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Posted on
16
Apr 2020

Combinatorics GMAT Problem: Movie Night

Today we’ve got a fairly straightforward combinatorics GMAT problem.

John is hosting a movie night where he will show 4 different movies from among the top 12 movies of the year. He will show the movies in the order in which they are chosen. How many unique movie nights can John throw? 

A. 8
B. 60
C. 495
D. 11,880
E. 154,440

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 and say “What’s my combinations formula?” “What’s my permutation formula?” “How do I know which is which?” And 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 GMAT cohort (the number of people who are taking the GMAT) are generally more familiar with Algebra or Geometry.

1. 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 formal combinatorics formulas.

2. 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 are 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 are 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. Hence, we can look for features that allow us to skip doing that heavy math.

3. 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.

4. Combinatorics GMAT 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 

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Should You Retake the GMAT?
Posted on
14
Apr 2020

Should You Retake the GMAT? All That You Need to Consider

There it is. A 690. Not what you wanted, but pretty damn good. Should you keep the score or cancel it? Do you take the exam again, after all the agony, or hope that it will be enough?

GMAT test takers face these questions each time they sit the exam, and there is no one size fits all answer. There are many factors to consider, from your personal situation, available time, career and MBA goals, and the draw of being done with the GMAT.

1. You Are Not Your GMAT Score

Let’s begin with a more general premise: YOU ARE NOT YOUR GMAT SCORE. As much as some might have you believe so, your GMAT score is not the be all end all of your life, self-worth, or MBA candidacy. It’s important to keep this fact in mind, and what follows from it. While a strong GMAT score is necessary to demonstrate academic skill and preparedness for an MBA or other graduate program, a strong score is not enough, especially if you’re applying to a top-ranked program.

Something that almost no one will tell you – nearly everyone struggles on the GMAT and spends months preparing. We often see clients from top consulting and banking firms who insist on not recommending us to others because they don’t want anyone they work with to know that they needed help!

2. How The Admissions Committees View Your GMAT Score

An admissions committee is looking at your entire profile – your resume, recommendations, accomplishments, and presentation in an interview setting. While they use the GMAT to determine how well they believe you’ll thrive in the academic parts of the MBA program, they’re really looking at the individual when making a decision.

Admissions committees want to see you at your best, so having a second score on your score report, or even speaking about your struggles on the GMAT and how you overcame them can work as a positive to your application. Many programs are also willing to “super score” – taking the best subsections and combining them into the best possible score, and, especially on the quantitative, want to make sure that you’ll be able to handle the rigors of the program.

Having an inferior score on your score report is a lot like running a race slowly… No one cares about your worst time, they only care about your best. You might be tired, ill, have a nail in your shoe, or some other calamity, so only your best time represents your capability, and admissions committees know this. So when should you retake the GMAT? Well ask yourself the following question before you make that decision:

  • What Does This Increase Really Mean To You?

Another factor to consider is how much an incremental increase in your GMAT score will be compared with spending the time elsewhere – adding another activity to your resume, spending more time on crafting your essays, or even feeling better by going out and seeing friends more regularly so you don’t absolutely freaking lose it!

These are real considerations, and being well rounded in fact, not just on paper, will provide a notable enhancement to your ability to market yourself effectively and accomplish your goals – career, romantic, and otherwise. Are you really prepared to give so much up for a number on a piece of paper?

  • Why Should You Retake The GMAT?

On the other hand, perhaps you had an off day, or perhaps it is really important to you to crack that 700 because your brother/partner/boss got there and you want to be in that same rarefied air. There’s nothing wrong with that, and that drive can be a healthy one. Retaking the exam, especially after significant preparation, represents an extra $250 GMAT retake fee and an afternoon. Additional retakes are “free” relative to the time and commitment you’ve spent to get to the first exam, so to the extent, it’s not damaging to your mental health, relationships, and lifestyle, there’s absolutely no reason you shouldn’t take the exam one or more additional times. Admissions committees can’t see that you’ve canceled your scores, so don’t worry about looking try-hard. Besides, like everything in life, you’re doing it for you, right?

3. GMAT Retake Strategy

In the end, there is no right or wrong answer, just the answer that is right or wrong for you. Consult with your family, partner, friends, and colleagues. If you’re working with a professional GMAT tutor, they should be able to provide you perspective as well, especially since they’ve seen this many times before, and maybe have gone through it personally. If you would like to talk about your GMAT prep or retaking the GMAT with an Apex instructor leave us your details.

 

By: Mike Diamond, Director of Curriculum, Apex GMAT

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Posted on
26
Mar 2020

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

Mike here with a special update video about how 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 2020.

1. 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.

2. 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.

3. 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. You can contact us directly through there by chat, phone, or email.

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.

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Posted on
13
Mar 2020

What Are GMAT Scoring Plateaus & 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 GMAT tutors we kind of know where they are but the important takeaway is not to focus on the score but rather on 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 GMAT 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 GMAT 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. Hence, 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 GMAT Scoring Plateau

As we progress further, the next scoring plateau comes in where the GMAT 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 GMAT Scoring 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/articles, 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 our channel on Youtube. 

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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 are 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 some sort of grade school math. On the other hand, this makes the solution path much more elusive.

Before we dive into solving this problem, let’s take a look at it:

The total cost of Company X to produce a batch of t-shirts is $5,000 plus $2 per t-shirt. Each t-shirt sells for $12. The gross profit earned from producing and selling these t-shirts is the total income from the sales minus total production costs. If a batch of 20,000 t-shirts is produced and sold, then Company X’s profit per t-shirt is?

A. $9.00
B. $9.50
C. $9.75
D. $10.00
E. $11.75

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 you 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 Wedding Guest GMAT problem.

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