# Tag Archives: GMAT math

## Go ahead, roll your eyes… but it’s GMAT quantitative reasoning, not GMAT math

If you’ve struggled with the GMAT quant section more than you think you should, this blog post is for you. If you’ve ever said, “I’ve always been a really good math student, but I can’t understand why the GMAT quant is so hard for me!” – then this post is definitely for you.

In my former life as a PhD student, I spent far too much time learning about the statistical science underneath standardized testing, known as psychometrics. My nearly three-year PhD odyssey didn’t result in much other than some grey hairs and a “thank you for playing!” Master’s degree in education, but I did experience a few things that probably helped me become a better GMAT and GRE tutor.

This is a story about one of those things – and at the time, I never would have guessed that it would be useful for my GMAT and GRE students.

In my first year as a PhD student, I went to a psychometrics conference, populated by academics and employees of major standardized testing organizations, including ETS (makers of the GRE and TOEFL) and GMAC (creators of your beloved GMAT). I attended a presentation by a high-ranking GMAT psychometrician, who discussed… well, nevermind that part, I’ll put you right to sleep if I start talking about it.

Anyway, here’s the useful bit: somebody in the audience asked a question about the “math section of the GMAT.” The GMAT psychometrician interrupted him politely: “Excuse me,” he said, “there is no math section on the GMAT. There’s only quantitative reasoning.”

I probably rolled my eyes. “What a dick,” I thought, “why would he make a big deal out of that? It’s math. S#!t, I’ve been teaching it for a decade. Whatever, dude.”

Sure, maybe the GMAT psychometrician wasn’t picking the best moment to make a big deal out of it, but he absolutely had a point. In the few years since I attended that conference, I’ve realized that my students – particularly Americans – actually perform better on the quant section of the GMAT when they stop thinking of it as “math” and start thinking of it as “quantitative reasoning.”

Here’s the thing: in the United States, “math” knowledge – at least through the high school level – is typically taught as sequences of mechanical steps that you need to memorize and follow. Throughout much of my public school education, our daily homework would consist of 10 or 20 nearly identical math problems. The problems were usually so similar that there was no reason to think about what any of it meant. If you could follow instructions, you’d get an A – even if you had absolutely zero understanding of the underlying mathematical concepts.

As a result, most Americans think that the word “math” just refers to a boring series of steps that you follow. Sadly, we don’t think of mathematics as a way of thinking, or as a set of useful tools for reasoning our way through useful problems. There are, of course, plenty of exceptions, but the overwhelming majority of Americans have learned math in a way that strips it of its logic, meaning, and intuition.

So it’s no surprise that I hear this over and over from GMAT test-takers, especially Americans: “I’m a really good math student, but I can’t understand why the GMAT is so hard for me!”

Obviously, there are a ton of reasons why somebody might struggle with the GMAT quant section, but plenty of GMAT test-takers make the subtle mistake of trying to learn too many formulas, memorize too many steps, and drill too many mechanical aspects of mathematics. The GMAT, for all of its flaws, brilliantly twists 10th-grade math into a hard-to-penetrate – or at least a hard-to-quickly-penetrate – tangle of logic.

In other words: if you’re trying to blindly apply mechanical techniques to GMAT quant questions above the 500 or 600 level, the exam will eat you for breakfast.

Let’s look at an example (with apologies for the blurry fractions):

Which of the following is greatest?

If you think of this as a mechanical “math question,” you’ll follow some well-worn steps here: find some common denominators, add the fractions, and THEN compare the sums.

Go ahead and try it if you’d like. If you can correctly solve the question that way in two minutes or less, I’ll give you a cookie.

But if you’re thinking of the GMAT as “quantitative reasoning” – with or without the eye-roll – then maybe you’ll try something quicker, smarter, and less arithmetic-intensive. In this case, we’re just looking for the greatest value – and we don’t care what that value actually is, as long as we know that it’s larger than the other four answer choices.

So since the question is just asking for the greatest of the five answer choices, you can just compare pairs of answer choices, and knock off anything that’s the smaller of the two. Let’s start with D and E. It’s easy to see why E is larger than D once you notice that 1 – ½ = ½, so D is gone.

Similarly, B looks a lot like E, except that the denominators in B are squared – and since larger denominators mean that the fractions must be smaller, we can cross off B. The same argument holds for C – it’s clearly smaller than E as well. And then A has smaller denominators than E – so A is your answer.

No computation required, right? If you’re approaching this wisely, you barely need to lift your pen.

So if you’re thinking of the GMAT quant section as a set of narrow mathematical tasks – formulas that need to be memorized, or boring-ass steps that need to be followed – then you’re barking up the wrong tree, at least if you want an elite GMAT quant score. Once you start looking for opportunities to apply flexible logic and identify multiple solution paths, then you’re on the right track.

If any of this strikes a nerve, then it might not be a bad idea to stop yourself whenever you start thinking about the GMAT “math section.” Roll your eyes at yourself if you’d like, but thinking of the GMAT quant section as “quantitative reasoning” might help you embrace the flexibility and logic you’ll need for a top GMAT quant score.

## How to find a good private GMAT tutor

Let’s suppose that you live in a city large enough to have a decent population of private GMAT tutors, and let’s suppose that you’ve collected a list of tutors from Craigslist or gmatix.com or Google or some other website. (And let’s suppose that you’re not looking for an online GMAT tutor, otherwise you would have called the number on the sidebar, right?) So how, exactly, should you go about figuring out which private GMAT tutors actually know what they’re talking about?

Before I continue, let me be painfully honest about my own history as a private tutor: when I first started teaching GMAT lessons at a major test-prep firm more than a decade ago, I barely knew what I was doing. I was always a lively teacher, but you really shouldn’t have hired the 2001 version of GMAT Ninja; the GMAT is an incredibly nuanced exam, and it took some time for me to truly understand how to help my GMAT students succeed. I worked hard at my craft from the very start, but I know—with the benefit of hindsight—that I wasn’t the world’s best GMAT tutor when I first started out.

So if you’re looking for a great private GMAT tutor, you want to avoid shoddy, inexperienced teachers (such as the 2001 version of GMAT Ninja) and find a veteran instructor who can really help you achieve your goals.

To help you in your quest, here are a six ways to help you separate the best private GMAT tutors from the rest of the crowd… with the caveat that this is probably the longest GMAT blog post I’ve ever written. Consider yourself warned.

Hire a GMAT specialist, not a math generalist

Once upon a time, I placed general advertisements that offered my tutoring services for every major standardized test, including the GMAT, SAT, ACT and GRE. You shouldn’t have hired me back then, at least not for the GMAT.

Here’s the problem: the GMAT has shockingly little in common with most other standardized tests. The GMAT is a frustrating experience for many students exactly because its questions are unusually twisted; the quant section of the GMAT tests your ability to read convoluted math questions and make tricky logical connections. Sure, a general math/GRE/SAT tutor can help you polish your algebra and geometry basics, but an ideal tutor will help you to understand the bizarre quirks that are unique to the GMAT.

So if you find a general math tutor who claims to teach the GMAT well, make absolutely certain that the tutor can tell you exactly what makes the GMAT different from other standardized tests. Ask the tutor to talk about the difference between the GMAT and the GRE or the SAT. If he tells you that the tests are basically the same, then you’re better off finding another private GMAT tutor.

Ask if the tutor has taken the GMAT

As you undoubtedly know, the GMAT is a strange little creature that features a painfully broad variety of questions. Sometimes, it feels like the GMAT is a test of psychological strength, not just a test of verbal and math skills.

Any great GMAT tutor understands what it feels like to struggle through the GMAT, and completely understands the physical and psychological stresses unique to the exam. If your tutor hasn’t taken the exam often enough, it’s unlikely that he truly understands how to help you succeed on the test. So make sure that your GMAT tutor can have an intelligent, detailed conversation about his experiences in the testing room before you hire him for a tutoring session.

Hire a teacher, not just a test-taking wizard

Although you definitely want to make sure that you hire a GMAT tutor who regularly takes the exam, you should never hire a private tutor based solely on a high GMAT score. Just because somebody got a high score doesn’t mean that he is a great GMAT teacher.

Think of it this way: many people who get extremely high GMAT scores actually think that the test is pretty easy. If somebody doesn’t struggle with the test, it’s possible (or probable) that he would be incapable of figuring out why somebody else might find the GMAT difficult. And if a GMAT tutor can’t understand why the GMAT is difficult for you, you’ll probably waste your money by hiring him.

Obviously, you want to make sure that your GMAT tutor knows the test well enough to earn a high score, but don’t fall in love with a tutor just because he scored a 780 or an 800. Make sure that your GMAT tutor is an experienced, dedicated teacher who can have an intelligent conversation about his teaching strategies.

If you’re interested in hiring a private GMAT tutor, you probably decided that a one-size-fits-all GMAT prep course isn’t the best thing for you. You probably understand that your challenges and strengths and weaknesses are different from those of your test-prep classmates. You know that everybody has a different way of learning… but does your GMAT tutor know that?

If you speak with a GMAT tutor and he offers a rigid “plan” or “program” that he uses for all of his GMAT students, you might be wasting your money. The point of private tutoring is to receive a customized program designed specifically for your needs. If you speak with a tutor and he doesn’t seem terribly interested in adapting his teaching to suit your specific needs, you might want to look elsewhere.

The bottom line: make sure that the GMAT tutor is willing to have a detailed, engaging conversation about your specific needs. He definitely shouldn’t have all of the answers based on a phone call, but he should be able to broadly outline a unique GMAT tutoring program tailored specifically to your goals, strengths and weaknesses.

Don’t let the tutor’s price fool you — in either direction

Many people make the mistake of thinking that high prices and high quality always go hand-in-hand. In the wonderful world of private GMAT tutoring, I don’t think that this is necessarily the case.

During my years as a private tutor, I’ve met some spectacular teachers who massively undercharge for their services, and I’ve met some great teachers who charge a small fortune. I’ve also met crappy teachers who charge \$20/hour, and crappy teachers who charge hundreds of dollars per hour.

To be honest, tutoring prices have very little to do with the quality of the teacher. Don’t assume that a high-priced GMAT tutor is necessarily good at what he does, and don’t assume that an inexpensive tutor is an unseasoned rookie. Some people are simply more aggressive than others from a pricing and marketing perspective—and that often has nothing to do with the quality of their teaching.

In the strange world of private tutoring, you don’t always get what you pay for. Ask the right questions, and you might be able to find a great GMAT tutor at a reasonable price.

Don’t hire a GMAT miracle salesman

Improving your GMAT score inevitably involves lots of hard work, and any great GMAT tutor will acknowledge that fact. If your GMAT goals are ambitious, and you hope to gain 100 or more points on the test, you should probably be prepared for a long, hard battle. The best GMAT tutors will always make that battle much easier, but if you call a private tutor and he says that you’ll be able to gain 200 points in a few weeks, you should definitely call somebody else.

Also, be very careful with score improvement statistics, which are frequently manipulated by test-prep firms. If a GMAT tutor claims to have an average score improvement of, say, 120 points, you need to look more closely at his claims. Many GMAT tutors and test-prep firms use questionable GMAT diagnostic test data as the “before” scores, and truth is that we rarely have truly accurate data on our students when they begin working with us.

Think of it this way: if a student has never taken the real GMAT test before hiring me as his tutor, how can I possibly take credit for a specific score improvement? If a student took the GMAT, then took a mass-market GMAT prep course, and then contacted me for tutoring, how do I know how much of her score improvement was due to my efforts, and how much of the improvement was a result of the GMAT prep course?

The bottom line is that statistics simply aren’t all that useful in the wonderful world of GMAT tutoring. Hire an honest person who willingly shares stories and references, and you’ll be much less likely to get burned by an ineffective GMAT tutor.

## GMAT timing “strategy”: how much math do you really need for a 720?

I pride myself on being a brutal realist: if I suspect that one of my GMAT students might need a ton of luck and a herculean effort to achieve her score goal, I’ll tell her… gently. A huge part of my job is establishing realistic expectations, and if I think that a student’s GMAT goals are utterly hopeless, I’ll say that, too… though I’ll usually say something far more diplomatic than “you’re hopeless.”

But sometimes my dire predictions of GMAT frustration are ridiculously wrong, and sometimes one of my students makes me feel like a complete idiot.

I love it when that happens.

Once upon a time, a warm and thoroughly loveable student (let’s call her Ms. A) came to New York for a four-week GMAT “crash course.” Like most of my GMAT students in New York, she was targeting a 700+ score; unfortunately, her math skills were pretty shaky. She wasn’t appallingly bad at math, but her academic background was in the humanities, and she hadn’t taken a math course since high school. Ms. A was clearly intelligent and competent, but I didn’t immediately see much evidence of math talent or training.

To make things worse, math—or at least GMAT math—seemed to scare the poop out of her. Ms. A would make a sad, cute whining sound (imagine a frightened puppy) whenever she saw a math question that intimidated her—and that happened with disturbing frequency. After a couple of sessions, I told her that she might need more than four weeks of GMAT tutoring, and that she would probably struggle to get her quant score near the mid-40s.

She proved that I’m an idiot. But thanks to Ms. A, I’m a proud, happy idiot.

After giving her a friendly warning to keep her score goals in perspective, I asked Ms. A to do her first math practice exam, knowing that it would be a painful experience. She got a 35, which didn’t surprise me at all.

I then reiterated my standard timing rant: if you read the question twice and don’t see a clear path to the answer, just guess and move on. Use the time you save to be ridiculously accurate on the other questions; always reread each question and check your work carefully before you click “next.” And I reminded her that she would probably miss roughly 15 questions on the quant section—but that her score would be determined by which questions she missed.

Put another way: the GMAT scoring algorithm severely punishes you for missing relatively easy questions, but your score is barely harmed by missing the toughest questions. The key to success—especially on the quant section—is to be 100% bulletproof on the questions that you understand, and to waste as little time as possible on the questions that are difficult for you.

(I repeat that advice constantly to all of my GMAT students, and I’m sure that my current and former students are rolling their eyes as they read this. If you hire me as your GMAT tutor, you’ll hear me say those same lines again and again… or at least until you stop making unnecessary mistakes on your practice tests.)

Anyway, back to Ms. A. Instead of rolling her eyes, Ms. A looked relieved when I begged her to skip the hard questions and spend her time on the easier ones—I think she was genuinely thrilled that she could ignore the questions that made her whine like a homesick puppy. The very next day, her practice test score jumped to a 43. A few days later, she scored 47 on another practice quant test.

I would love to pretend that I taught Ms. A enough GMAT math to improve her quant score by 12 points, but she took all three practice tests in the same week, and I can’t honestly take much credit for improving her math skills in such a short time frame. Sure, she was working hard and her underlying quant skills were improving steadily, but the key was that she executed her timing strategy to absolute perfection. After her first test, she never wasted time on overly difficult questions, and she almost never made careless errors on questions she understood.

In the end, Ms. A kicked some GMAT ass: 720 composite, with a 47 on the quant section.

Was Ms. A special? In a way, no: she worked really hard at her math skills, but could never be mistaken for a natural math genius.

But in another way, Ms. A was truly amazing: she has an unbelievably flexible mentality, and she was able to train herself to approach the test in a completely different way. She didn’t let the GMAT clock rattle her—no matter where she was in the test, she carefully re-read each question and re-checked her work, and she understood that it was worth spending an extra 10-20 seconds to do so. (It also helped that she was naturally gifted at verbal, and could afford to spend her study time focusing almost exclusively on math.)

At the end of the day, Ms. A beat the GMAT with a insanely simple quant strategy: if she understood a question, she answered it carefully. If she didn’t immediately understand a question, she wasted very little time on it. Her approach was simple and elegant. The GMAT world is filled with a cacophony of advice about test-taking “strategy”, but you don’t really need most of that stuff: just work as hard as you can to become better at answering questions correctly, and don’t waste your time chasing the nasty questions that you still can’t easily answer.

Could you be the next Ms. A? If you have a tendency to make careless errors on your homework, you’ll need to thoroughly re-orient yourself. I constantly hear MBA aspirants say “I missed 10 questions on the homework, but they were just stupid errors—I understood all of the questions”… as if that’s a good thing! The GMAT will rip you to shreds if you make silly mistakes on easy questions, no matter how well you understand the hardest concepts covered in the GMAT Official Guide.

So take Ms. A’s simple approach: be mind-numbingly accurate on the quant questions you understand, and save time by letting the toughest questions go. If you can do that with flawless consistency, your quant score will be perfectly solid, even if your math skills aren’t exactly incredible.

Math-phobic students have always been a part of my life as a GMAT tutor, and I currently work with several New Yorkers who used to sweat profusely whenever they heard the words “slope” or “equation.” One of my favorite current students is a 34-year-old actor who has taken exactly no math since high school, and he is raising all sorts of interesting questions as he starts to ascend toward a decent GMAT score.

This particular guy (let’s call him Mr. L… that’s short for Law & Order, since he once appeared on an episode as the main victim) took a Princeton Review GMAT course, got a horrendous score on the math section (21, which is probably on the wrong side of the 10th percentile), demanded his money back from Princeton Review, hired a GMAT tutor in India (he was volunteering there at the time), and then managed to get a 33 on the math–a huge, huge improvement. (If anybody needs a GMAT math tutor in Ahmedabad, India, I can recommend a great one. Oddly enough, I also know a great auditor who lives there, too. And no, I’ve never set foot in Ahmedabad or anywhere else in India.)

Upon his return to NYC, Mr. L contacted me for GMAT tutoring, and we’ve been working together for about a month. His patience for the GMAT started to wane recently, and I suggested that he take a few practice math tests–not because I thought that he was almost ready to take the GMAT, but because I thought that online practice tests would keep him a little bit more engaged than paper-based practice problems.

And Mr. L pretty much crapped himself when he saw his first score: on a Manhattan GMAT test, he scored 40 on the math. I figured that it wasn’t a complete fluke–Mr. L had improved by quite a bit. But he was highly skeptical, so I asked him to take another MGMAT math test. And he scored 40 again. Clearly, the 40 wasn’t a fluke, unless you’re skeptical of MGMAT’s scoring (that’s another topic entirely, but I usually find that the math scores are fairly accurate for students who haven’t taken their course).

I haven’t quite succeeded in convincing Mr. L that he deserved the 40, and here’s why: on both tests, he got 20 questions right, and missed 17. In the American educational paradigm, getting just over half right usually means that you barely passed, which means that you suck. Mr. L couldn’t really get his head around this: he missed enough GMAT math questions to suck pretty badly, but his score was higher than he ever dreamed possible.

So here’s the deal: adaptive tests such as the GMAT and GRE are designed to make you miss lots of questions. (That’s one of many reasons why taking these tests can be such a painful experience.) Each GMAT question is essentially assigned a difficulty level–if it helps, you can think of each GMAT question as, say, a “700-level” or a “520-level” question. The test basically tries to figure out the level of question at which you get 50% right. It seems logical that you might be able to get 55-60% of the questions right, and still get a decent score–your score is based on which questions you miss, not necessarily on how many you miss.

If you don’t believe me, check out a recent entry in the official GMAT blog that addresses this issue.  Or keep reading.  Whichever you prefer.

If it helps, imagine that you’re destined to earn the equivalent of a 650 on the math section of the GMAT. (For the sake of simplicity, I’m going to ignore some of the complexities of GMAT scoring. Forgive me.) The first question of the test will be a 550-level question (roughly), and let’s suppose that you get it right. You’ll get a harder question next, and you probably won’t start to screw up consistently until you see a few 650- or 700-level questions. But it won’t take too long to get to that level–if you get the first three questions right, the fourth question of the GMAT quant section will probably make you sweat.

Now, imagine that the fourth question is a 650-level question… seems reasonable enough, right? If you’re a 650-level test-taker, you’re likely to miss about half of the remaining 34 questions. I’m obviously making some gross oversimplifications here, but it isn’t hard to imagine that you could get a 650 on the GMAT, or perhaps something even higher… without getting more than about 20 questions right.

My point is this: in all likelihood, you have a huge margin for error on the GMAT. As long as you don’t fall apart at the beginning of the test, you can miss tons of questions, and still get a fantastic score. So when you see some crazy, indecipherable GMAT combinatorics problem, there’s really not much harm in guessing and moving on–one missed question won’t hurt your composite score by much, and you’ll have plenty of chances to recover.

So if you’re reading this, Mr. L… have I convinced you yet? You actually deserved those 40s, and we’re not even warmed up yet. Crazy as it sounds, getting 60% of the questions right might be enough to get you wherever you want to go on the GMAT math section.

## why you shouldn’t worry (too much) about percentile rankings

I’ve already met some brilliant MBA candidates in my first few weeks here in New York, but the most gifted GMAT student I ever tutored was probably a young woman I met in DC, before my Manhattan days.  She was a cum laude graduate of Duke University’s economics program, and she had already earned a ridiculously high score on the GRE.  She was solidly scoring in the 700s on her GMAT practice tests, and just wanted help getting her math score “as close to perfect as possible.”

I’ll be honest:  there’s a pretty good chance that this particular GMAT student (let’s call her Susan) was smarter than I am, and that’s a beautiful and intimidating situation to be in as a GMAT tutor.  I suspected (correctly) from the start that she didn’t have any fundamental GMAT math weaknesses; all I could offer was some practice questions designed to help her make connections on the hardest GMAT math questions.  (Basically, math formulas are of limited value on hard GMAT questions, and you need to be able to “see” a connection before you’ll have any prayer of getting the right answer.  I’ll expand on this in a future blog post.)

Basically, tutoring Susan meant spending two hours inventing the hardest GMAT-style questions I could possibly come up with.  I loved it, and I probably learned more from the experience than she did.  Occasionally, I’d manage to stump her, and that was great.  After about eight or ten GMAT tutoring sessions, we decided that she had probably “worked her GMAT math muscles” as much as was reasonable, and she went to take the test.

And she was bitterly disappointed when she looked at her percentile ranking on the GMAT.  She scored in the 99th percentile on the verbal, and her composite score was also in the 99th percentile.  Her quantitative score, however, was only in the 84th percentile.  How could this be true?  She scored a 760 on the GMAT, but somehow wasn’t even in the top 10% in math? WTF?

If you have any experience with the GMAT, you surely realize that a score of 48 on the quant section is pretty darned impressive.  (Frankly, anything above a 45 should, in theory, be good enough to allay any legitimate fears that an MBA admissions committee might have about your quant skills, but that’s another topic entirely.)  For whatever reason, however, there are lots of impressive math whizzes taking the GMAT.  A full 20% of GMAT test-takers earn a score between 47 and 51.  The score distribution, then, is not a bell curve at all for the quantitative section–it basically looks like a slowly increasing function, with an extra little jump at the end.

I admiringly call this the “Asian effect.”  Based on anecdotal evidence, I’m convinced that most of the people who achieve quantitative scores in this range are not products of the United States education system.  (News flash:  by global standards, we Americans are generally pretty lousy at math.)  Basically, there are a ton of people in Asia who demolish the quantitative section of the GMAT, and they make a whole lot of GMAT-takers feel inadequate when they see their percentile score.

Interestingly, the GMAT verbal score distribution is almost a perfect bell curve.  Similarly, the GMAT composite score distribution is also a fairly non-skewed bell curve.  This suggests that most of the GMAT “quant ninjas” are not particularly great at verbal.

The bottom line?  If you’re trying to get into top MBA programs, it’s probably OK to have a math score “only” in, say, the 70th or 75th percentile.  Don’t let the percentile score mess with you:  if your raw GMAT quant score is well into the 40s, it probably won’t, by itself, sabotage your MBA dreams.

## stealth exponents

It’s always a little bit tricky and annoying to write math problems on a GMAT blog (there’s no way to comfortably write equations, unless you want to import images), but I’ll do my best with this topic.  I just want to make a few little comments about exponents, and about the ways in which the GMAT Official Guides (including the GMAT Quantitative Review Guide) can lull a perfectly good GMAT student into complacency on the topic.

Hopefully, you know all of the basic exponent rules.  If you’re multiplying two terms with the same base, you’ll add the exponents (example:  x^3*x^4 = x^7).  If you’re dividing, you know that you subtract the exponents, and then you might encounter something like a “power of a power” question (example:  (x^6)^2 = x^12).  If you know these rules and a few other basics (i.e. what happens if an exponent is negative, a fraction, or zero), you’ll be fine on the GMAT.  Right?

If you’re focused on the GMAT Official Guide questions… well, yes, you’ll be mostly fine.  Let’s take a quick survey of the exponent questions in the problem solving section of the 12th edition of the GMAT Official Guide:  #15, #28, #46, and #108 all contain exponents, but they’re mostly a matter of calculating (or simplifying) some numbers.  #104 and #110 look like exponent problems, but both are really about factors, not exponent properties.  #137 could be solved using exponent properties, but is just as easily done with some simple calculations and logic…

I could go on.  My point is, most of what you encounter in the GMAT Official Guides doesn’t require much knowledge of exponent properties.  And when you do need to use exponent properties, they’re just covering the basics.

Funny, I didn’t see anything basic last time I took the GMAT, and neither did most of my students who scored above 600.  I keep hearing the same refrain:  the exponent problems looked nothing like they do in the GMAT Official Guides.

I’m convinced–based on the GMATPrep, GMAT Focus, and the real thing–that the GMAT is much more likely to show you an exponent question that has something to do with factoring and/or “base conversion.”  Neither of these topics necessarily receive the attention they deserve in GMAT test-prep books.

Please accept my profuse apologies for the crappy notation, but here are a couple of examples of realistic, harder exponent problems (NOT from official GMAT materials, lest I incur the wrath of some bigshot NYC lawyer sent by the bigshots who write the GMAT):

(7^10 – 7^8)/3 = (2^x)(7^y).  If x and y are integers, then what is the value of x + y?

3^(x-1) – 3^(x+1) = -(9^5)(2^3).  What is the value of x?

I’m not going to post solutions until I’m begged repeatedly, but hopefully you see where I’m going with this.  You’re going to see GMAT exponent problems that require some factoring, as well as the ability to make some ostensibly unlikely connections.  Unless you’ve seen these problems, you might be wondering where the heck the 2’s are coming from.

Welcome to the GMAT.  If you’re not uncomfortable, you’re probably not doing well.  Either that, or you’re way smarter than I am, and you shouldn’t be wasting your time reading a blog posting about exponents on the GMAT.