Posted on
28
May 2020

Gas Mileage GMAT Problem

The Gas Mileage problem is a classic example of the GMAT triggering one of our DSM’s: Our Default Solving Mechanisms for applied math. Yet there are three higher level solution paths that we can engage instead. So we are going to skip the math entirely on this one. In reading the question stimulus, there’s a signal that estimation is going to be a very strong and viable solution path and in fact for most folks estimation is the dominant solution path for this problem.

What to Take Note Of

Notice in the first sentence here that we are given the relationship between the efficiency for Car X and the efficiency for Car Y. When comparing 25 to 11.9, 11.9 is a little bit less than half. Whenever we have a relationship that is a little less or a little more than a factor, that’s a clear signal that the GMAT wants us to estimate.

Now, we have an inverse relationship here, between the efficiency of Cars X and Y and the amount of gas they use. So if Car Y is using a little half or rather if Car Y has a little less than half efficiency it’s going to use a little more than double the amount of gas. Managing the directionality of estimation is essential to make full use of this solution path.

Estimation Solution Path

Right off the bat, we have a sense that Car Y is going to use a little bit more than double the amount of gas. Now, all we need to do is figure out how much Car X will use. This is an exercise in mental math. Instead of dividing the 12,000 miles by 25 we want to build up from the 25 to 12,000.

Ask ourselves, in a scenario type of way, how many 25’s go into 100 – The answer is 4. 4 quarters to a \$1. Then we can scale it up just by throwing some zeros on. So, 40 25’s are 1,000. How do we get from 1,000 to 12,000? We multiply by 12. So 40 times 12, 480 25’s gives us our 12,000 miles. Car X uses 480 gallons.

Therefore, Car Y is going to use a little more than double this and we point to answer C because we just need to answer the amount Y uses in addition to X. SO there is a bit of verbal play there that we also have to recognize. That’s the estimation solution path.

Graphical Solution Path

We can see this via the graphic solution path by imaging a rectangle, where we have the efficiency of the engine on one side and the amount of gallons on the other. With Car X, 25 miles per gallon time 480 gallons is going to give us the area of 12,000 miles. That is we’ve driven the 12,000 miles in that rectangle. If we are cutting it in half on efficiency, or a little more than half, we end up with two strips and if we lay them side by side we see that we’re doubling of going a little more than double on the amount of gas that we use to maintain that 12,000 mile area.

Logical Solution Path

Finally, we can look at this from a logical solution path which overlaps a bit with the estimation. But the moment we know that Y uses a little more than double the amount of gas of X, we can also look at and not manage that directionality and just say it uses about double. The only answer choice among our answer choices that is close but not exactly, is C – 520. 480 is our exact number and the A answer is way too low. It’s not close enough to 480 to be viable. So here is an example where, while best practices have us managing the directionality, we don’t even need to do that.

Similar Problems

For similar problems like this take a look at the Wholesale Tool problem, The Glucose Solution Problem and for a really good treatment of the graphic solution path check out Don’s Repair Job. There should be links to all three right below and I hope that this helps you guys on your way to achieving success on the GMAT.

If you enjoyed this Gas Mileage Problem but would like to watch more videos about Meta strategy, try “How coffee affects your GMAT performance“.

Posted on
19
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.

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, w

Posted on
14
May 2020

The Effects of Coffee on GMAT Performance

Let’s talk about caffeine and the effect of coffee on GMAT performance. Caffeine is a neuro-stimulant. Drinking coffee or tea while you prep and particularly being appropriately caffeinated when your test is a decided advantage. Caffeine is a nootropic, which means it helps you be smarter. It also helps your cognitive abilities become enhanced due to increased blood flow and oxygen flow to the brain.

It’s important to understand how much caffeine helps, not just to wake you up in the morning. More than that, it’s about how much caffeine is needed to get you to that a really nice steady state of alert focus-ness (where you’re making up words like alert focus-ness) where you kind of feel on top of the world and you have that gentle energy.

You want to understand exactly how much caffeine your body can take because there’s nothing worse than being over caffeinated, jittery and anxiety ridden on the exam. But if you calibrate it properly caffeine is an important part of your GMAT diet.

If you enjoyed the Effects of coffee on GMAT Prep, watch: Why a 4.0 does not equal GMAT success.

Posted on
16
Apr 2020

Combinatorics GMAT Problem: Movie Night

Today we’ve got a fairly straightforward GMAT combinatorics problem. If you’ve been self-prepping in a rigorous, let me review the rules sort of way, you’ll pick up that there’s orders, combinations here and you might be inclined to really dive in. What’s my combinations formula? What’s my permutation formula? How do I know which is which? Then plug in numbers.

While that will get you there understand that most GMAT combinatorics problems are more about being familiar with combinatorics than any really heavy duty math. That is because the number of people who are taking the GMAT are generally more familiar with Algebra or Geometry.

Combinatorics & The GMAT

Combinatorics, by virtue of being less known, is considered more valuable. It is scored more highly than problems of similar complexity in Algebra or Geometry. So you’re really being rewarded just for knowing basic combinatorics and in fact most permutation/combination problems fall into this basic category. The good news here is that you can use your reasoning to solve this problem without being burdened by the formal combinatorics formulas.

Solving The Problem

Let’s take a look at this problem. John’s having a movie night. We need to ask ourselves a series of pivot questions. How many different movies can John show first?

Well there’s 12 movies, he could show any of the 12. Leaving 11 movies to be shown second, any of 11. 10, 9. So the answer is 12x11x10x9 or 11,880. But even this math is a lot to do. Notice that by walking it through as a story, as a narrative, we don’t need to cancel out the 7 6 5 4 3 2 1. We don’t need to worry about division or anything else. We just know that there’s 4 movies and each time, each step we take, there’s one less movie available. Here we have this product 12 times 11 times 10 times 9, but we don’t really want to be forced to process this and so we can look for features that allow us to skip doing that heavy math.

Transforming The Numbers

We’ve got this really neat triangular shape in the answer choices where each answer has a different number of digits in it. 12, 11, 10, 9, we can look at and say on average each one’s about 10. The 9 and the 12 sort of compensate, but overall we’re going to have something that’s close to 10 times 10 times 10 times 10.

That is our answer should be somewhere around 10,000 or possibly a little more because we have an 11 and a 12 offset only by a 9. So what we’re looking for is something in that just above 10,000 range this prevents us from doing the math and very rapidly lets us look at those four movies, those numbers 12 11 10 9 and zero in on that 11 880 number.

Problem Form

Try it again with a similar number. Notice that you can’t do this with a hundred different movies selecting 17 of them. The math, the numbers would be too cumbersome.

The GMAT is really restricted here and you should restrict yourself to ones that are reasonable to keep processed in your head without doing heavy duty math. Similarly, notice how this one clusters around ten, it doesn’t have to cluster around ten, but when you’re rewriting this problem think about that clustering and think about how your knowledge of common powers or how other identities can help you rapidly get to an answer because the GMAT will present you with numbers that have a neat clean way to jump from your understanding directly to the answer without all that messy math in between.

This is Mike for Apex GMAT with your problem of the day.

If you enjoyed this combinatorics GMAT problem, try more GMAT practice problems:  Remainder Number Theory

Posted on
26
Mar 2020

How COVID-19 Is Affecting The GMAT And Its Test Takers

Mike is here with a special update video about how the COVID-19 is impacting the GMAT testing world. I wanted to share some big news with you guys from the GMAC, the makers of the GMAT, about a substitute exam that they will be using and that you should be able to take from home starting in the middle of April.

General Inquiries

So, first off, a lot of people are finding themselves in uncertainty about their application process and about their GMAT preparation. To be sure, we have been getting a lot of calls about people wanting to make the best use of their time while they are furloughed from work, or while they are working from home and have a bit more flexibility and to be sure it’s an opportune time to bite off this task which for most people is really hard to fit into their existing professional and personal lives.

Additionally, we have a lot of inquiries about what’s going to happen with admissions. We can’t speak for any particular schools, however, we expect that the window of the virus crisis is such that it won’t meaningfully impact applications for Fall of 2021, that is that by the time your first round comes around in September or October, you are going to be able to get in, take the GMAT as normal and be able to apply and go to other events.

That of course is the hope and this is an emerging phenomenon, and emerging circumstance on the world stage without much precedence. So of course things are bound to change and we promise to keep you updated through the entirety of this crisis.

The New Exam

The new exam that the GMAC is rolling out will be taken from home and they are planning on rolling it out sometime in the middle of April. It will have three of the four GMAT sections, Integrated Reasoning, Quantitative and Verbal. So you will be able to get your score out of 800 with Quant and Verbal as well as your score for the Integrated Reasoning. The only section that will be missing is the writing section which I say is the least important of the entire GMAT from an admissions standpoint. The exam will be priced at a lower price point; they have not announced what that price point is but certainly at some discount to the normal \$250 that’s charged.

Test Considerations

There are also some strategic considerations that come with this exam and some things we don’t yet know. For example, it is unclear as to whether you will get to choose the order of the sections when you take the exam or if it will be predetermined. Additionally, because the GMAC is likely using a different problem bank than they use for the actual GMAT, this makes some subtle time allocation and strategic guessing decisions change compared to the normal GMAT and I will be talking about that in another video.

If You Need Any Help Give Us A Call

I know that this is a stressful time for everyone who has business school and GMAT plans that have been disrupted. So if you need any help or need any advice, please feel free to visit our website: www.apexgmat.com.

You can contact us directly through there by chat, phone or email and from our entire family, we wish you health and safety in this difficult time and we’ll look forward to keeping you updated as soon as we have new information. Thanks so much and stay safe.

Watch other videos about COVID-19 and the GMAT:

Posted on
14
Mar 2020

Remainder Number Theory Problem

Today we’re going to be looking at this problem and our big question is that originally we’re given this unknown number N and we know we just have a remainder 3. So the problem is presenting us information in a way that we’re not used to seeing it and what we need to do is work backwards from this to drive the core insights.

Sorting Through the Information

So, if we have a remainder of 3 on 23, this means that the chunk that isn’t remainder is 20.

So what can our n be in those cases that will allow us to divide out by 20 and leave this remainder 3?

Well, first, we know that n has to be greater than 3 because in order to have a remainder the amount we’re dividing by has to be something greater. The moment the remainder equalizes the thing we’re dividing by of course we get one more tick in the dividing by box and the remainder goes back down to zero.

Solving

So with 23 and a remainder of 3 our key number to look at is 20. Our factors of 20, that is the things that divide evenly into 20, are 1, 2, 4, 5, 10 and 20. Of course 1 and 2 are below 3 and so they’re not contenders. So we end up with n being 4, 5, 10 or 20.

Check Against the Statements

So for number 1: Is N even? If N can be 4 but can also be 5 then we’re not assured that it’s even. Notice the data sufficiency problem type embedded here. So N is not necessarily even.

Is N a multiple of 5? Once again N is not because N could be 4 or 5. Finally, is in a factor of 20? And in this case it is because 4, 5, 10 and 20 as we just said are all factors of that 20 that we’re looking for. So our answer here is 3 alone, answer choice A.

More Practice

Now here’s a more challenging problem at the same form, see if you can do it and we’re going to come back and in the next video talk about the solution and give you another problem.

So if 67 is divided by some integer N the remainder is 7. Our three things to look at are whether:

• N is even?
• If N is a multiple of 10?
• Or N is a factor of 120?

So give this one a try and see if you can use the principles from the easier problem on this more challenging one to make sure that you actually understand what’s going on. If not, re-watch this video and see if a review might allow you to answer this question.

If you enjoyed using this video for practice, try this one next: Wedding Guest Problem.

Posted on
12
Feb 2019

If you’re doing math on the GMAT, watch this.

I want to discuss one of the core tenents of Apex’s quantitative philosophy on the GMAT. “If you’re doing math, you’re doing something wrong.” Meaning, if you find yourself doing math, that’s a signal from the exam that you’re using a sub-optimal solution path. By math I don’t mean any calculation whatsoever, but any calculations that aren’t reasonable — that don’t come out easily, neatly and cleanly, once you’re well practiced with mental math. So it’s not that we’ll never do a calculation, but every calculation we do should be deliberate and smooth.

The Most Overused Solution Path

Let’s go a little deeper into this, because it’s a really important concept. Many, many people preparing for the GMAT spend way too much time worrying about the math. Being freaked out about the math and on the exam doing the math. The applied mathematical solution path is the most over used solution path on the quantitative side of the GMAT. Particularity among engineers, and with people who do a lot of self-prepping. They look to the back of the book or look to previous experience as students and get caught up in the idea that their answer needs to be precise. This gets in the way of using our estimation solution path or other higher solution paths, which can get us to the correct answer much more quickly.

The GMAT isn’t Testing Your Math Skills

How do we know that math is not what the GMAT wants us to do? It’s quite simple. If the GMAT was the referendum on how well you can do mental math, then the scores would reflect your ability to do so. MBA programs at top business schools would be filled with people with extraordinary, almost savant like mental math abilities. We know this isn’t the case.

Actually, as we improve on our mental math, we get diminishing returns with it. So we see a lot of clients getting up to the 70th, 80th, or 90th percent level even, on the quantitative side of things. Then, all of a sudden they plateau; they can’t get any higher. The reason is they are so focused on the math. They are missing the bigger logical reasoning picture or the structure of quantitative problems that doesn’t rely on doing math that allows both quick and accurate solutions.

Key Things to Avoid

While math has its place, we want to be sure that we’re not putting it on a pedestal. And that when we’re performing computations, we’re doing so with great deliberation, intentionality, and that we have a good reason for doing any computation we’re doing. If you find yourself diving into the equation or doing a lot of processing, stop. Say “Wait a minute, there must be a better way to do this.”

Another option is that sometimes you make a basic error early on and that leads to ugly numbers and math. But you should never, never, never be multiplying decimals out to the fourth decimal. That sort of math is the true trigger, the true signal, that there’s a better way to solve the problem. When you’re self prepping, this is what you want to look for.

So by the time you get to the exam, you’re not catching yourself doing math, but you’ve already incorporated it into your process, the fact that math shouldn’t be your default.

So, remember, guys, if you’re doing math, you’re doing something wrong and you can take this one to the bank.

Posted on
12
Feb 2019

Profit & Loss Problem Form

The profit and loss problem form that this problem fits into is one that has strong DSM’s into mathematics. Here we are tempted to do the math in part because that’s so easy. It’s so available to us.

This is characteristic of a mid-level arithmetic problem where there’s some shifts and shimmies but overall it’s a fairly straightforward problem that utilizes no more than the four basic operations. So, on the one hand, this profit and loss problem is pre-algebra or even sort of grade school math. On the other hand, this makes the solution path much more elusive.

Solving the Problem Using Math

So of course we can follow the math. We can add up all the costs, five thousand plus two dollars, times twenty thousand. Then contrast that with the revenue that comes in which is 12×20,000. But then we’re left with the ugly division problem that brings us to the profit per t-shirt, this is where the GMAT sticks us.

Instead of handling this in aggregate, it’s strongly preferable to handle it with a higher level solution path. Let’s take a look at a few:

Higher Level Solution Path: Distribution

One way to do this is to distribute the fixed cost over the cost per t-shirt. This is actually a lot easier than it seems. Twenty thousand t-shirts, five thousand dollars, five over twenty is one-quarter.

Therefore, it costs one-quarter per t-shirt in addition to the two dollars in variable cost. So, twelve minus two is equal to ten dollars, minus one quarter is equal to nine dollars and seventy-five cents.

Higher Level Solution Path: Graphical Equalization

We can also use a graphic equalization method in order to get to the same conclusion. If the numbers were more complicated, understanding that that shift is one-quarter down. That is the fixed cost is one-quarter down.

Then we know we’re looking for something that ends in a seventy-five cents. That allows us to eliminate all the answer choices that don’t end in 0.75. Then we can use scale to determine that 9.75 is the correct answer.

Practice Problems

There are more complicated versions of this problem form. In particular, I’d encourage you to explore being told that the t-shirt company is breaking even. Then determining the amount of variable costs or fixed cost that’s there or even the production run. Similarly, you can be given a target profit or loss, the break-even just being the zero, so it’s a bit easier and have to reverse engineer the relationships.

Once again, this doesn’t have to be done algebraically. As you begin to appreciate the subtlety of the ratio between costs production run and total P&L all of these problems should be simplified and should be very straightforward.

Continue your GMAT practice with the GMAT problem.