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Posted on
Sep 2020

Which Is The Greatest – GMAT Problem

Today we’re going to look at a GMAT problem that screams for estimation but can really tie you in knots if you don’t have the right pivot question, the right perspective. Of the following which is greatest? And on its surface this would seem like a straightforward question except of course the GMAT being the GMAT they’re going to give you a bunch of numbers that are going to be hard to interpret. One part of this problem is simply training. The square root of 2, the square root of 3, the square root of 5. These are common, especially root 2 and root 3 because we see them a lot on triangle problems.

Get Familiar With Identities

And knowing these identities by heart as an estimate is really, really valuable just for being able to get a bearing whether you’re on a geometry problem and you’re trying to navigate or make sure that your answer seems correct or if you’re in a problem like this knowing these identities root 2 is 1.4, root 3 is 1.7, root 5 is 2.2 is useful as a touchstone.

Break Down The Problem

But this problem in general and the greater problem can be broken down not by saying oh well this is 1.4, this is 1.7, but by asking ourselves well logically which is bigger which is smaller. Remember it’s a multiple choice exam and they’re asking for the biggest or the smallest or whatever it is but these are opportunities to compare not nail down knowledge and this attitude is exceptionally vital for the data sufficiency but it crops up in problem solving a lot more than people might care to admit.

Especially if you’ve been there just trying to study and study and study and get to a precise answer on a lot of these things. So, let’s start just by taking a look at a few things. First square root of three square, root of two which one’s larger? If you said root three you are correct. How much larger? That might be a little bit more difficult to ascertain but if you say 1.7 versus 1.4 maybe 20 percent larger 3 is 50% larger than 2 so root 3 is going to be some smaller percentage larger than root two. But either way we know that root three is the bigger one it’s going to be the dominant value so the question becomes how much larger? Or which part of the answer drives the answer choice?

What Do We Know?

So we know that the integers 2 and 3 are more meaningful, larger than the square roots because the square roots are components of those integers. So between A and B, a drives the question that is the three drives the root two more than the two drives the root three. We can take a look at the following two and notice that both of them are around root three.

That is if we take apart the ugly part, which is the square root and take a look at the rest of it – four over five, five over four, these numbers are about one and compared to the two root three we have and the three root two which we’ve already decided is even stronger we don’t really need to entertain C and D all that much. Just to understand that oh they’re about a root three and that’s not going to be enough.

Looking At Answer Choice E

Finally, we have E. E is a little funky but we can ask ourselves how many times will root 3, will this 1.7 go into 7 and we get this answer that it’s a bit below 4. Compared with 3 root 2 which is 4.2 (3 times 1.4), we still have a driving the answer. You guys see how this is a marriage of doing a little bit of estimation but also really keeping your framing as is this greater or less than. Now we’ve included a bunch of other different answer choices here for you to take a look at play around with it and see if you can get yourself familiar with comparing these things because the GMAT is only going to come at you with things like square roots that are unfamiliar.

So it’s a fairly defined GMAT problem in that sense. I hope this helps, questions below, like us, subscribe, keep checking in and we’ll see you again real soon.

If you enjoyed this GMAT problem, try these problems next: Probability problem, and the Speed Distance problem.

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Posted on
Aug 2020

Probability GMAT Problem

Probability GMAT Problems can be super complex if you don’t frame it correctly. One of the keys to looking at probability problems, particularly conditional probability and independent probability problems, is breaking each part up into its own entity, and a lot of times this clarifies the problem.

Introduction To The XYZ Probability Problem

Let’s take a look at this ‘XYZ’ probability problem. Xavier, Yvonne, and Zelda are solving problems. We’re given the 3 probabilities for correct answers and we’re being asked what’s the probability of X being right and solving it, Y solving it, and Z not solving it.

The first thing we can look at is, say: “Well what’s the probability of Zelda not solving it?” And it’s just going to be the flip, the other side of 5/8 to bring us up to 1. If she solves it 5 out of 8 times, she’s not going to solve it the other 3 out of 8 times. So, we’re dealing with 1/4, 1/2, and 3/8.

Doing The Math May Seem Simple

The math here is straightforward, multiply them together. But that might not be readily apparent, or at the very least, just plugging it into that formula can get you into trouble. So, here’s where owning it conceptually and mapping it out with a visualization helps you take command of this problem. 

Xavier Getting It Correct

Since each probability is independent of the others we can look at them independently. What’s the probability of Xavier getting this correct? 1 out of 4 times. So, we can say in general, for every four attempts, he gets it correct once or 25%. If, and only if Xavier gets it correct can we move on to the next part – Yvonne.

Yvonne Getting It Correct

Xavier gets a correct 1 out 4 times then what are the chances that Yvonne gets a correct? 1 out of 2. So to have Xavier get it correct and then Yvonne get it correct it’s going to be 1 out of 8 times – 1/4 times 1/2.

It’s not that we can’t look at a Yvonne when Xavier gets it incorrect, it’s that it doesn’t matter. From a framing perspective, this is all about only looking at the probability for the outcome that we want and ignoring the rest.

Zelda Getting It Incorrect

Xavier: 1 out of 4, Yvonne: 1 out of 2, gets us to 1 out of 8. Then and only then, what are the chances that Zelda gets it incorrect? 1 out of 8 trials brings us to X and Y are correct, then we multiply it by the 3/8 that Zelda gets it incorrect. That gets us to 3/64. 3 out of every 64 attempts will end in ‘correct’, ‘correct’, ‘incorrect’.

This is one of those problems that may have to go through a few times but once you attach the explanation to it, you can’t mess up the math.

If you enjoyed this GMAT probability problem, try your hand at these other types of challenging problems: Combinatorics & Algebra

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Posted on
Jul 2020

GMAT Problem – Speed Distance Problem

Speed and distance problems are among the most complained about problems on the GMAT. Numerous clients come to us and say they have difficulty with speed and distance problems, word problems, or work rate problems. So we’re going to look at a particularly difficult one and see just how easy it can be with the right approach.

The Two Cars Problem

In this problem we have two cars – car ‘A’ and ‘B’. Car ‘A’ begins 20 miles behind car ‘B’ and needs to catch up. Our immediate DSM (Default Solving Mechanism) is to dive in and create an equation for this and that’s exactly what we don’t want to do.

These types of problems are notorious for being algebraically complex, while conceptually simple. If you hold on to the algebra, rather than getting rid of it, you’re going to have a hard time.

Solution Paths

In this problem we’re going to build up solution paths. We’re gonna skip the algebra entirely. We’re going to take a look at an iterative way to get to the answer and then do a conceptual scenario, where we literally put ourselves in the driver’s seat to understand how this problem works. So if we want to take the iterative process we can simply drive the process hour-by-hour until we get to the answer.

Iterative solution path

We can imagine this on a number line or just do it in a chart with numbers. ‘A’ starts 20 miles behind ‘B’ so let’s say ‘A’ starts at mile marker zero. ‘B’ starts at 20. After one hour ‘A’ is at 58, ‘B’ is at 70 and the differential is now -12 and not -20. After the second hour ‘A’ is at 116, ‘B’ is at 120. ‘A’ is just four behind ‘B’. After the third hour ‘A’ has caught up! Now it’s 4 miles ahead. At the fourth hour it’s not only caught up but it’s actually +12, so we’ve gone too far. We can see that the correct answer is between three and four and our answer is three and a half.

Now let’s take a look at this at a higher level. If we take a look at what we’ve just done we can notice a pattern with the catching up: -20 to -12 to -4 to +4. We’re catching up by 8 miles per hour. And if you’re self-prepping and don’t know what to do with this information, this is exactly the pattern that you want to hinge on in order to find a better solution path.

You can also observe (and this is how you want to do it on the exam) that if ‘A’ is going 8 miles an hour faster than ‘B’, then it’s catching up by 8 miles per hour. What we care about here is the rate of catching up, not the actual speed. The 50 and 58 are no different than 20 and 28 or a million and a million and eight. That is, the speed doesn’t matter. Only the relative distance between the cars and that it changes at 8 miles per hour.

Now the question becomes starkly simple. We want to catch up 20 miles and then exceed 8 miles, so we want to have a 28 mile shift and we’re doing so at 8 miles an hour. 28 divided by 8 is 3.5.

Conceptual scenario solution path

You might ask yourself what to do if you are unable to see those details. The hallmark of good scenarios is making them personal. Imagine you’re driving and your friend is in the car in front of you. He’s 20 miles away. You guys are both driving and you’re trying to catch up. If you drive at the same speed as him you’re never going to get there. If you drive one mile per hour faster than him you’ll catch up by a mile each hour. It would take you 20 hours to catch up. This framework of imagining yourself driving and your friend in the other car, or even two people walking down the street, is all it takes to demystify this problem. Make it personal and the scenarios will take you there.

Thanks for the time! For other solutions to GMAT problems and general advice for the exam check out the links below. Hope this helped and good luck!

Found it helpful? Try your hand at some other GMAT problems: Profit & Loss Problem.

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Posted on
Jun 2020

Snack Shop GMAT Problem

The Snack shop GMAT problem is an average or a mean problem. A characteristic of many average problems is that one big takeaway right at the outset is that the answer choices are clustered tightly together. We want to refrain from making any calculations.

The problem is below:

snack shop problem

Selecting A Solution Path

If they’re looking for a level of precision, the estimation solution path isn’t available to us. If we dive into the problem, right from the first sentence we have sort of a conclusion that we can create via either a graphic or accounting solution path.

If you were the business owner immediately you’d say to yourself: Well for 10 days and an average of $400 a day I made $4000. 

This is how we want to think about averages. Many times they’ll tell us a parameter about a length of time or over a certain universe of instances and here we want to treat them all as equal.

Solving the Problem

It doesn’t matter if one day we made 420 and another day we made 380. We can treat them in aggregate as all equal and start out with that assumption. That’s a very useful assumption to make on average problems. So, we start out knowing that we made 4,000. 

What I want us to do is do a little pivot and notice from a running count standpoint how much above or below we are on a given day. So we’re told that for the first six days we averaged $360 which means each of those six days we’re short $40 from our average. That means in aggregate we’re short $240. 6 days times $40 –  and this has to be made up in the last 4 days.

Notice how we’re driving this problem with the story rather than with an equation. In the last four days we need to outperform our 400 by 240. 240 divided by 4 is 60. 60 on top of the 400 target 

that we already have is 460. Therefore, our answer is D.

Graphical Solution Path

If we are more comfortable with graphic solution paths, imagine this in terms of 10 bars each representing $400. Lowering six of those bars down by 40 and taking the amount that we push those first six down and distributing it among the last four bars gives us our $460 total per day.

snack shop graphic solution path

If you enjoyed this Snack Shop GMAT Problem, watch “The Gas Mileage GMAT Problem” next.



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Posted on
May 2020

GMAT Scoring – Demystified

One of the most common questions asked by those who are new to the GMAT is how exactly does the computer adaptive test or CAT work? The long and short of it is that if you get a problem correct, they give you a harder one, if you get a problem incorrect, they give you an easier one. By doing this the GMAT is able to bounce up and down and calibrate to your skill level.

Should You Spend more time on the first 10 questions?

A few things come out of this including questions about how to spend your time. Whether certain questions are weighted more than others, whether your timing, that is the amount of time you spend on a problem factors into the score.

To start, there’s a common misconception that you should spend more time on the first 10 questions because they tend to adjust your level for the computer adaptive test at a greater rate. While that’s true in the sense that the computer adapted model on the GMAT does influence it more at the outset, whether you should spend more time is actually a more complex question because generally the GMAT is going to give you problems that are about average and build up or down from that average.

Planning To Score An Elite GMAT Score

If you’re planning on performing at a top level, at an elite level, if your goal is 700 or even 600, you need to assume that those early problems that are average level problems you’re going to do well and in a timely manner anyway.

That is spending extra time to ensure you get them correct is a grandiose version of spending extra time to make sure that you’re getting two plus two correct. You wouldn’t check that because you’re confident enough in your skills and if you’re in the GMAT and you’re getting ready to shoot for a 700 you should already be confident enough in your skills not to have to spend extra time on average level problems. To take these problems on a problem-by-problem basis rather than with blanket statements.

Does The Test keep Track of Other Information?

A common question is whether or not the test keeps track of the type of problems you do. This can refer to:

    • subject matter
    • problem solving versus data sufficiency 
    • reading comprehension versus critical reasoning versus sentence correction

However, we can still go about it with the core rule: if you get it right you’re going to see something more challenging, get it wrong, less challenging. We tend to believe that they don’t keep a great track of that but really rely upon the bouncing up and down to calibrate you to your average performance level. You don’t want to sweat any single problem or worry about any single problem type in regards to the Computer Adaptive Test.

Certainly,  sometimes you’ll know that certain types of problems require more or less attention from you or that you make common errors on those problems. However, that’s not a CAT thing, that’s just a general GMAT thing. 

You are penalized for spending too much time on a problem but not in the way you think.

The other big question we hear a lot is whether or not the amount of time you take on a problem factors into the score. The answer here is subtle, it’s yes and no. No in the sense that the GMAT scoring algorithm does not track the amount of time that you spend on a problem. But, yes in the sense that the more time you spend on problems the less time you have for other problems. In particular, if you’re scoring above average, you’re on this ascendant curve so that the difficult problems at the end require more time than the less challenging problems at the beginning.

Therefore, if the GMAT kept track of your time and penalized you for spending longer on problems they would actually be penalizing you twice and this gets us into our timing decisions and the trade-off between time and score.

Time and Score Trade-off

When you’re armed with confidence and knowledge about how something works you don’t have to worry about how it works or how what you’re doing affects how it works and you can focus on the task at hand. 

The more that you can offload the burden of worrying about the scoring and the mechanisms by which the GMAT measures you, the more success you will find. As always, I hope this helps and keep prepping!

If you enjoyed GMAT Scoring Demystified, watch The Effects Of Coffee On GMAT Performance.





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Posted on
Mar 2020

Stupid Mistakes – How to Avoid Them on the GMAT

Stupid Mistakes On The GMAT

Hi guys. Welcome back to Apex GMAT’s channel. It’s Mike here and today I want to talk about stupid mistakes and let’s start how just with nomenclature. The idea of a stupid mistake is something that we really don’t like here. We don’t like the word dumb. We don’t like the word stupid because even if you’re saying it in a “haha” joking way and you’ve got high self-esteem and a lot of intellectual rigor you’re suddenly putting yourself down. You’re also drawing away attention from the core reasons for these errors.

Careless Mistakes

So we like to call them careless mistakes or careless errors and this allows them to be addressed to be solvable. If you’ve done a stupid mistake either you’re stupid, hopefully not, or you’ve done something foolish. What you’re doing is offloading the responsibility for that error to it being unavoidable. I was not functioning well so I did it rather than addressing the root cause. This is not that you made an error but that there’s a step before the error was made where you failed to catch the error. That step can be before or after the actual processing error was made. Most often it’s sourced from a lack of attentiveness. You’ve missed a detail because you haven’t read closely enough or you crossed your wires through what they call labeling error. Where you’ve called one thing by the wrong name and stored it incorrectly in your head.

Difficulty of Addressing Careless Mistakes

Careless errors are notoriously difficult to address, but the first step is recognizing what they are. They’re processing errors that require your attention and this is something very different than any intellectual failing. It doesn’t matter how smart you are, everybody makes careless errors. Frankly the more rapidly you think the more sort of cycles your brain goes through in a given second or minute the more likely you are to make a careless error. So what differentiates people who make many versus those who make few? Infact the people who make fewer careless errors make just as many as those who make more except they tend to catch them.

How to Work On Them

There are heuristics that we can work on both to preempt careless errors but also to recognize them. Numerically for example you often catch a careless error by noticing that the number doesn’t sound right. If I tell you that it is 150 degrees out. Fahrenheit or Celsius you know that that number doesn’t sound right because it’s anchored to a reality. A lot of times when we’re doing math on the GMAT or in life we don’t have a good anchor for those numbers so the idea of a reasonable or unreasonable number doesn’t get to go through that cognitive filter. So anchoring whether it’s to temperature or money or number of pumpkins in a field, gives us this added check in order to catch a careless error when we make it.

Pivot Questions

Similarly, when we’re reading a word problem or we’re looking at a verbal problem a lot of times using pivot questions to prioritize and understand and really call out what it is we’re trying to do allows us to be both sensitized when we do make the inevitable error but often get in front of many of the errors that we might otherwise make.

Once again, I want to emphasize that careless errors are not intellectual errors. It has nothing to do with being smart or knowing your stuff and so the moment you write off a dumb or stupid error as oh I need to study that again or I forgot that but I’ll remember it next time you’ve already missed your opportunity to improve. So thanks for watching this video guys check out more below. Remember careless errors are both inevitable and solvable. So looking forward to catching you next time and continue prepping.

If you enjoyed this video you can watch: GMAT Scoring Plateaus

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Posted on
Mar 2020

What Are GMAT Scoring Plateaus and How To Overcome Them

Mike from Apex GMAT, here to talk about scoring plateaus on the GMAT. You might be surprised to learn that I don’t really want to talk about specific scores. Plateaus exist and as tutors we kind of know where they are but the important takeaway is not to focus on the score but rather the skills that you have or don’t have that cause you to plateau at a certain level.

Scoring Plateaus Explained

Everyone goes through one or two, sometimes three plateau levels during their prep. This is very normal, but it can be disconcerting especially if it’s the first time that you’re encountering this. Or if you’re used to being excellent in school or with a particular subject matter. These scoring plateaus have everything to do with the way you approach a problem and what we call the level of abstraction that you understand the problem at. Whether we’re talking about quantitative problems or verbal problems. At different levels on the GMAT, it requires us to look at them from an increasingly abstract wide angle lens to understand what’s going on and what’s being asked of us.

The First Scoring Plateau (mid 500s)

At the most basic level, certainly through the first 40, 50th percentile on all the sections. So up to the mid-500s let’s say, most of what you’re being asked is skills oriented. That is if you understand the mechanisms of action the formulas the basic English construction behind problems you should be able to get to an answer. That’s not to say that your correct answer will have been done in a timely manner. That is that you’ve used the correct solution path or rather a time efficient, optimal solution path but you should be able to get there. But then the GMAT has to differentiate among all the people who have the base level skills and they really expect you to have these skills.

Implementing Your Knowledge

It’s not that they’re testing you on whether you know how to compute the volume of a cube. They want you to know that. They want to see what you can do with that when you’re presented with a more complicated problem. And so the first level skill set is to see a problem not as a, identify the problem, plug in a formula, analyze an argument, get to an answer, but rather be aware of the construction of a problem and understand what an optimal solution path looks like. Recognize shortcuts, recognize signals in the problem that permit you to have a greater understanding and a quicker decision process.

The Second Scoring Plateau

As we progress further, the next scoring plateau comes in where the GMAT that presents something in such a new way that you are not unprepared for it. Where you have to utilize and bring to bear some of your creative thinking skills to a problem because it’s presented in a way that’s less familiar or less practiced. The GMAT can do this at any level. But this means that your focus needs to go from understanding what’s in the problem to understanding what the problem is asking for and the common mechanisms of action that the GMAT will use to enhance the complexity of a problem. Once you’re aware of how they complicate a problem you can more readily address it. And directly utilize your knowledge of the underlying subject matter to come up with a creative on the spot solution.

Final Plateau

At the highest levels, this is in overdrive. Where you’re given a problem that’s highly complex and usually requires inductive rather than deductive thinking. Deductive thinking is starting with some premises and breaking them down further. Inductive thinking is taking your premises and what they break down to but adding something at the level above that. This causes us to be able to see something in this pyramid further down the line. This is a type of thinking that’s taught much less at schools. It is one of the core characteristics that allows for success at the highest levels of the GMAT. Where you need to think beyond what you’re given and create a new nest a new home for this problem that gives it additional definition.

This is of course much easier said than done. The scope of this video is to outline this thematically. If you look at our other videos, you’ll start to see hints of this framework as we talk about different problems, the way to approach them and of course what the GMAT exam tests. So check out some of our videos below and give us a call if you need some help. We’re here to help and we want to see you succeed.

If you liked this video, check out: GMAT: Not a Standard Standardized Test. For more videos visit: Apex GMAT Vlog

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Posted on
Jul 2019

GMAT Confidence

Mike Diamond, Head of instruction and Jaymes Kine one of the lead instructors here are going to talk about some of the questions that we’ve gotten on our social media platforms.

We asked for you guys to give us some questions you have asked the questions and I guess kind of talked ourselves into a corner because now we have to answer them. Do you have the answers? I have the answer guide!

Prep Materials

What materials to use? But I want to talk especially about the quality materials out there. There’s a wide variety of materials. Wide variety of quality but even the good materials in terms of the problems often do a great disservice to our clients by saying this is how you do it.

You look in the back and you see this especially, it’s more apparent with the quantitative. Here’s all the algebra you need to do, and so many times it’s not about the answer, it’s about thinking about other solution paths and getting around the answer. Yeah, and this is actually something that happens a lot, it’s mainly one of the major pitfalls for self-prep.

When you’re studying on your own we read through the official guide or whatever books you may have. By the way, we recommend always getting the official guide, other books to supplement are great, but at least the official guide.

We have our own materials that we would we would recommend obviously, but let’s go to the official guide on the answers there. When people are self-prepping they will go through the official guide, then they’ll be reading the official answers which they start with here’s the algebra problem and work you all the way through every algebraic step.

GMAT Confidence

I don’t know if you guys can tell we haven’t rehearsed and this is actually a GMAT moment. Yeah, we maybe should have rehearsed, you know failing to plan is planning to fail I think is what we say. Yes and no though, but we have all the answers.

We don’t need to go over the answers in advance we don’t need a script because we live and breathe the GMAT, this is all we do. And in that way this is a strong parallel for the GMAT. When you’re sitting the exam you don’t need to know the answers in advance ABCD whatever. If you have the tools and the knowledge, the experience, the expertise, then the answers are going to flow. And all that I think adds up to GMAT confidence to know you can go into that test and you can take it right.

Now we may be over confident here but it’s something we’re working on. But being confident when you get to the test is definitely key. And it’s often a characteristic of really high achieving test takers. To be sure none of our instructors went to the test saying, “Oh, I’m nervous I’m not going to do well,” and when we take follow-up tests from time to time that’s that’s not a question.

That’s characteristic of just about everyone I’ve met, clients, instructors, whatever that have scored above that 720/730 mark.

I think irrational confidence is probably my best my best characteristic as a test taker. That’s your best characteristic overall! Oh, thanks man!

If you enjoyed this video, see: Quant Versus Verbal.

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Posted on
Jul 2019

Quant Versus Verbal

It’s time for quant versus verbal, one of the most common questions we get. Where should I start?


It won’t surprise our lovely viewers that it all depends on the person, but let’s talk in some generalizations. One thing you might be surprised by, maybe not so surprised to learn, is that a distinct majority of the people we work with come to us for quantitative help versus verbal help.

At least that’s what they state upfront. Many of them end up only getting quant anyhow but a lot of people state that they only need quant and then they end up needing verbal help as well. Once your quant outstrips your verbal you want to bring them up to parity because that’s highly rewarded by the scoring algorithm.

We talk, we read, we write, we live, we’re immersed in a world of language, a verbal world. Where even math professors only math a few hours a day. Okay yeah there is a verb – to math! This is not a GMAT word but it’s an Apex word because we math frequently. Yes!


So the issue there is fluency. If you’re already fluent in English, all the lessons you need to learn are much more easily attainable. Whereas with quantitative concepts even ones you think you know, often there’s more context. So you need a longer time period and more contact density with them in order to absorb all the stuff you need to then be flexible with them the same way you’re likely already flexible with the English language.


A big part of that is that the verbal section is the verbal section but the math section is math in English. They’re not just equations. They’re not just giving you specific mathematics problems per se. They are giving you math problems wrapped up in words.

That goes both ways, there are quantitative problems particularly on the critical reasoning and a lot of times these aren’t: here are some numbers; figure it out. Rather, the cost-of-living index is growing more quickly than inflation, more than pensions or something like that. Where you have some sort of abstract inequality buried in a property – they require mathematical reasoning.

That’s how it goes, so anyway there’s a lot of overlap on the GMAT but especially on the quantitative side, a lot of the difficulty is puzzling out what you need to answer, not doing the equation but you’re saying: what that hell is this asking me for?

Non-Native English Speakers

This is something else that we feel like a lot of the other test prep factories don’t really do a good enough job in my opinion. Emphasizing what many of you may be thinking right now which is verbal help and mathematical help with verbal for non-native English speakers. There are plenty of students who come to us who are actually very good mathematicians as it were and it’s the English that they need a little bit of help with. Not as it pertains to the verbal section but actually it’s the English on the quant section that’s difficult.

Absolutely, there’s vocabulary, there’s context, but what’s really important here is that native speakers and non-native speakers pick up language differently. Even the way you learned English if you’re a non-native speaker affects how we approach working with you on the verbal. So if you’re a non-English speaker don’t be too concerned that that’s a disadvantage.

Something I’d like to point out to my students quite often is that the GMAT is actually created specifically for native English speakers and a lot of the test itself is meant to trick native English speakers. So coming at it actually from a non-native speaking background can actually help you kind of skip over all of the little traps that are set up for native speakers. So don’t despair, it’s not that you’re at a distinct disadvantage, you just have some different kind of work to do to prepare.

Yeah, different advantages, having access to secondary grammars whether it’s your native language or whether you took say, Spanish in high school.

If you enjoyed this video, watch GMAT Confidence

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Posted on
Jun 2019

Number Theory Problem Form – Wedding Guest

Today we’re going to be looking at what at first seems to be an allocation problem. But on further reflection, actually turns out to be a much simpler number theory problem.

If we take a look at the problem stem these numbers 143 and 77. They stick out to us and they stick out not just because they don’t seem to have any relative association but also because they’re sort of odd-looking numbers, they don’t look like most the numbers were used to seeing. Say 48 or 24 or 36 something easily divisible clearly breakable into factors. Here were given these two disparate numbers and we’re being asked to formulate not what the tables are made up of but how many tables there are.

Solving the Problem

So we look at these two numbers and we examine first the 77 because it’s a simpler lower number. 77 breaks into factors of 7 and 11. This clues us in as to what to look for out of the 143. 143 must have a factor of 7 or 11. And in fact 143 is evenly divisible by 11 and it gives us 13.

Which means that the maximum number of tables is 11. Each one has 13 people from the bride’s side and 7 people from the groom’s side. 13 plus 7 there’s 20 people at each table. Times the 11 tables is 220.

And we can back check our math, 143 plus 77 is 220. We don’t need to go that far but that might help deliver some comfort to this method. So in reality this is a very creative clever way the GMAT is asking us for a greatest common factor.

Graphical Solution Path

Another way to think about this is that we need an equal number of groups from the bride and groom side. The number of people on the bride’s side doesn’t have to equal the number of people on the groom’s side. We just need them broke in into the same number of equal groups. Graphically, the illustration shows us how a certain number of different sized groups combined into this common table. So 13 and 7 and we have 11 groups of each.

Problem Forming

This is a great problem to problem form. It will give you some additional mental math or common result experience by forcing you to figure out numbers that you can present that at first don’t look like they match but in fact do have a common factor. You’ll notice that if they had given you 16 people and 36 people finding that common factor might be easier.

So as you problem form this try and do it in a way that sort of obscures the common factor. Either try it maybe where they have multiple common factors and you tweak things like what is the greatest number what is the fewest number of tables. Or even do a perspective shift and take a look at say how many guests are represented at each table. Or on the bride’s side or on the groom’s side. Of course there are conceptual shifts to this and you can make this story about anything. Once you control the story or rather the structure of the story this problem becomes very very straightforward.

Hope this helped, I look forward to seeing you guys soon.

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