ve ever seen before, either on tests or in their undergraduate math classes. In “Online Lesson: Introduction to GMAT Data Sufficiency”, we cover the basics of GMAT Data Sufficiency to familiarize you with your new favorite GMAT question type and give you strategies you can apply on test day.

Since this Introduction to GMAT video is relatively long, we’ve broken it down into bite-sized sections focused on key Data Sufficiency topics:

In Overview of GMAT Quant, we discuss the makeup of the GMAT Quantitative section, answering the question “How many Data Sufficiency questions are there on the GMAT?” In Structure of Data Sufficiency questions, we review the three components of a Data Sufficiency problem (the question stem, the statements, and the answer choices) and discuss Data Sufficiency GMAT tips related to this structure. We then delve into the answer choices with What is Sufficiency?”by discussing what the “sufficiency” in GMAT Data Sufficiency means and looking at the two different kinds of sufficiency we see in Data Sufficiency questions.

Once we’ve covered the foundations of GMAT Data Sufficiency, we take a detour for What’s the Point of Data Sufficiency? to discuss how Data Sufficiency problems test skills critical to success in business school and careers. We then discuss How to Approach Data Sufficiency Questions at a broad level, walking chronologically through the steps test takers can apply on every Data Sufficiency problem and providing additional GMAT Data Sufficiency tips. Finally, we walk through more specific Data Sufficiency GMAT Strategy in Data Sufficiency Strategies, covering four of the most useful strategies for GMAT Data Sufficiency.

Watch the video to learn more!

To stay updated on our latest GMAT videos, you can subscribe to our new PrepScholar GMAT YouTube channel — we’ll have three new free videos every month.

Happy GMAT Data Sufficiency studies!

The post Online Lesson: Introduction to GMAT Data Sufficiency [Video] 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.

Can you use a calculator on the GMAT? Yes, but probably not as much as you’d like.

In this article, I’ll ago over which sections of the GMAT have an onscreen calculator, the functions of the GMAT calculator, and how to use it most effectively on test day.

Is There a GMAT Calculator?

So, can you use a calculator on the GMAT? The short answer is sometimes.

There is an onscreen calculator on the Integrated Reasoning (IR) section, but there is no calculator on the Quantitative (Quant) section. On that section, you’ll have to do all your calculations by hand.

No GMAT Calculator on the Quant Section?!

If that last sentence scared you, don’t panic. There are several reasons not to worry:

1. The GMAT Quantitative section is not designed to test you on complicated mathematical skills or specific calculations. Instead, the Quant section draws from secondary-level math skills like basic algebra and geometry. In fact, the majority of Quant questions can be answered without any calculations beyond estimation.
2. You will have a notepad with plenty of space provided to you by the proctor on test day. If you absolutely need to do some calculations, you can complete them manually there.
3. Even if you feel uncomfortable doing arithmetic without a GMAT calculator, it won’t take long for you to improve with practice.

Working without a calculator may take some getting used to, but it’s not as scary as it sounds.

How to Succeed Without a Calculator in the GMAT Quant Section

While you shouldn’t be overly concerned about not having a calculator during the Quant section, there are ways to prepare effectively so you can do your best come exam day.

#1: Practice, Practice, Practice

If you don’t feel comfortable doing arithmetic quickly in your head, you should start practicing now. Of course, you should complete all your Quant practice tests without a calculator, but you can also add, multiply, subtract, and divide when you pay bills, check out at the grocery store, or calculate a tip. Try to use a calculator as rarely as you can in preparation for the GMAT.

#2: Estimate

The key to completing many Quant questions efficiently is estimation. You should always try to round up or down to find more manageable, less unwieldy numbers (often ones that end in zero or 5) for the purpose of calculations. If a problem or answer choice requires you to multiply 44.6 by 11.15, for example, you can multiply 45 by 10 instead and still end up with the correct answer.

#3: Use Halving and Doubling to Simplify Calculations

Another useful skill when completing the Quant section without a GMAT calculator is called ‘halving and doubling,’ which doubles (or otherwise multiplies) one number in a calculation and halves (or otherwise divides by the same factor) the other to result in a friendlier pair of numbers for someone without a calculator. Let’s take 25 times 24, for example. Divide 24 by 6 to get 4–easy enough–and multiple 25 by 6 to get 150. What you’re left with is 4 times 150, a much easier calculation (600).

GMAT Calculator: What It Does and How to Use It

Unlike the Quant section, the Integrated Reasoning (IR) section does have an onscreen calculator available. You’ll simply click on “Calculator” at the top lefthand corner of the screen, and the calculator will appear in the middle:

As you can see, the GMAT calculator has standard basic functions. The fairly self-explanatory top row of the calculator consists of Backspace (which clears only the last digit you typed), CE (clear entry, or what you entered in the line), and C (clear all, or everything that is stored in previous operations).

The right column of the IR calculator contains a few other basic functions. The ‘sqrt’ (square root) button will calculate the square root of any number you just typed.

The % percentage button will help you if you want to increase or decrease a number by a certain percentage: for example, typing 100 + 10% will result in 110.

The ‘1/x’ button calculates the reciprocal of the entry currently on the screen. For example, typing “5” and then the 1/x button will show you .2, which is the decimal equivalent of ⅕.

The left column consists of the ‘memory’ functions. These are especially helpful for calculations that require several steps.

1. MS (memory store) stores the current entry in the calculator’s memory for subsequent use.
2. MR (memory recall) displays the latest number stored in memory on the screen so you can use it for the next step of your calculation.
3. M+ (memory addition) adds the current entry to whatever is in the current memory. This button is helpful when you need to add a long series of numbers and don’t want to retype each one.
4. Finally, MC (memory clear) erases whatever is in the current memory. You should click this button before every new calculation scenario.

While the IR GMAT calculator can be a helpful tool, you don’t want to use it too often or you’ll waste more time than you save. You can use many of the same tips and tricks on the IR section that you’ll use on the Quant section, where you don’t have a calculator. The same skills you practice to prepare for the Quant section will also help you on the IR section.

Review: Can You Use a Calculator on the GMAT?

There is no calculator available on the Quantitative section of the GMAT, but there is one on the Integrated Reasoning. The GMAT calculator has the same functions as a standard four-function calculator with square roots.

Though the idea of taking a math test with no calculator can be intimidating, you shouldn’t panic. The GMAT Quant section doesn’t test your ability to do complex arithmetic — you’ll only need to do basic calculations and can rely on estimation for anything more complicated.

What’s Next?

For more information on how to make effective use of the scratch pad you’ll be provided with during the GMAT, read our article on GMAT scratch paper.

Wondering what topics you need to review before trying to master the Quant section? Our guide to the math you need for the GMAT can help.

To delve more deeply into GMAT Math strategies, check out our guide to mastering the Quant section.

The post GMAT Calculator: What Is It? When Can You Use It? 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.