The newest GMAT Strategy Guides have hit the shelves! We’re really excited about these new books, the perfect stocking stuffers to make all of your dreams come true. (Well…your GMAT-related dreams, anyway.)

Yesterday, we talked about the Quant Guides and today I’ve got the Verbal scoop for you. Let’s start with Sentence Correction.

The SC Guide begins with a new strategy chapter that discusses our 4-Step SC Process and lays out drills that you can do to get better at such skills as the First Glance and Finding a Starting Point. We’ve also significantly expanded the Subject-Verb Agreement chapter to include a full treatment of Sentence Structure, an area that has been becoming much more commonly tested on the GMAT.

We’ve added important segments to Modifiers, Parallelism, and Verbs and we’ve woven relevant Meaning topics into every chapter in the book.

Finally, we’ve streamlined the Idioms material. The main chapter contains a strategy for tackling idioms as well as the most commonly tested idioms found on the GMAT. A separate appendix contains the less-commonly-tested idioms. We recommend taking the time to memorize the ones listed in the main chapter, but to use the appendix more as a resource to look up the correct idiom when you struggle with a particular problem. (It’s impossible to memorize every idiom in a language; there are thousands, if not tens of thousands!)

What about RC and CR?

Glad you asked! Our Reading Comprehension Guide was re-written from scratch. We’ve streamlined the process for reading passages and added lessons designed to help you wade through these dense passages and extract the kernels you need to answer questions. We’ve also expanded our lessons for each question type and provided you with end-of-chapter cheat sheets that summarize what to do for each question type and what common traps to avoid. (I’m most excited about this book; students often complain that RC is hard to study, and I’m hoping that this book will change your minds!)

Of all of the books, Critical Reasoning has changed the least, although we did add more information about Fill-In-The-Blank question types. This Guide also provides you with end-of-chapter cheat sheets that summarize how to recognize each type of question, what to look for in the argument, what kind of characteristics the right answer needs to possess, and how to spot the most common trap answers.

What is the best way to use the books?

Here’s how we typically study each topic in class:

Sentence Correction

First, we learn how to use the SC Process and we discuss the main topics being tested (grammar and meaning); these correspond to chapters 1 and 2 of the book. Then, we work through one new chapter a week, starting with Chapter 3 (Sentence Structure). The order of chapters in the book is the same order we use in class.

You can use the same approach mentioned for quant (in the first half of this article): do some end-of-chapter problems first to see what your skills are. If you know that you don’t really know this material, then you can also skip this step. After you’ve finished a chapter, try some of those end-of-chapter problems to ensure that you did actually internalize the concepts that you just learned. Then, if you have the OG books, follow up with some questions from the OG Problem Sets, located in your Manhattan Prep Student Center.

Reading Comprehension

The class contains three RC lessons. First, we learn how to read. Bet you thought you already knew how, didn’t you?

Of course you do know how to read, but the way you read in the real world may not work very well on the GMAT. You’ll learn a new way to deal with the short timeframe we’re given on the test. After that, you’ll learn how to handle General questions, the ones for which you need to wrap your brain around the main ideas of the passage.

Then, you’ll move on to Specific Questions, including Detail, Inference, and Purpose questions. The test writers are asking us to do something a bit different for each one, so you’ll need to learn how to recognize each type in the first place and then how to handle it.

In class, we finish off with a Challenging RC lesson. You can create something similar for yourself by tackling harder and harder OG passages.

Critical Reasoning

Critical Reasoning begins with a thorough treatment of argument building blocks and the 4-Step CR Process. After that, you’ll learn about each question type (do actually use the order presented in the book). Pay attention to what the book says about frequency of each type; some types are much more common than others (and those types should obviously get more of your attention).

For both CR and RC, tear out or photo-copy the cheat sheets and use them to quiz yourself. Alternatively, put the material onto flash cards yourself (the act of rewriting the material will help you to remember it better!) and drill while you’re sitting on the subway or waiting for that meeting to start.

Is that all I need to do?

That will certainly keep you busy for a while. As you get further into your studies, note that you also need to lift yourself to the 2^nd Level of GMAT Study. Yes, of course, there are lots of facts, formulas, and rules to memorize, and your brain will be focused on those areas at first. It’s crucial, however, for you to learn the various strategies presented in our Guides, as well as your own decision-making strategies based on your own strengths and weaknesses, and timing strategies.

In short, get ready to make a commitment. Think of studying for the GMAT as a university-level course: you’re going to spend hours every week for about 3 to 4 months to get ready for this test. With a solid plan, you’ll achieve your goals.

Visit our store and be the first to own the full set of our brand new Strategy Guides. Happy studying!

Studying for the GMAT? Take our free GMAT practice exam or sign up for a free GMAT trial class running all the time near you, or online. And, be sure to find us on Facebook and Google+,LinkedIn, and follow us on Twitter!

The newest GMAT Strategy Guides have hit the shelves! We’ve been working all year on updating our materials to give you the best and most up-to-date study materials possible.

What’s so great about the new books?

So many things, I don’t know where to start! Okay, let’s talk about quant first.

Every quant book contains between 1 and 3 entirely new chapters. These chapters are devoted to strategies that will help you solve quant problems more efficiently and more effectively. These strategies are a crucial reason why all of our teachers score in the 99^th percentile on the GMAT (I certainly wouldn’t consider taking the test without using them). We’ve always taught them in class and now we’re putting them in our books for the first time.

These strategies include:

Choosing Smart Numbers: you can turn certain algebra problems into arithmetic problems by substituting in your own numbers for the variables. We’re all better at arithmetic than we are at algebra, so you’ll definitely make your life easier (and be able to answer harder questions) by choosing smart numbers.

Testing Cases: On many data sufficiency problems (and even some problem solving problems), you’ll want to test cases in order to determine whether a statement is sufficient (or to eliminate wrong answers on PS). These problems are “theory” problems: the question may ask “Is n odd?” and then provide information that doesn’t allow you to determine a specific value for n, just whether specific characteristics are true of n.

Working Backwards: Sometimes, the problem is pretty annoying to set up and solve but the answers are all “nice” numbers: relatively small integers. In this case, you may be able to work backwards from the answers: pick one and try it in the problem to see whether it’s correct. The beauty of this technique: if you get good at it, on many problems you won’t have to try more than two answers in order to get to the correct one. I tested three answers on the solution in the article linked here, but I only really needed to test the first two; see if you can figure out why.

Estimation: Sometimes, the problem would be really irritating to solve exactly, but the answers are all decently spread apart. When this is the case, you can just estimate to solve! There are also a bunch of strategies for jumping between fractions, decimals, and percents to solve more quickly.

Combos: The GMAT likes to ask us to solve for a combination of variables, such as x + y. Sure, it’s possible that you may have to find x and y individually and then add them up, but it’s actually more likely that you’ll want to solve directly for that combo (x + y), especially on Data Sufficiency. Learn how to do this and also how to avoid DS traps in which the statement is not sufficient to solve for the individual variables but is sufficient to solve for the Combo.

Draw It Out: You can often solve the extra-annoying story problems, such as rates & work, via a “back of the envelope” approach: you sketch out a picture of the scenario and just “step” through it. For instance, you’d draw a timeline and map out exactly where those two trains are after 1 hour, 2 hours, 3 hours. It’s a little bit shocking how often this kind of strategy will get you all the way down to a single answer.

What is the best way to use the books?

I’ll leave you with a few tips about studying for quant. First, here’s the order that we use in our own classes:

1. Fractions, Decimals, & Percents
2. Algebra
3. Word Problems
4. Geometry
5. Number Properties

I actually think Number Properties is a more important topic than Geometry, but geo requires you to memorize a bunch of formulas; that takes some time, so we do it in class first. If you feel okay with that type of memorization, then do the Number Properties book first. (By the way, the Geometry Guide now contains a 1-page sheet with all of the important rules and formulas to memorize! Tear it right out and keep it handy for studying or use it to make flash cards for yourself.)

Next, I’d recommend starting with a few problems from the problem set at the end of the chapter—that’s right, before you even read the chapter! This creates curiosity, which really wakes your brain up and primes it to learn. Don’t do a bunch and don’t do the hardest ones (unless you think you’re really good at that topic). Just do about 2 or 3 problems and then dive into the chapter. (This will also help you to know how much time you’re likely going to want to spend on the chapter; if the problems are really a struggle, you may even want to review the equivalent chapter in our Foundations of Math Guide, if you have that book too.)

When you get to the end of the main chapters of that book, do the OG Mixed Questions Quiz that we’ve devised for you. (Certain longer books also have mid-way quizzes.) You can find these quizzes on our web site, where our Official Guide Problem Set study lists live. You’ll receive access to these problem sets and quizzes, along with other bonus materials, when you register your books on our site.

We moved the OG problem sets online because GMAC is going to start publishing new versions of their Official Guide books every year (in July, we’ve heard), so by moving the problem sets online, we’ve ensured that you’ll always be able to go and get the sets for the specific OG editions that you own.

I also have a ton of updates to share on the Verbal side as well, which are detailed in Part II. Also, a plea: if you get the new books, tell me what you think down in the comments. (Compliments or criticisms—I do want both.)

Visit our store and be the first to own the full set of our brand new Strategy Guides. Happy studying!

Studying for the GMAT? Take our free GMAT practice exam or sign up for a free GMAT trial class running all the time near you, or online. And, be sure to find us on Facebook and Google+,LinkedIn, and follow us on Twitter!

If you’re going to do a great job on Data Sufficiency, then you’ve got to know how to Test Cases. This strategy will help you on countless DS problems.

Try this GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “On the number line, if the number k is to the left of the number t, is the product kt to the right of t?

“(1) t < 0 “(2) k < 1” If visualizing things helps you wrap your brain around the math (it certainly helps me), sketch out a number line:

k is somewhere to the left of t, but the two actual values could be anything. Both could be positive or both negative, or k could be negative and t positive. One of the two could even be zero.

The question asks whether kt is to the right of t. That is, is the product kt greater than t by itself?

There are a million possibilities for the values of k and t, so this question is what we call a theory question: are there certain characteristics of various numbers that would produce a consistent answer? Common characteristics tested on theory problems include positive, negative, zero, simple fractions, odds, evens, primes—basically, number properties.

“(1) t < 0 This problem appears to be testing positive and negative, since the statement specifies that one of the values must be negative. Test some real numbers, always making sure that t is negative.

Case #1:

Testing Cases involves three consistent steps:

First, choose numbers to test in the problem

Second, make sure that you have selected a valid case. All of the givens must be true using your selected numbers.

Third, answer the question.

In this case, the answer is Yes. Now, your next strategy comes into play: try to prove the statement insufficient.

How? Ask yourself what numbers you could try that would give you the opposite answer. The first time, you got a Yes. Can you get a No?

Case #2:

Careful: this is where you might make a mistake. In trying to find the opposite case, you might try a mix of numbers that is invalid. Always make sure that you have a valid case before you actually try to answer the question. Discard case 2.

Case #3:

Hmm. We got another Yes answer. What does this mean? If you can’t come up with the opposite answer, see if you can understand why. According to this statement, t is always negative. Since k must be smaller than t, k will also always be negative.

The product kt, then, will be the product of two negative numbers, which is always positive. As a result, kt must always be larger than t, since kt is positive and t is negative.

Okay, statement (1) is sufficient. Cross off answers BCE and check out statement (2):

“(2) k < 1” You know the drill. Test cases again! Case #1:

You’ve got a No answer. Try to find a Yes.

Case #2:

Hmm. I got another No. What needs to happen to make kt > t? Remember what happened when you were testing statement (1): try making them both negative!

In fact, when you’re testing statement (2), see whether any of the cases you already tested for statement (1) are still valid for statement (2). If so, you can save yourself some work. Ideally, the below would be your path for statement (2), not what I first showed above:

“(2) k < 1” Case #1:

Now, try to find your opposite answer: can you get a No?All you have to do is make sure that the case is valid. If so, you’ve already done the math, so you know that the answer is the same (in this case, Yes).

Case #2: Try something I couldn’t try before. k could be positive or even 0…

A Yes and a No add up to an insufficient answer. Eliminate answer (D).

The correct answer is (A).

Guess what? The technique can also work on some Problem Solving problems. Try it out on the following GMATPrep problem, then join me next week to discuss the answer:

* “For which of the following functions f is f(x) = f(1 – x) for all x?

“(A) f(x) = 1 – x

“(B) f(x) = 1 – x²

“(C) f(x) = x² – (1 – x)²

“(D) f(x) = x²(1 – x)²

“(E) 

Key Takeaways: Test Cases on Data Sufficiency

(1) When DS asks you a “theory” question, test cases. Theory questions allow multiple possible scenarios, or cases. Your goal is to see whether the given information provides a consistent answer.

(2) Specifically, try to disprove the statement: if you can find one Yes and one No answer, then you’re done with that statement. You know it’s insufficient. If you keep trying different kinds of numbers but getting the same answer, see whether you can think through the theory to prove to yourself that the statement really does always work. (If you can’t, but the numbers you try keep giving you one consistent answer, just go ahead and assume that the statement is sufficient. If you’ve made a mistake, you can learn from it later.)

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

Studying for the GMAT? Take our free GMAT practice exam or sign up for a free GMAT trial class running all the time near you, or online. And, be sure to find us on Facebook and Google+,LinkedIn, and follow us on Twitter!

Last week, I attended the annual GMAT Summit, held by the fine folks at GMAC (who own / make the GMAT), and I have some interesting tidbits to share with you.

It really is a myth

You know what I’m going to say already, don’t you? The first 7 (or 10, or 5) questions are not worth more than the questions later in the exam. I’ve written about this topic before but I’m going to mention it once again because of something that happened at the conference.

Fanmin Guo, Ph. D., Vice President of Psychometric Research at GMAC, was answering questions after a presentation on the test algorithm. A couple of people were peppering him with questions about this myth and apparently just didn’t seem to believe that it could possibly be true that the early questions aren’t worth more. One of the questioners also made a pretty significant faulty assumption in his arguments—and now I’m worried that an article is going to pop up trying to revive this debate. I don’t want any of my students led astray on this topic.

First, to understand why the early questions actually aren’t worth any more than the later ones, see the article I linked a couple of paragraphs back.

Second: here was the faulty assumption that I heard:

“You said that the earlier questions aren’t worth any more than the later ones. So you’re telling us that students should spend the same amount of time on every question.”

Dr. Guo was saying the first part: that the location of a question on the test doesn’t impact its weighting in the overall score. He and the other GMAC folks weren’t saying anything, though, about how you should take the test.

In fact, it would be silly to spend exactly the same amount of time on every question. Some questions are harder than others. In addition, you have various strengths and weaknesses in terms of both accuracy and speed. There are, in fact, very good reasons not to spend the same amount of time on each question. All Dr. Guo was saying was that the location of the problem in the section is not one of those reasons.

So, if you read something that says that you should spend more time on the earlier questions, roll your eyes and click away. Alternatively, if you read something that concludes that you should spend the same amount of time on every question, drop that source as well. Take a look at the data in my other article to see that GMAC actually does know what it’s doing and the GMAT is not just a test of how you perform on the first 7 or 10 questions.

GMATPrep offers more data

GMAC has been building more score reporting functionality into GMATPrep to give us a better idea of how we do when we take the official practice CATs. In fact, this capability has already launched! I need to go download the newest version of GMATPrep to see exactly what’s offered (and I’ll report back to you once I’ve done so), but they’ve started to offer data for sub-categories such as question type and content area.
Read more

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

This is the original version of a piece that has since been updated. See Stacey’s latest tips on maximizing the last two weeks before your GMAT.

As we discussed in the first half of this series, Building Your Game Plan, during the last 7 to 14 days before you take the real test, your entire study focus changes. In this article, we’re going to discuss the second half of this process: how to review. (If you haven’t already read the first half, do so before you continue with this part.)

What to Review Read more

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

This is the original version of a piece that has since been updated. See Stacey’s latest tips on maximizing the last two weeks before your GMAT. 

What’s the optimal way to spend your last 14 days before the real test? Several students have asked me this question recently, so that’s what we’re going to discuss today! There are two levels to this discussion: building a Game Plan and how to Review. We’ll discuss the former topic in the first half of this article and the latter in the second half.

What is a Game Plan?

Read more

It’s October again. People are starting to panic because they want to apply second round (early January!) and they don’t yet have the score they want on the GMAT. Let’s talk about what to do.

What’s your goal?

First of all, you need to set a realistic goal for yourself. What is your current score? How far are you from your goal?

We’re only about 2.5 months from most 2^nd-round deadlines. In that timeframe, it might be reasonable to make the jump from 550 to 650, from 600 to 670, or from 650 to 700. (The higher you go, the harder it is to go even higher.) Those ranges are just rough benchmarks; some people will be able to make larger jumps, while others unfortunately won’t hit even those rough benchmarks.

If you are currently at a 550 and want to get to 720, it’s likely that you’ll need more time (especially considering that you also have to complete applications in the same 2.5 month timeframe!). You may need to choose between lowering your goal score and delaying your application—to the third round or to next year.

You might also need to reduce the number of applications you’re planning to submit. It would be challenging to apply to 6 schools and commit to a full GMAT study schedule at the same time.

How have you been studying?

Have you already taken the real test? Perhaps you have been studying for months using a comprehensive set of materials but, though you have improved your score, you haven’t reached the level that you want. If this is the case, then you may need specialized help in the form of a class or tutor to help you break through the plateau that you have reached. (Note: this isn’t true in every case, of course, but when you have only a couple of months left and you have to do applications simultaneously, then you need a new approach to help you break the logjam quickly.)

Or maybe you have been studying a bit and know what you need to do, but you haven’t found the time to do a comprehensive review. If that’s the case, it’s time to commit 100%, get your study plan together, and start a daily study regimen.

Finally, perhaps you’ve been procrastinating altogether—life is busy and nobody really wants to study for the GMAT. If this describes you, my best advice is to get yourself into a class immediately. You likely don’t have the time to evaluate the various resources available, put together a full self-study plan, and then execute. At this stage, it’s better to dive into a complete program and get cracking.

The one exception to that is someone who has done very well on standardized tests in the past. If you self-studied for the SAT (or a similar test) and did a great job in a relatively short period of time, then self-study may be the way to go for the GMAT.

What do I need to do to lift my GMAT score?

Finally, we get down to the important question. J

First, the single most important mistake that people make on the GMAT is to treat it as an academic test, especially on the math section, where every question has a right answer (vs. a “best” answer on verbal). The GMAT is not an academic test! I know it feels like one, but it’s not.

This is what the GMAT really tests.

If you want to hit your maximum potential, you have to wrap your head and heart around the mindset described in that article. You can’t just know it intellectually; you actually have to believe it, or you are likely to revert to the old “school test” mentality under the stress of the real test.

Next, you of course need to know the content—the facts, rules, and concepts tested on the exam—as well as how to handle the various question types. That’s all the 1^st level of GMAT study; if you’ve been studying for a while, you likely have a decent handle on a lot of that material.

Beyond that, you need to learn how to think your way through GMAT-type questions, what we call the 2^nd level of GMAT study. If you have hit a plateau in your scoring level, then it may be because you haven’t made the leap to the 2nd level.

I’m going to go back to the “set a realistic goal” idea for a moment. The higher you want to score on this test, the more you will need to master that 2^nd level. If you haven’t really begun to study yet, and you want a 700+, then you are setting yourself the task of getting through both levels in 2.5 months (or sooner). That is a very ambitious goal—too ambitious for most people.

So you’re saying there’s not enough time? I should just give up?

No, of course not. You’ve got to try! Just be realistic and, as with anything important in life, have a back-up plan. If you just can’t make it happen this year, you can always apply next year.

(I know that you’ve probably already told people in your life that you’re going to apply this year. You’re allowed to change your mind, and you don’t have to tell people why. Just say that you decided it was better for your career to wait another year—after all, if you can get a substantially better score by giving yourself more time and applying next year, that may very well change your admissions prospects, and that could change your career!)

I’m actually within 50 points of my goal score. I just need a little boost…

If you’ve been studying and are decently close to your goal already, then there are some additional things you can do to try to secure a final boost to your score.

You need to figure out exactly what’s pulling you down. Most people have timing problems on this test. (If your current thought is that you don’t have timing problems, you’re likely wrong. More than 95% of people have timing problems on this test! Many, if not most, are just unaware of it.)

The good news is this: it’s reasonable to pick up 20 to 30 points (sometimes more, if your timing issues are severe) in about 2 months by fixing timing issues alone. Analyze your most recent one or two Manhattan GMAT CATs to determine what your particular timing issues are. Then learn how to manage your time on the GMAT, starting with developing your 1-minute time sense (section 4 of the article).

Next, focus on the low-hanging fruit. Don’t try to turn your biggest weaknesses into strengths—that will take forever. Instead, minimize careless errors. You already know how to get those questions right, so make sure you earn those points! The article in the previous paragraph that details how to analyze your CATs will help you to place your strengths and weaknesses in one of several “buckets.” Focus on bucket 2.

If you want to enlist a tutor to help you over that final hump, the best thing you can do is take a practice CAT (not GMATPrep, but one that actually provides good data to analyze) and have your tutor analyze it. Use that to set up a study plan, making sure to focus on timing as well as low-hanging fruit. When you feel you’ve made good progress on the issues identified in that first CAT (approximately 2 to 3 weeks, if you’re studying regularly), take another CAT, have the tutor analyze it, and start all over again. Repeat until you’re ready to take the real thing.

You don’t have to use a tutor of course—you can analyze your tests yourself, using the article I linked above. Just go through slowly and carefully to give yourself the best shot of catching everything. Expect to take at least an hour for the analysis; if it takes less time than that, then you are probably missing some important clues that could help you in your studies.

Finally, pick your battles. Don’t try to learn everything. Your best strategy for your bucket 3 categories is just to get them wrong fast and use that time and mental energy elsewhere. Don’t bother trying to turn your biggest weakness into a strength. Don’t spend 10 hours studying combinatorics, when most people see 0 or 1 combinatorics question on the real test. Focus on the low-hanging fruit in bucket 2.

In sum…

If you’re within 100 points of your goal score, then you may be able to get there in the 2 to 2.5 months before second-round deadlines. If you’re more than 100 points away, you can (and should!) still go for it, of course, but be realistic and have a plan B. (In fact, I would have a plan B even if I were within 100 points of my goal.)

In general, make sure to:

(1) Cement the GMAT mindset. (It’s not a school test; it’s a business / decision-making test.)

(2) Fix your timing. Everyone has timing issues; figure out your own issues and make them better.

(3) Focus on the low-hanging fruit! Start with careless errors. Next, concentrate on improving moderate weaknesses. Guess quickly on your biggest weaknesses and use that time elsewhere on the test.

Manhattan GMAT

Studying for the GMAT? Take our free GMAT practice exam or sign up for a free GMAT trial class running all the time near you, or online. And, be sure to find us on Facebook and Google+, LinkedIn, and follow us on Twitter!

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

A student in one of my classes recently asked me how best to set up his GMAT scratch paper while taking the exam, so my first task is to give a shout-out to Robert and thank him for giving me the topic for this article!

I shared a few things with him during class and I’ll share these things with you below. Plus, now that I’ve had a chance to reflect, I have some other ideas for you. Read more

How did it go last time with the rate problem? I’ve got another story problem for you, but this time we’re going to cover a different math area.

Just a reminder: here’s a link to the first (and long ago) article in this series: making story problems real. When the test gives you a story problem, do what you would do in the real world if your boss asked you a similar question: a back-of-the-envelope calculation to get a “close enough” answer.

If you haven’t yet read the earlier articles, go do that first. Learn how to use this method, then come back here and test your new skills on the problem below.

This is a GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “Jack and Mark both received hourly wage increases of 6 percent. After the wage increases, Jack’s hourly wage was how many dollars per hour more than Mark’s?

“(1) Before the wage increases, Jack’s hourly wage was $5.00 per hour more than Mark’s.

“(2) Before the wage increases, the ratio of Jack’s hourly wage to Mark’s hourly wage was 4 to 3.”

Data sufficiency! On the one hand, awesome: we don’t have to do all the math. On the other hand, be careful: DS can get quite tricky.

Okay, you and your (colleague, friend, sister…pick a real person!) work together and you both just got hourly wage increases of 6%. (You’re Jack and your friend is Mark.) Now, the two of you are trying to figure out how much more you make.

Hmm. If you both made the same amount before, then a 6% increase would keep you both at the same level, so you’d make $0 more. If you made $100 an hour before, then you’d make $106 now, and if your colleague (I’m going to use my co-worker Whit) made $90 an hour before, then she’d be making…er, that calculation is annoying.

Actually, 6% is pretty annoying to calculate in general. Is there any way around that?

There are two broad ways; see whether you can figure either one out before you keep reading.

First, you could make sure to choose “easy” numbers. For example, if you choose $100 for your wage and half of that, $50 an hour, for Whit’s wage, the calculations become fairly easy. After you calculate the increase for you based on the easier number of $100, you know that her increase is half of yours.

Oh, wait…read statement (1). That approach isn’t going to work, since this choice limits what you can choose, and that’s going to make calculating 6% annoying.

Second, you may be able to substitute in a different percentage. Depending on the details of the problem, the specific percentage may not matter, as long as both hourly wages are increased by the same percentage.

Does that apply in this case? First, the problem asks for a relative amount: the difference in the two wages. It’s not always necessary to know the exact numbers in order to figure out a difference.

Second, the two statements continue down this path: they give relative values but not absolute values. (Yes, $5 is a real value, but it represents the difference in wages, not the actual level of wages.) As a result, you can use any percentage you want. How about 50%? That’s much easier to calculate.

Okay, back to the problem. The wages increase by 50%. They want to know the difference between your rate and Whit’s rate: Y – W = ?

“(1) Before the wage increases, Jack’s hourly wage was $5.00 per hour more than Mark’s.”

Okay, test some real numbers.

Case #1: If your wage was $10, then your new wage would be $10 + $5 = $15. In this case, Whit’s original wage had to have been $10 – $5 = $5 and so her new wage would be $5 + $2.50 = $7.50. The difference between the two new wages is $7.50.

Case #2: If your wage was $25, then your new wage would be $25 + $12.50 = $37.50. Whit’s original wage had to have been $25 – $5 = $20, so her new wage would be $20 + $10 = $30. The difference between the two new wages is…$7.50!

Wait, seriously? I was expecting the answer to be different. How can they be the same?

At this point, you have two choices: you can try one more set of numbers to see what you get or you can try to figure out whether there really is some rule that would make the difference always $7.50 no matter what.

If you try a third case, you will discover that the difference is once again $7.50. It turns out that this statement is sufficient to answer the question. Can you articulate why it must always work?

The question asks for the difference between their new hourly wages. The statement gives you the difference between their old hourly wages. If you increase the two wages by the same percentage, then you are also increasing the difference between the two wages by that exact same percentage. Since the original difference was $5, the new difference is going to be 50% greater: $5 + $2.50 = $7.50.

(Note: this would work exactly the same way if you used the original 6% given in the problem. It would just be a little more annoying to do the math, that’s all.)

Okay, statement (1) is sufficient. Cross off answers BCE and check out statement (2):

“(2) Before the wage increases, the ratio of Jack’s hourly wage to Mark’s hourly wage was 4 to 3.”

Hmm. A ratio. Maybe this one will work, too, since it also gives us something about the difference? Test a couple of cases to see. (You can still use 50% here instead of 6% in order to make the math easier.)

Case #1: If your initial wage was $4, then your new wage would be $4 + $2 = $6. Whit’s initial wage would have been $3, so her new wage would be $3 + $1.5 = $4.50. The difference between the new wages is $1.5.

Case #2: If your initial wage was $8, then your new wage would be $8 + $4 = $12. Whit’s initial wage would have been $6, so her new wage would be $6 + $3 = $9. The difference is now $3!

Statement (2) is not sufficient. The correct answer is (A).

Now, look back over the work for both statements. Are there any takeaways that could get you there faster, without having to test so many cases?

In general, if you have this set-up:

– The starting numbers both increase or decrease by the same percentage, AND

– you know the numerical difference between those two starting numbers

? Then you know that the difference will change by that same percentage. If the numbers go up by 5% each, then the difference also goes up by 5%. If you’re only asked for the difference, that number can be calculated.

If, on the other hand, the starting difference can change, then the new difference will also change. Notice that in the cases for the second statement, the difference between the old wages went from $1 in the first case to $2 in the second. If that difference is not one consistent number, then the new difference also won’t be one consistent number.

Key Takeaways: Make Stories Real

(1) Put yourself in the problem. Plug in some real numbers and test it out. Data Sufficiency problems that don’t offer real numbers for some key part of the problem are great candidates for this technique.

(2) In the problem above, the key to knowing you could test cases was the fact that they kept talking about the hourly wages but they never provided real numbers for those hourly wages. The only real number they provided represented a relative difference between the two numbers; that relative difference, however, didn’t establish what the actual wages were.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

In the past, we’ve talked about making story problems real. In other words, when the test gives you a story problem, don’t start making tables and writing equations and figuring out the algebraic solution. Rather, do what you would do in the real world if someone asked you this question: a back-of-the-envelope calculation (involving some math, sure, but not multiple equations with variables).

If you haven’t yet read the article linked in the last paragraph, go do that first. Learn how to use this method, then come back here and test your new skills on the problem below.

This is a GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

“(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

“(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.”

You work in a factory. Your boss just came up to you and asked you this question. What do you do?

In the real world, you’d never whip out a piece of paper and start writing equations. Instead, you’d do something like this:

I need to figure out the difference between how long it takes X alone and how long it takes Y alone.

Okay, statement (1) gives me some info. Hmm, so if machine X takes 1 hour to do the job by itself, then the two machines together would take two-thirds…let’s see, that’s 40 minutes…

Wait, that number is annoying. Let’s say machine X takes 3 hours to do the job alone, so the two machines take 2 hours to do it together.

What next? Oh, right, how long does Y take? If they can do it together in 2 hours, and X takes 3 hours to do the job by itself, then X is doing 2/3 of the job in just 2 hours. So Y has to do the other 1/3 of the job in 2 hours. Read more