Featured Video Play Icon
Posted on
Jun 2019

Number Theory Problem Form – Wedding Guest

Number Theory Problem – 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 there are 11 possible tables that is the maximum number of tables are 11. Each one has 13 people from the bride 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.

Read more
Featured Video Play Icon
Posted on
Apr 2019

Sleep Affects Your GMAT Preparation

Sleep Affects GMAT Preparation

So what is the number one thing that gets in the way of GMAT performance and preparation for that matter? It’s not quantitative, it’s not verbal, it’s no problem type or rule or anything like that. In fact, it’s a good night’s sleep or more particularly, it’s consistently having a good night’s sleep.

Sleep hygiene and allowing the brain to absorb the information it’s learned in the day past, as well as prepare to absorb new information in the coming day is absolutely essential to learning any new process or skill. Yet, most professionals preparing for the GMAT are already running at a continuous sleep deficit. The best thing that you can do for yourself is to get a full eight hours of sleep every night!

Prioritization of Time

And if you say well I don’t have time between my work and my social life and the GMAT. Consider this, people who get a full night’s sleep are significantly healthier and happier than those who do not. So if you don’t have enough hours in the day, re-prioritize your time. That might mean taking yourself out of the GMAT for a little while. Actually, it should make you more cognizant of all the things you’re not doing with your time. Thereby, allowing you to refocus towards the future and why you’re preparing for the GMAT.

Way too often it’s too easy to rob Peter in order to pay Paul. That is borrow now, to pay later. When we do this with our time, we put ourselves in this downward spiral. This downward cycle where we’re focused more on the job at hand than where we’re looking to go. We see this a lot with our clients who are preparing for the GMAT.

Invest in Yourself

Being committed professionally is vital to success, it’s vital to growth and learning. At the same time, if you’re so committed that you’re putting in 12 or 14 hour days, every day, then maybe it’s time to revisit the resources you’re giving to your employer rather to yourself. Ultimately, the amount of time you invest in the GMAT, in yourself and your sleep is entirely up to you. Realize that the best outcomes come from prioritizing yourself, your learning and your career and leveraging them to be as productive as you possibly can at work, on the GMAT, at business school and ultimately beyond.

So turn the computer off, put on some soft music and go to bed.

If you liked “Sleep Affects GMAT Preparation”, be sure to watch 6 Things Most GMAT Preppers Get Wrong

Read more
Featured Video Play Icon
Posted on
Feb 2019

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

If You’re Doing Math You’re Doing Something Wrong

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 it’s 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.

Read more
Featured Video Play Icon
Posted on
Feb 2019

Profit & Loss Problem Form

Profit and Loss Problem

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 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
twelve times twenty thousand. 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. It’s sitting right there for us in literally a moment.

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 Wedding Guest GMAT problem.

Read more
Featured Video Play Icon
Posted on
Feb 2019

Six Things That GMAT Preppers Get Wrong

Six Things GMAT Preppers Get Wrong

I’m Mike Diamond Head Instructor for Apex GMAT, here to talk about the top six things GMAT preppers get wrong.

1. Thinking that a correct answer means you’re done with the problem.

When you arrive at a correct answer, that should mark the beginning of your preparation, not the end of it. There are almost always better solution path’s that are more time efficient. That work better with the way your brain engages the problem. Or that will add understanding either to the content or more importantly to the underlying structure of the examination. So when you arrive at a correct answer look for alternative solution paths, and for shortcuts. Give yourself the latitude to explore. Moreover, try to identify what permitted you get to get the problem correct in the first place. A lot of times people focus much more on the problems they get wrong; on what they’re doing wrong than on what they’re doing right. And what you’re doing right can often inform those problems where you are struggling. So remember once you arrived at the correct answer, that’s your starting point.

2. Overusing practice tests.

Practice exams are a crucial part of GMAT preparation, but they’re often misused and overused. Most people use a practice exam to see how they’re doing. But being focused on your score is absolutely the wrong way to approach the GMAT. Rather, you want to be focused on your process and if your process is tight, if your process is correct. Then the score is going to take care of itself. Practice tests are best used for a number of reasons, none of which have to do with your score. They can be used to calibrate your timing decisions. They can be used to identify weak points in your conceptual understanding. Finally, they can be used to identify where you DSM, default solving mechanism, back into old time consuming and unconstructive solution pathways. So, the next time you have an urge to do a test remember that this is going to rob you of two to three hours of valuable prep time. When you’re doing a practice test, you’re not learning, you’re doing.

3. Caring about your score.

I know it’s counter-intuitive, you want that 700-plus score. It’s all you think about; it haunts your dreams. And yet caring about your score is the quickest way to a test anxiety problem and it’s actually entirely unconstructive. Rather, you need to focus entirely on your process and let the score handle itself. Imagine you’re running a race and you’re running as fast as you can. Whether you’re a super fit marathon runner or a couch potato, you can only run as fast as you can. And the time on that race is going to reflect that. So don’t sweat the score, sweat your fitness! Understand what things you can do to improve your GMAT fitness and the score will take care of itself.

4. Studying under a time constraint.

Time trials are really important as you mature in your GMAT progress. But at the start, you want to focus on the mastery of skills in an un-timed environment. Only once you’ve achieved mastery try to do them ever more quickly. By focusing on the time before you have the underlying process conquered you end up rushing yourself in a way that exacerbates your mistakes rather than allows you to correct them. So as you’re prepping, focus on total mastery and understanding first and then begin putting them under time pressure.

5. Low-yield self-prep.

Most people spend entirely too much time preparing from the GMAT. They do so because they’re not getting enough out of their prep time. Does this sound familiar? Okay, I’m going to do a group of 10 questions, maybe on a timer for 20 minutes. Afterwards I’m going to look in the back of the book. When I get the problem right I’m going to say, “yeah, I never have to deal with this problem again.” When I get it wrong in going to go a little bit further and normally I’m going to find something that I knew but I sort of forgot. I’ll say, “You know what I won’t forget that, I’m going to get that right next time.” But it doesn’t happen that way does it? That’s a very low yielding strategy. Instead, you need to become responsible and accountable for your learning and Apex shows you the way to do so by not just being reactive to problems but proactively creating problems of your own.

6. Doing the math.

We have a saying around here and you may have heard it on some of our materials or online videos. If you’re doing math, then you’re doing something wrong. Most of the GMAT quantitative section requires little to no processing and if you’re scribbling tons of stuff on paper it means you’re missing the bigger picture. So remember if you’re doing math there’s always a better way!

Enjoyed “Six things that GMAT preppers get wrong?”, find more videos here.

Read more