This video will take you through the Integrated Reasoning GMAT Test sections and show you strategies. The video transcript follows.
Integrated Reasoning GMAT Strategies [Transcript]
Chris: Hello and welcome to our IR Workshop. Strategies and Tactics for Integrated Reasoning, this brand new section of the GMAT that I know everyone’s super excited about. Introductions & housekeeping. First of all, that’s me there with the bad haircut. I’ve been teaching here since 2003. I was a high school science teacher for a number of years, and then went back to business school. So I totally know what you all are going through in putting your applications together, worrying about this GMAT thing, and trying to present your best foot forward to schools.
So, I empathize and sympathize. We’re also joined by, working from the bottom of the list up, up here in the moderators. Whitney Garner who’s not only a star GMAT Instructor, but also who’s written a number of IR problems that are in our online materials that’ll be posted very shortly. We’re also joined by Molly Dutton, in student services, and Garnett Burke, who is in our tech department. And so if you’ve got any questions of a logistical nature, text them in and we’ll be sure to answer them.
So, a couple housekeeping notes. We got a lot to cover. So you can see the list of participants here is quite long. A lot of folks, and so, I hope you don’t mind, but what we’re going to do is actually turn off the chat now. That means you’ll be able to chat to us, but it’ll be a little less distracting for all concerned to not have public chat. I’ll definitely be hanging around afterwards to answer questions. Please text in your questions. If they’re related to what we’re doing content-wise right now, I will at that moment, I’ll try to work it in. If I don’t get to your question, please ask it afterwards and I’ll be sure to answer it.
We’ll also make a recording available. It’ll be emailed out to you in a link form tomorrow. So if there’s any point that you want to review, please watch the recording. So what we’re doing tonight is, first of all, covering some IR basics, then we’re going to spend a big chunk of time, and the bulk of our time, on practice problems, so these four kinds that the GMAT throws at you on this IR section. Don’t worry about the names yet, we’ll hit them shortly. And lastly, we’re going to wrap up with some themes and notes on additional resources that are out there, available to you.
So, quick facts on Integrated Reasoning. It’s this new 30-minute section that’s replacing the issue essay. Tests the same stuff, the same core skills as the main part of the GMAT, but there’s a twist or two that you’re going to encounter. The rest of the GMAT stays exactly the same. That’s really important to note, that all the stuff you’re doing to prepare for GMAT Quant, GMAT Verbal, that’s all going to hold whether it’s before June 5th or after June 5th.
IR’s going to have a separate score, which is great. Moreover, that separate score is relatively unimportant. This thing is not going to affect the 200-800 score, which is what schools really care about. So, if you take away nothing else on this slide, take this away, relatively unimportant score. It’s not the main event. This is just an appetizer. Again, reiterating, June 5th. The last old test, according to mba.com, is on June 2nd. So don’t wait till the last minute if you’re trying to squeeze one in before then.
How about resources? I’ll talk more about this at the end, as I mentioned, but we’ve got a book coming out that will be accompanied by question banks online. Practice exams will be empowered with IR sections very shortly, as well, from us. And the GMAC, which are the folks who publish the GMAT, they’ve got the OG 13, Official Guide 13, with IR questions online, and their new GMATPrep, which just went online last week, contains an IR section. And I’ll talk about that in a few slides, what we’ve gleaned from that thing.
So, again, it launches on June 5th. If you take a look here, right now, and up until June 5th, you’ve got two essays, then the Quant, then the Verbal. June 5th, and after, you’ll still have one essay. It will be the argument essay, and it will come first, but IR replaces the second essay, the issue essay. And everything else is exactly the same, so do not think of this as a big change. It is a minor change to the GMAT.
It’s going to be separately scored. Here’s how the scoring now works, and how it’s going to work. All that stuff is the same, except you got this brand new score of 1-8 on this IR section. So, it’s not part of that score. The only way it can affect the 200-800 is if you let it. Psychologically do so. And that’s one of the key points I want to make to you. Don’t let it affect the rest of your test. If you think about why it’s going to be unimportant, the reason it’s going to be unimportant is that the GMAT was developed back in the ’50s, and has been calibrated since then, and correlated against business school academic performance.
So, you take your 200-800 score, you also take the GPA, you put those things together, and you get something that predicts business school grades with some degree of accuracy. It’s not perfect, but that’s what the GMAT is pitching to business schools. “Hey, you use this GMAT, in fact that’s why it was developed. Help us predict how people are going to do academically.” This is the main event, backed up by decades of research. How about this new thing? This new thing. I don’t care whether it predicts your income 10 years from now perfectly well, they won’t know for years whether it does. This thing could be the greatest thing since they decided to slice the bread before selling it, and it doesn’t matter, because they can’t calibrate it against business school performance.
Now I think it’s a pretty well designed section. It’s pretty cool, and it’s another bit of data on you. It’s not completely useless. But it’s relatively unimportant, so put it in perspective. Do not over stress about this section. As I mentioned before, tests the same core skills, all those things, fractions, decimals, percents, algebra, reading comprehension, all those things that you’re doing. You’re studying and practicing to get ready for the regular, the real GMAT, are getting you ready for integrated reasoning, too. So, by preparing for the main part of the GMAT, the main event, you’re also preparing for IR. In fact, you’re doing the most important thing, to prepare for IR that you could be doing.
You’re learning fractions, and decimals, and percents. You’re making sure that you understand how to draw good inferences. But that said, of course there’s some weird emphases. Hey, IR really emphasizes decimals and percents, just by its nature. We’ll see why in a minute. And something’s got to give. It doesn’t emphasize number properties that much. Does that mean there won’t be a single number properties question on the test? No. You could get something with some weird divisibility problem, but it would only show up in a particular kind of problem, that I’ll talk about towards the end of tonight.
Likewise, on Verbal, you just aren’t going to see anything that tests your knowledge of grammar. You’re going to have to understand reading comprehension, though. You’re going to have to be able to draw inferences. In addition, IR has these brand new formats, and those are the scary, these things are like, well I got to sort this table, I got to put something in each column. Those are weird looking, sure. Okay. Fine. Deal with it. It’s going to be cool. It’s smoke and mirrors, it’s noise, not signal.
So, just like the label says, IR integrates Quant and Verbal. That’s what integrated reasoning is. Think of, here’s Quant, and then here’s Verbal, what do those things do? This is the chocolate, this is the peanut butter. You put them together, and you get a Reese’s Peanut Butter Cup. You have Quant with a lot of words, you have Verbal with numbers. Hey, cool. And guess what? You’re also going to see real word data. You’re going to have numbers of Alphaville, and Baskerville, and wherever else, and they’re going to be ugly looking. You don’t see those kind of numbers that much on the GMAT.
There’s some depressing economic chart. And to deal with those numbers, you also have an on-screen calculator that will help you deal with them. Why on Earth is this thing the way it is? Well, it’s actually a pretty good reason. When you get to business school, you’re going to be analyzing business cases. What’s a business case? A business case is Quant with a lot of words, or it’s Verbal with numbers. It’s a story of a company or some dilemma facing a company, and you get a whole crap ton of numbers in there, but it’s also integrated with narrative, with text. So you got to parse through, sort through all that stuff, and you got to deal with ugly numbers because they’re real world in the business case.
So, this is actually kind of a smart move on the GMAT’s part to incorporate a section that deals with this stuff, because that’s what IR’s doing. It’s giving you a case of mini-case analysis. That’s really what it’s there for. So here we are. You’ve got the IR section. It’s got lots of crazy data, text and numbers. And it’s only 30 minutes long, so you got to hustle. But the title of this slide is Do Not Let IR Mess Up the Rest of Your Test. Why? Because the main event comes after this thing.
Man, we’d all feel differently about IR if it came at the very end of the test. Yeah, but it’s ifs and ands, were pots and pans, right, Molly? As we talked about earlier, the world would be a kitchen. It is at the beginning of the test. IR comes where it comes. So you got to deal with it. How do you deal with it? Well, there are a couple of ways you’re going to deal with it. One way you’re dealing with it is you got to build stamina in advance. You’re doing a little bit of that right now by participating in this workshop, but you are going to have to take some practice tests with Integrated Reasoning, just like you should with the essay. You should take some exams doing the essay.
I would advise you not to have it be your first exam. Your first exam, just do the Quant and the Verbal, because that’s what matters. That’s the main event. If you do IR’s in your first exam, you might over stress about it. You’re going to pay too much attention to how you did on that. But then later exams, yeah, build it in, just so you suffer through it. Now what else? You got to study the fast and easy way to do things. On IR, you got a calculator. That calculator’s going to make some things easier. Yeah, you can lift the weights on your own, but why not use a pulley? Why not actually use the tools you give you? Why? Because you’ve got to save your energy and your thoughts for the main event.
In fact, if you burn up a lot of energy, as you are going to do on IR, just naturally, your brain gets depleted of its food. And go ahead and text in if you know what your brain eats. What food does your brain actually subsist on? Oh yeah, I’m seeing it. Becky, your point, grapes. I’ve got some grapes sitting here, that’s funny. It’s sugar. It’s Gatorade. It’s GMAT questions. It’s glucose.
Your brain needs sugar, and so if you do, research is coming out. If you make a bunch of decisions in a row, your brain uses up sugar, and you’re less able to make later decisions. It’s called ego depletion, it’s called decision fatigue. Look these things up on the Web. It’s crazy but it’s true, and in fact, if you put some sugar back in, I’m not talking about eat a whole birthday cake, or chug a, I’m not talking chug a 64 ounce Gatorade, just drink some. And the reason why use, have it be dissolved already in water, is it’ll go the fastest to your brain. Believe it or not, that is a true thing, and you should do that, by the way, not only here, but here. So drink the other half of your Gatorade, or your Powerade, I’m not trying to be specific to one brand here, but I guess I did.
After you do IR, you should make a couple of adjustments, though. There are a couple of points I want to make about, it’s kind of like taking off roller skates and putting on roller blades. You’ve got to skate slightly differently. So, in IR, you got ugly numbers so you’re going to use that calculator. Not all the time, but at least some of the time. When you go to Quant, you got to give up the calculator. But you know what? You don’t need it anymore. You’ve got clean numbers, you got rigged numbers. So it’s okay to not use the calculator after IR, so give it up with a glad heart and, “Thank you, calculator, for getting me through IR.”
The other big change is that, hey, you got extra data on IR. You got to sift through it, but then when you move the Quant section, you’re going to have to get used to using everything they give you. It’s a good strategy on regular GMAT Quant. Say, “Wait a second, I didn’t use that little fact they give me. I didn’t use that piece of information. Did I do this right?” That’s a good strategy on Quant. Don’t do that on IR. So you come into IR, you got all this crazy data. You sort through it, you ignore a bunch of stuff. You sift, and then when you get to Quant, use everything they give you. It’s pretty rare that they don’t give you something to use. Occasionally happens, but not a big deal.
Though there’s one other quick mention in Verbal. Very few IR questions we’ve seen have you interpret a dialog, some kind of email exchange, or something. And you’ve got to assess mindsets, like what is someone really thinking? What are they willing to do that they’re sort of hinting at in this email? And it’s pretty subtle, but you don’t have to do that in Verbal. You stay more on the surface. That’s the one change I would say, that you might not even encounter that with Verbal, but you will encounter these other things in Quant, as you move from IR to Quant, so make those couple of adjustments.
Into the nittys and the grittys, the 10 prompts that you’re going to encounter on IR. First, multi-source reasoning. What’s that? That’s three tabs, maybe two tabs, of information that you’re clicking around between. So it’s just like reading comp plus some charts, and numbers, and graphs, potentially. And it’s not all in front of you at once, so you got to click around. You’ll get two table analyses. These table analyses are tables that you can sort, so you click right here, and you can choose the column you want to sort by. We’ll talk about those in a few minutes.
Notice that on both of these, you’re going to interact. You’re going to click around. So, you click on the tabs and you’ll see different stuff. Here, you’ll click and you’ll re-sort. You get the one multi-source reasoning and two tables. You also get three graphs, and those could be these kind of graphs, which we’ll come to a little bit later on, or other kinds, columns, and pies, and all those things. You’ll get three of those.
Last but not least, you’ll get four so-called two-part analyses, where you’re going to answer a two-part question. You’re just going to answer like, “What’s ‘X’ and what’s ‘Y?'” at once. The interesting thing is not the prompt here. It’s actually the question. We’ll come to that in a second. Notice that both of those later types, the graphs and the two-parts, they’re static. You don’t do anything to those like clicking around. You’re just reading them.
Okay, you got 10 prompts, but you’re going to be asked 12 questions of 4 types. So, you’re going to have one traditional multiple choice, and oh, the question coming in. Becky, it’s a good question. Do we know how many? Let me click back to this scene. One multi-source reasoning, two tables, three graphs, and four two parts. That’s what the GMATPrep software contains as its sample section, and so we’re very, very confident that that’s what all the sections will contain. It’s such a short section that they can’t mess with these numbers too much without changing it to something else. Could they do something to us and surprise us? Yes, maybe. And we’ll make sure to let everyone know if these numbers change at all, but this is what they’ve released publicly and we really doubt it’s going to change.
We know that they’re going to ask 12 questions of 4 types. So, these four questions. One of them’s traditional multiple choice, nothing that interesting there. You’re going to be asked four what we call either/or statements. Either/or, yes/no, true/false. You’re going to have three statements, and you’re going to pick true or false for each one of those statements. Notice what’s crazy here is this is a whole question, but it’s got three parts to it. So, you’ve got to put in three responses, which kind of sucks, but that’s life. You got to answer three little mini questions.
So, you’re getting one traditional multiple choice, four either/or statements. And Tony, I’ll answer your question in a second, how these questions line up to the prompts, on the next slide. So, three drop-down statements. You’ll get three questions that are each a set of two statements, and you’ll click here and you’ll make a choice, like 200 CCs or whatever. You’re just completing the statement there. And the last kind, remember the two-part thing? Well, there’s a two-part question, and what you’re doing here is you’ve got a set of five or six answers to questions, and you’re making one selection in this column, and one selection in this column.
Notice what you’re doing here is you’re making two choices, one in each column. Whereas here, you’re making three choices, one in each row. You’ll never mix them up. They’re completely different looking. So that’s the weird thing about these new bells and whistles. They’re just different looks, different ways of asking a question. Could they have asked these things as multiple choice? Sure. But they didn’t. They want to be sexy. Okay, sexy GMAT. Go ahead, ask your new sexy types of questions.
There are two or three responses per question, that’s the actual thing that’s kind of annoying. You got to keep going, because you don’t want to dilly dally on, say, statement three, taking a long time to answer. Full 30-Minute Section. This NSR, the three tabs, actually has three questions involved with it. One traditional multiple choice, and two either/ors, which are, each of them composed of three statements there. So, this thing here, you’re going to have a bunch of time to do.
The tables, each of those tables gets one either/or set, so you’ll have three statements for each of the tables. Each graph gets a drop-down set, so for each graph, you’ll have two statements to answer. And then the two-parts, you’re going to get four of these things, and you’re going to have two answers to put in each of those two parts. So here are your 10 prompts, here are your 12 questions. And the order we’re not sure about, but they’ll be probably pretty mixed up. Two-thirty per question. That’s 12 in 2:30.
So, two and a half minutes. That gives you seven and a half minutes for this whole bad boy here, so take your time, figure that out. We’re going to do one later on tonight. Not adaptive. These things are just put into a panel of 12 questions. Bang, you work your way through it. You can’t go backwards, so you just keep going. The motto on this thing is take your shot, and move on.
Now, how is this thing scored? This is what I did on Easter Sunday last, which is I sat there with GMATPrep 2.0, and I ran it through 21 times. And to answer your question, Becky, they came in all different order every time I ran it, it came in a different order of was it two parts, and then the MSR, whatever. It was all jumbled up. Same 12 questions, but all jumbled up.
And what I did was deliberately try to get different numbers right and wrong, and see what score came out on the 1-8 thing. There are not percentiles yet, of course, with it. The first thing that I found is, unfortunately, there is no partial credit. Those two or three responses that you give, they had actually intonated to us last fall at a meeting that there might be partial credit, but it looks very strongly as if it’s not the case. You get a problem right completely, or you get it wrong.
Nothing to really worry about there. Again, you’re just taking your shot, so don’t stress about this thing. One thing that’s nice up at the upper end is that you get one or two of these questions wrong, and there’s some forgiveness. It’s all right. You can handle it. You can even still get a “perfect score” getting some wrong. Another reason not to stress.
You might notice this little weird thing in the middle here, this gap, and some of this same on the right giving you different scores coming out. Well, I don’t know why they don’t like six. I could not get the thing to give me a six no matter what I tried. Easter Bunny was trying to help me out. No love, could not get a six on the IR. The difference seemed to be whether or not I was getting the MSR problems right.
So, that was the driver of getting higher scores in this range. So it might be that the MSR problems are worth a little bit more. This is all, again, research from our research on GMATPrep 2.0. MBAA folks, the mba.com folks, GMAC will probably come out with some official word on how this thing works. And we’ll be sure to post and you’ll know all about it once they go public with it, but in the meantime, surprise, number right correlates really strongly with the score you get. So, you try to get more right.
This is not an adaptive test, so it very much correlates with number right. No surprise there. All right. A couple of other little logistical things. There’s an online calculator up in the upper left. Click on that link, and you’re going to get some bad boy that looks like this. Does it look exactly like this? Actually, of the three versions they’ve put up, they’re all different. That’s annoying. Thanks GMAT. They made them all look different, and the most recent one they put up on GMATPrep does not, it has keys that are labeled % and 1/x, and they’re grayed out. You can’t use them.
I am showing you these keys but you cannot use them. Thanks. But you know what? They all got digits and they all do arithmetic. That’s all you need, folks. So that’s all you do. If you can click on the digits, and you can click on plus, minus, times, and divide, you’re all cool. And there’s an equal sign and there’s a decimal point, and a plus/minus. Don’t go stressing about how does memory work, and everything like that. Jot it down, if you need a number in there. These things clear it. That’s all you need. You’re good to go.
As I said before, don’t think of this thing as a luxury. Don’t ignore it. You got to make some fast calculations, you got some messy numbers, and it’s a tool that you should use. Why are trying to pound that nail in with your fingers when there’s a hammer sitting there? Go ahead and use the hammer. So, actually, I want you to have one for the rest of tonight. In fact, you can keep it open as long as you want.
Go to your, if you’re on a PC, go to your start menu, go to All Programs, Accessories, and the calculator. If you’re on a Mac, open up a finder window, go to Applications, and open up a calculator. Open up a simple calculator and just have it in the corner, running in the background, and keep it on the simple version. You don’t need any weird functions or anything like that. This is all you need.
All right, all right. So, let’s go on to some practice problems. Let’s get into the meat of this thing. Before doing so, one slide I’d like to reinforce with all of you is about how to solve problems. In fact, here’s a strategy for universal problem solving. And the reason I’ve highlighted the “U,” and the “P,” and the “S” there is because they’re the same letters in Understand, Plan, and Solve. So Universal Problem Solving, understand the problem, plan your approach, solve.
Some particular points of how to understand. It’s a little bit more complex with these IR problems because I want you to first focus on understanding the prompt, especially when you got one of these ugly bad boys here, like a big old graph or something like that. So, I want you to ask yourself what and so what? You’re looking over one of these things. What is this, so what about it? And that will help you to construct a mental map of what’s going on. What is this thing, and so what about it?
We’ll see that in action. You’re going to put it into action. This is good for GMAT, the real GMAT, as well. So, we’re saying this for the IR, but this really applies to everything on the GMAT, and in particular, Quant.
Understand the prompt. Then understand the question, and the theme I want you to think about here is focus on the precise language, what it is exactly asking you for, and in fact, sometimes you should really translate to concrete terms. Make it very concrete. Make it very real for yourself.
Then plan your approach, and always look for an easy path. What’s the easiest way? Sometimes you’re going to be doing some, like, seventh grade, or even third grade kind of task, like, “Hey, how many dots are below this line?” And don’t be too cool for school. Go ahead and jot it down. Point at the screen, and go one, two, three. Point and mutter. Mutter under your breath. Five, seven, eight. I’ve got eight of them. And then use the calculator. Punch that eight into the calculator.
So, we’ll come back to UPS, understand, plan, solve, over the course of the evening. So, table basics. Take a moment and look this thing over. I want you to understand the prompt. What and so what about this thing? Extra credit, text in if you know where this thing comes from. What’s the pop culture reference? Surprise, Hunger Games, that’s right, big ol’ movie.
So, a way that I want you to think about approaching tables. Now, this table isn’t so crazy, but we’re starting with a smaller one, then you’re going to see a crazy table in a few slides. So, I want you to think first, “Okay, let me read the text. What does the text say?” Then what’s in each row? What does each column tell you about what’s in each row? And finally, what kind of info is in each column?
So, I’ll walk through this one. What does the text say? It tells me hey, there’s 16 participants in a contest. What’s in each row? A participant. Surprise. Okay, that’s who’s there. What does each column tell you? It tells me, and I read the labels, it tells me the name, the gender, and the age of each participant. And then what kind of info is in each column?
I want you to think about two kinds of big questions. Numbers or text, and are there repeats or not? So let’s see that in action. Name, it’s obviously text. And I glance down and there are no repeats. And I’m not sitting there trying to prove it. I just sort of glance down and get the sense in a glance. Gender, it’s text as well, but there are lots of repeats, as I’d expect. Male and female. And it’s really important to notice repeats because then I’m going to have subgroups, I’m going to have groups of males and groups of females.
And lastly, I’ve got age, which is numbers, of course, and it turns out there are a couple repeats in there. Not so important, but good to spot. One other thing I do want to mention is occasionally you get a weird table where in which, there are multiple entries in this cell. It’s as if you’ve got two names in a single row, or two ages in a single row. And that might seem weird here, but it could happen in certain circumstances. Don’t let that throw you, just keep your eyes open.
So, let’s talk about the sorting capability. Sort, when you click on that thing up at the top, that pull down menu, you’re going to see something like this, and it’s the names of all the columns. If you pick Name, then you’re going to be in that original sort from low to high. Most tables are, by default, sorted by the left-most column. Not every single one, but most of them. And that’ll be alphabetical.
Weirdly, if it’s yes/no, then the yeses go to the top, for some reason, because they just do. If you choose gender, you’re going to get this one. And it will always show you what you’re sorting by. It’ll say gender. It won’t say low and high, but it will always go from low to high. And Age will go something like this. Important note, if you’re used to sorting tables in Excel or in the Web, it’s always ascending. You cannot choose to sort from high to low. It’s always low to high.
What kind of sort is missing here? What kind of sort might you want, that you don’t see here? Go ahead and text in if you’ve got an idea for a sort you’d want that ain’t here. By one of these three columns, anything else? Sorting by repeats. We’ve got repeats here. We sorted all the males together, the females. Alphabetical by name. How else could we sort this? Combine sorts, sorting by more than one column at once. Yeah.
That’s what I’m getting at here, is that we’ve got a group of females, but we also have within the females the ages nicely sorted like dominoes. We’ve got the male ages nicely sorted. Notice what was happening here. I sort by gender, and I don’t have the ages sorted. So, it seems that it’s the names sort. Well, if you work with Excel, then you know that this is not so hard to do in Excel, to create this thing. You can either do it all at once, or you can do it in two steps by literally choosing age first, and then gender next.
So, you click and sort by age, then you re-sort by gender, and boom, this is what you get, and you try it. Oops. You try it over here. You sort by age first, and then you sort by gender, and guess what? It scramble egged your ages. It scrambles up your ages like so many egg beaters. Sorry, folks.
Even though it would be super useful, especially for any kind of subgroup data, subgroup stats. Hey, what’s the range of female ages? What’s the median male age? That’d be awesome to have this sort, and it’s impossible. You can only choose the primary sort. You can only choose to sort by gender, or by any other column by itself. And they’ve chosen how the secondary sort will work, and usually, not to your advantage.
Why did they do that? We’re not sure but our guess is they did it to minimize the advantage that people who had a lot of experience with Excel have. There’s already probably some advantage if you work a lot with Excel. You’re not frightened by tables, but if you work a lot with Excel, you might know some tricks, and things that they might not want you to necessarily have to be able to use.
So, you only get this sort, where the ages are scrambled, but you do have the males together, and the females together, or you have straight up age sort, or you get the name sort. So, that puts you at a disadvantage in certain ways to do some calculations. You have to come up with ways around it.
Notice what two main sorts are going to do here, are gender and age. So let’s put them both on the same page, as if they, you can see both at the same time. And I’m going to ask you some questions, and ask you to text in which sort should you use? And to answer what questions. So let’s imagine you want to match some criteria. You want to figure out who are the, let’s say the four or five oldest people?
Let me change that to the five oldest people. How would you figure that out? Which sort would you use? All right, I’m giving you the gimme first. Yeah, age sort, because that’s what it does, right? It would give you these five people. Cashmere through Coriolanus, right? How about the four oldest females? If we only had that double sort.
You wish you could do female as the primary, and then age, but you can’t. You have to pick one or the other of these. So, pick one of them, and then you got to do the rest of your work by hand. If you decide to sort by gender, you got to go okay, here’s Mags, as first oldest. And my two 20-somethings, Cashmere and Johanna. Then I got to glance, and then my teenagers. I’ve got Glimmer. Okay, those are my four oldest.
Or you sort by age, and you just start from the bottom and work your way towards the top, ticking off females as you go. Eighty, 24, 23, 17. Okay, so it’s Mags, Cashmere, Johanna, and Glimmer. I would rather do the second one of those versions myself, so typically, when I’m just looking for the oldest, or the youngest, I just sort by the numeric. That’s how I do it.
But it’s up to you. Whatever’s easier for you. Now I’m going to ask you a few questions here, and then I’m going to get off the mic and let you noodle on these things. Which sort are you going to use? And then actually try to answer the questions. Okay. So, here you go. Answer these questions. I’m going to add something to the third one. Go ahead.
All right, I’m going to start revealing these a little bit at a time. I’ll do the first one. All right, here comes the next one, median age of all the people. What I’ve written there is the text note is useful, because you see, oh, it’s 16 people in a contest, so if I want the median age, I should look between 8 and 9. One, two, three, four, five, six, seven, eight, nine. Hey, they’re both 18, so the average of those 2 numbers is 18. There’s my median age.
Now to figure out whether the average age is greater than the median age for everyone, I would definitely sort by age and then look at these sets of numbers. Do not, please don’t type in all these and divide by sixteen, add them all up, to figure out the average age. That’ll take you a long time.
Rather, look and see, hey, I got a couple of outliers here. A couple of really old folks like me. I’m up there. And so average age is dragged higher. This is the arithmetic mean. It’s dragged higher by these old fogeys, whereas there’s no one that’s that young who’s dragging the ages down, so the average age is going to be greater than the median age.
And you find that from the outliers. That is the 80, 81 year olds. Now how much greater is the range of female ages than the range of male ages? I would use here probably the age sort as well, and I would compare the two end points. Female versus male, the young ‘ens, and female versus male of the old ones.
Now, you can do this by saying, okay, the range of female ages is 80 minus 12, for 68, and the range of male ages is 81 minus 16. Or a fast way to do it is just to say hey, these ages differ by four, these ages differ by one, they offset each other, so the difference of the ranges is three. That’s a fast way to do it without having to do the subtracting.
So you’re still using tricks like that on this part of the GMAT. Ways to save yourself from even having to use the calculator. So, how about the median age of the males? What do you do here? Well, you might sort by age, and then look only at the males, and say okay, median age of the males, I got one, two, three, four, five, six, seven, so I go up to the fourth one. Sixteen, 18, 28, 23. Boom, that is the answer.
That’s doing it by age. Or I could do it by sorting by gender, and gathering all the males together. That easily tells me I got seven males, and then I count from small to large or large to small. I say I need the fourth oldest person, so I’m going to count from large to small. Eighty-one, then knock out the 42 year old, and then 24, and 23.
There’s no great way to do it. Or you might even split back and forth. You get that there’s seven from the gender sort, and then you flip over to the age sort. There’s no price. You don’t have to put a penny in the till every time you re-sort. It’s fast. You can do it as many times you like.
Whatever way, just be flexible, and then you’re literally pointing at the screen. Your finger should look like this. One, 2, 3, 4, 23. Or one, two, three, four, and you’re muttering under your breath. Don’t be too cool for school. No one’s looking at you. Who cares? Get the answer, right?
All right. Before going to the next one, I’m here to tell you, this next problem is pretty ugly. This next table is from mba.com. It’s posted on there. It’s an example of a really messy, big, old, ugly table. You’re going to have a collective groan when you see this thing. That’s all right. Just go ahead and groan.
And apply the Understand the Prompt idea. Here it is. That’s the collective groan. All right. Do the Understand the Prompt thing. I’ll get off the mic and let you think through this. Read it through the next half a minute or so.
All right. I’m going to jump back on the mic here. Wouldn’t it be nice if you could just highlight as you go? But you should be mentally highlighting. And in fact, what does the text say? Read the first sentence. Go ahead and skim stuff that’s in parentheses. That’s the definition of total passengers. Don’t let that throw you. Or the definition of total movements. Oh, okay, landing and takeoff.
There are 21 airports throughout the world. Okay, 21 airports. That’s what my rows are going to be. So at this point I would stop right there. I’m going to go ahead and put in a little red line to show I’ve stopped right there after reading sort of the, here’s the big picture of this table. And then I go up to the table and study it.
So that’s why I revealed bounce between text and table to you. It’s a good technique when you got a big ol’ bunch of text in a big ol’ table. Now what’s in each row, notice that you got distinct cities, and they’re also called airports, so each of these is different. There are no repeats here. So, there’s a 1 to 1 correspondence, 1 to 1 relationship between airport and city. You can think of them either way.
Now there are countries. Oh, USA showing up a couple times. Okay, a number of these are repeats. You could group up the USA airports. And then there are these codes. Okay, looks like they’re all different.
What does each column tell you? One thing I want you to notice here is that the columns have two levels of labels to them. Airport, okay, this is all about the airport. This is all about the passengers. And this is all about the movements. Oh, cool, that’s really helpful.
I’m getting the question, can we ignore the country and the code columns here? I wouldn’t ignore them yet. I would just see there they are. And then, if you’re asked a question that involves them somehow, then go back to them. For instance, you might be asked a question about U.S. airports. Okay, then I might have to group them together, or at least pay attention to that.
But you know where they are. You don’t have to do anything with it. The two level labels are really useful because notice, the passengers and the movements are organized the same way. You got number, and then you got percent change, and then you got rank. This is now getting into what kind of information you’re being given.
Notice the repeats that you have, such as USA, but then also notice, if you got something like percent change, oh. So I want to be sure of percent change of what to what. Okay, percent of increase and decrease over the numbers from 2007, and we’re in 2008 in this table. So this is getting to these numbers. This is the percent change from the previous year to that number. Okay, cool.
And then there’s also rank of the airport. Hm. Rank. That means what? Well, Rank number one means that’s the highest number. Rank number one here means that’s the highest number. And then the number two rank is the second biggest number, number three rank as the third biggest number, etc.
We’ll come back to why they might have even put that in here at all. But now we’ve understood the prompt and it’s okay to have taken a little bit of time to do so, especially with such a giant table. Yuck. You won’t get both of your tables looking like this. You’ll get some tables that’ll look just like the Finnick, the Hunger Games table we were just looking at.
So, let’s now actually get to a problem. Want you to realize that for a table, you’re going to have some statements. We’re just going to have two statements on this, typically you’ll have three. And it will be an either/or, so in this case, they tell you the either/or is true or false. Here it is.
I’ll read it aloud. The airport experiencing the greatest percent decrease in total passengers from 2007 to 2008 also experienced the greatest decrease in the percent of movements. Well, that’s weird. What does that last bit say? It’s really the same thing as greatest percent decrease in total movements.
And what I want to ask you now is not actually to answer the question, it’s just what column or columns should we sort by? Go ahead and text that in. What column or columns should we sort by? Good. It’s lighting up. I love seeing percent change. And I would start with a percent change of passengers, because that’s in the subject of the sentence.
The airport experiencing the great percent decrease. Okay, that’s a percent change in something. Passengers, bango. Let me sort by that. Notice that’s part of the subject, so it’s really helpful when you’re reading these things, these statements, analyze subject and predicate separately. What’s the subject, and what’s the predicate? So deal with them separately. Big point, we’ll come back to that.
So greatest percent decrease. I re-sort by that, and bango, that whole long phrase, the airport experiencing the greatest percent decrease in total passengers from 2007 to 2008 is Chicago. That’s all that means. That’s disguised, that’s code for Chicago.
Now, the rest of the sentence, the predicate, it also experienced the greatest decrease in percent of movements. That’s what they’re claiming. You go ahead and answer this question. Good, you all are nailing it, and notice we didn’t re-sort here. I think you can just glance and say, okay, is -4.9 the lowest number on this table, for this 0 negative? And I glance down, I immediately see some numbers that are even further from zero, they’re even more worse, that are greater decreases.
Right there, and there, so I didn’t even have to go anywhere. I could see this one happens to be the greatest, but fine. I can just glance at that point. Or I could re-sort and in fact, you could even solve this one without re-sorting, so I just want to confirm claiming that Chicago has the smallest red number is false, so false is the correct answer. More worser.
Now, how could you have done this? You could have done this with no re-sorts. I’ll show you the original slide again. Could you have answered this by glancing, oh, I want to sort by this. Well, the idea of oh I want to find the smallest number on this list, you might as well just click and say sort by passenger percent change. Save yourself the mental energy, but you could just look there and say, oh, that’s -9, okay, that’s Chicago, and is Chicago also got the lowest number?
I glance down and see no, that’s lower. So you could do it without re-sorting. But why not use the sort? It doesn’t cost you anything. They don’t know whether you re-sorted or not. So just make it easy on yourself. You can do it whichever way you want, with one sort, with two sorts, or with no sorts. And the two sort thing, what would happen here, is that you just sort by this thing, and then you quickly re-sort by that, and you see that the things at the top of the table moves.
Chicago’s no longer at the top of the table if you sort this way. Done and done. Just again, make it easy on yourself. All right, let’s try another statement. Go ahead and tell me what I should re-sort by. And it’s interesting here because it says the airport with the median rank based on number of passengers, and so in theory, I can sort by either the actual number of passengers, because rank has to correspond to number, or I can sort by passengers ranked.
I’m lazy, I’d probably just keep it in rank. And then I’ll say, “Wait a second, median rank? There are 21 airports, wouldn’t that just be number 11?” I don’t even have to re-sort. So I look down here at number 11, and I see it next to number 29. Huh? What? Why is the median rank not 11? And I have a surprise here. Woah, what’s that all about?
Median rank, is it 11? I see things that are different, that don’t correspond to my expectations that the maximum rank would be 21. What’s going on here? And I go back to my text and it says that the 21 airports are chosen for inclusion because in 2008, each was among the busiest 30 airports. Oh, there’s number 30. So, I had some gaps in rank. That’s why they threw it in here. So I can sort by passenger rank, or I can sort by number of passengers, but when you see a surprise in the table, just go figure it out. It’s okay.
So I would sort by rank, and notice that’s a way to get number to be descending. So if you sort by rank, you’re going to get rank ascending, which means this is descending. If you sort by passenger number, Atlanta’s going to be at the bottom. Either way, you have the same number in the middle, so here again, we have our subject airport with the median rank based on total number of passengers is Amsterdam.
Is Amsterdam the same as the airport with a median rank based on total number of movements? I better re-sort this because I don’t trust myself. There’s 21 rows here and is that the median rank? I don’t know. I’m not going to try that. Just re-sort it, it costs you nothing. You re-sort and you keep track. Is Amsterdam still in the middle?
It ain’t. So you don’t care what’s in the exact middle, you just see it jumped. So, yet again, make it easy, and one way to make it easy is to stop at proof. Here the proof is that Amsterdam moved out of the middle. It’s not in the middle, so the answer to this one is also false. And notice how what we did is we really translated to concrete terms.
This concrete term is Amsterdam. It’s in the middle when you sort by the passenger rank. And this concrete term is, hey, it’s got to stay in the middle when its movements rank. It didn’t. It happens to be that one but who cares? All right, let’s keep rolling here.
Take away so far for tables. I want you to understand the prompt by asking what and so what? If you got a lot of text and a lot of table, bounce between them, and notice things like percent change and rank. Translate to concrete terms as much as you can. Separating that subject and that predicate if you have a long statement that’s complicated. Don’t try to do it all at once.
Pick the easy path for you, y’all. Just point at the screen and count. Sort them or don’t. There’s no penalty for not sorting. Just make it easy for yourself. Stop at proof. And I want to say one last thing. With these true/falses or either/ors in any kind of way, it’s very easy to do the problem right and then just pick the wrong thing.
You’re like, oh wait, I wanted it to move, so I picked true. Just confirm, wait, which side am I picking again? This is a false statement, so especially with these either/or things, confirm your answer. Don’t flip it around.
Okay, take a look at this table. I’ll get off the mic and this is one we’ve cooked up. And if you can tell me what the theme of all the names is, I’ll give you a prize of adoration. Here you go. The question that I’m asking is just a fun question, what is the theme that links all the names of these fake companies?
David’s got it. It’s lizards. Sorry for the weird reference here. If you read the text first, see how it’s eight publicly traded companies, and it gives you all this stuff. Okay. About those companies. Here’s what they might ask you. Which company has the highest market capitalization per employee? But which one has the lowest market cap per employee?
Now my question to you is what should we sort by? What should we sort by here? We don’t have a column that’s market cap per employee. I’d love to be able to just add on another column. That’s what we do. But we don’t have one, so which column should I sort by?
To make it easier on yourself, I would go ahead and sort by market cap. When you have one of these derived numbers, I don’t have this exact thing, so I would sort by whatever goes in the same direction as the thing I’m looking for. Whatever column goes in the same direction, and in this case, it would be the market cap number. The numerator.
This is just, again, make it easier. You don’t have to do it, but then glance and avoid completing the number for every row. Scan it for outliers, benchmarks. And it’s this number, market cap, divided by employees. So I glance down. I’m like whoa, wait what’s that thing about? That’s way smaller than this number.
Most of these other market cap numbers are bigger than the number of employees, with the exception of Varanid. So, I don’t even have to use the calculator. Hey, I can figure out it’s Mosasaur that’s got the biggest market cap per employee, without touching a digit on the calculator.
How about lowest? Go ahead and type it in if you can figure out what the lowest market cap per employee is. This one’s a little harder, a little harder to spot, because it doesn’t have that nice outlier of 701 employees. So what I might use here is, say, okay, most of the market caps are smaller than the number of employees in this unit. So I might cut off a digit. Take a 10% benchmark, and then do my comparison.
Ten percent of employees would be those numbers. And I compare them, and I see, hey, this one’s bigger, but it’s bigger by only a little bit. Five seventy-nine versus 510. It’s only, percentage-wise, a little bit bigger. Whereas all these other numbers, even Skink, that’s a lizard, even Skink seems to be a lot bigger.
So, the lowest market cap per employees, I could confirm by actually computing, but the market cap is down towards 10% only for Basilisk and Skink, and this one’s definitely closer. So I can answer market cap per employee without even touching the calculator just by using outliers and benchmarks.
That’s not always the case. How about this one? Which company has the highest profit margin? First, answer me this, riddle me this, Batman. Which column should I sort by? First tell me that, and then we’ll sort it.
I think you should sort by the numerator, not by the denominator, because the denominator goes in reverse for these kinds of things. So sort by the numerator. Sort by net income. Because the higher the net income for a given amount of revenue, the higher profit margin. This is just a way around the fact you don’t have a margin profit column.
Then scan. Okay. And you might have to use the calculator. Go to it, folks.
All right, so which ones are greater than 10%? Only Mosasaur, Clubtail, and Varanid. You can probably knock out Clubtail because 605 is only slightly bigger than 590, proportionally, whereas 286 is a lot bigger than 170, and 8,634 is a lot bigger than that one. Now you got to whip out the calculator. And notice how close these numbers are.
These are real numbers, actually. These are disguised numbers of eight companies that are in the same industry, in reality. And so these were the numbers that happened to come really close, and so that’s what they’re going to do to you. Don’t be too cool for school at that last moment. Okay, I’ve got two that are close. Bust out the calculator, y’all.
And you do the same kind of thing for lowest net income. All right. You can knock out the ones that are high, right? I’m going to go ahead and do those. And then go ahead and tell me which ones I should actually calculate. Type in which ones I should actually calculate.
Yeah, here I might even use a 1% benchmark and see can I get how much more than 1% are these. And the ones that are even down towards 1% are Basilisk and Skink, and of those two, Skink is the winner, in a bad way, by a nose, 1.8% profit margin. Don’t invest in Skink, Inc. And there you just got to bust out the calculator.
All right, so what we’ve learned at this point is sort by the aligned column, if you can help it. You don’t have to, but it helps you to organize what you’re doing, and if you’re subtracting, say, instead of using a ratio, I would sort by, again, the aligned column. To find the largest expenses, sort by revenue. Find the smallest expenses, sort by revenue.
And then scan for outliers, benchmarks, and use a calculator judiciously. All right, last table. Now we’re spending a lot of time on tables, but there’s a real meat here. Take a look at this one, and give me a little check mark when you’re done understanding this prompt. The little check mark is down at the bottom of the list of names, on the right side. Green check.
All right, cool, cool, cool. This one’s a much more graspable table than the other two. No real text to read other than the title of the thing. Where this one gets interesting is actually in the statement, and the question that you’re meant to answer.
For each of the following statements, select “Would help” explain it if it would, if true, help explain some of the information in the table. Otherwise select “Would not help explain.” Hm. This one’s a little bit like a critical reasoning problem. What they’re asking you to do is take some outside fact, and you’re trying to connect that to the table.
You’re trying to see, would this fact help explain some of the info here. So, this really isn’t about so much crunching numbers on the table, as much as trying to find a way to bridge the gap between the outside world and this table. So what’s the meaning of these things?
So here’s my three step quick process for a table like this. You’ve got this outside fact. Try to figure out or predict what kind of data it would explain. Make a hypothesis about what kind of data in the table would it explain, then go to the table and figure out what it actually says, and lastly, compare those two. Do they agree? If yes, cool. If not, no.
So here you go. Here’s an example. Go ahead and give me an answer to this question. All right. Getting some different answers here, and that’s why this thing’s a little tricky. It is definitely a little tricky. So, I look at the question, at the statement, and it says Brazil, Russia. All right, so I know I’m going to focus on these two, and in fact, I don’t really have to re-sort. The sort here, it turns out, is by, the default sort is the public library sort, or so it seems.
The proportion of the population of Brazil that lives within close proximity to at least one museum is larger than that of Russia. So, more people, proportionally, live close to a museum. And this is percentage of population that visits among other things museums. So, if more people in Brazil live close to a museum, percentage-wise, then I would expect those people to visit the museum more. I would expect, this is my hypothesis, the Brazil museum visit, they live closer, more of them live close to a museum, than in Russia, then I would expect this.
Then I compare it to what the table actually says. This step is actually…you might say oh, I’m making assumptions. Sure, you’re making assumptions. This is not proof. This fact would prove what kind of data, of course it won’t prove it. Just would help explain. It’s very loosey-goosey, but there is a pretty clear common-sensical connection between you live close to a museum, you got a lot of people living close to a museum, you expect more visits out of them, that’s all.
They’re not going to ask you to make huge logical leaps there. The table, though, says hey, Brazil museum percent is 11, Russia, putting those two together. Russia museum percent is seven. Do those agree? Yeah, they agree.
So I would say this one is yeah, it would help it explain. And that’s what they say, too, because this is a real problem on mba.com. Let’s try another. Give me your answer to this one. All right, so I’m doing some highlighting there to draw connections between this fact would help explain what kind of data. Again, you’re making leaps here, but the three that spend the most money to promote natural history museums, you’d say well, I’m expecting that to be the three with the highest natural history museum visits.
All right, because that’s what I would expect. Spend more money to promote it, higher visit percentage. And if they’re saying those are also the ones in which science is most valued, yeah, it’s a bit of a leap, but it’s what they want me to do. Those should be the same as the three countries or regions, with the highest science visit percentage.
And then to see what the table actually says, I can either just look at it or I can re-sort. And I see that these top three here, when I sort by natural history museum, and I might have to think about, oh, is European Union versus Japan in the top three? Well, it doesn’t matter because there’s 19 over there. Here’s 10 here. Those are not the same groups.
So, here it’s would not explain. They do not agree. The answer is no. Again, this is not one we’re making up. This is one from mba.com, so illustrating the importance of how this is really integrated reasoning at its finest, in a way, kind of weirdly. You’ve got numbers and you have this making hypotheses and drawing inferences between them.
So what we have here is the take away for tables. You’ve already seen all this stuff. You get some weird special demands. One might be derived numbers. Yeah, you sort. You look for these outliers and benchmarks, and you use your calculator judiciously. And then explain the table. Yeah, you hypothesize what kind of data would the fact help explain, or you might have to hypothesize in the other direction.
You confirm what the table actually says, and you compare the two. Andrew’s asking a question about we don’t know how much money they spend, it’s true. We should just assume that yes, we should make the clearest assumption. You spend more money to promote your museum, we’re going to expect a higher visit.
If science is highly valued, you’re going to expect higher visits. It’s not about the gap that you have to go there. You say all else being equal. Ceteris paribus, all else being equal. Science is more highly valued, I would expect this. So, again, it’s not proof. It’s just would help explain.
All right. Shrug your shoulders, stretch your back. That’s a lot on tables, but tables are really important. Let’s look at graphs. Graphs are just like tables. All that’s different is now you’re making position or size have some kind of meaning, and you know what? You’re going to understand the prompt with what and so what?
You’re going to understand the question by translating in concrete terms, and you’re going to pick the easy path. All right. Here’s one from the New York Times quiz. The GMAC folks created this for the New York Times to illustrate how this would work, and it’s a good illustration. Hey, here it is.
What and so what? You understand the prompt the same kind of way. What do you do? What does the text say? Now ask what kind of graph this is. It’s a little different from tables, because tables, are a table, are a table, but graphs come in different varieties, so ask what kind it is. And then you start to narrow in on bits and pieces.
So what is each point or a column or something like that? And what does each axis tell you? Because there are axes here. What does the text say? Year-over-year sales growth for 12 businesses. All right, cool. I got 12 businesses. Looking at this sales growth year-over-year.
What kind of graph is this? Type in if you know the name of this kind of graph. It has a coordinate plane, and then dots flying all over it. What’s it called? Those dots are sprinkled over it. It’s called a sprinkle plot. No it’s not, it’s not called a sprinkle plot. It’s called a scatter plot, because the dots are scattered like dust in the wind. Yup. Scatter plot is just like an old Kansas song, Dust in the Wind.
So you got each of those points is a business, one of these 12 businesses. And then each axis tells you something about that business. So zoom in on one if you’re having trouble when you’re looking at these things and you say okay, let me pick that one right there. That yellow one right there that I highlighted. What does it mean to be there? What does that mean?
It means, okay, look at the axis. The x-axis, start there, is percent growth from sometime in ’08 to ’09. How much the sales grew. And the y-axis is percent growth from ’09 to 2010. Why? Because they told you. You don’t know why, they just said so, so that particular business, I don’t know, Mososaur, our old friend from the last one. It grew by five and change percent in one year and in the next year, it grew 4%.
More growth here, less growth there, yup. So that’s what you’re doing. You’re just figuring out what these things say, what each piece means. And what can be really helpful is if you’re looking at a weird graph, and you’re trying to make sense of it, don’t try to make sense of it all at once. Do what and so what.
What is this little guy right here, make it real, with a specific case, okay? Scatter plots, in particular, you can think of as representing a table with two columns. So you got 12 businesses that correspond to 12 points. Each row corresponds to a point. Say there’s Business A, Business B, etc. C, D, etc., etc.
And this is the x-axis and this is the y-axis. So sometimes it can be helpful to imagine the source table and sort of go back to that. Not always, but sometimes it’s helpful. For a scatter plot, let me just cover this up for a second. All you’re doing is filling in a blank by a pull down menu. So you’re just completing a statement, that’s all you’re doing. Nothing sexy.
So, here’s the statement, and see if you can come up with an answer to this. Type it in if you can. Know what you all are doing at the end of the day? You’re going one, two, three, four. Four dots are in this region of the screen, out of twelve dots. Or you can count the rest. One, two, three, four, five, six, seven, eight. That’s what you’re doing, that’s what I’m talking about. Translate to concrete terms, and then point at the screen, and shoot.
So, it’s a pull down, so it’s not fill in the blank. You don’t got to type anything in. But you’re pointing and counting. Four dots out of twelve dots, 33.3% approximately. All right. So that’s one of the questions on this. Try this question, and the answer to this is here, I’m going to type in on the left hand side. So make sense of this and then give me your answer.
All right, -12 on the x-axis, by definition, means that the thing shrank, sales shrank by 12% in 2009, from ’08 to ’09. Plus 13 on the y-axis, yeah you can plot it up there, but what does it mean in the world? It means you added 13% in 2010, from end of the ’09 to the end of ’10. So if something falls, sales, or your stock price, or the amount of your back hair falls by 12% in 1 year and then it grows by 13% in the next year, this is all too real for me, in my investments.
What kind of net growth did you have? And you’re asked positive or negative. You got to know your percent math here. Subtracting 12% from something is the same as multiplying it by what? Multiply by what? Mult by .88, which is 1 minus .12. So minus 12% is subtracting 12% of that thing or multiplying it by 1 minus .12, or .88.
Similarly, adding 13% to something is multiplying it by 1.13. One plus the percent change, expressed as a decimal. Same thing for a minus, you’re just saying one plus the percent change expressed as a decimal. And it’s minus .12. So this is the way that you do successive percent changes, .88 times 1.13 gives you a number that’s slightly less than 1. Think of starting with 100 bucks, and I lose 12 of them. I don’t gain back 13 bucks because it’s not 13 of the original 100, it’s 13% of my 88 bucks, and 13%, they were smart here.
They chose a number that’s small enough that you don’t get back to the original, even though it’s a greater percent change in the second year. This is why last year, I lost 50% in a stock. I own some stock in some stupid thing, and I lost 50%. You know how much I have to grow by to get back to where I was? Not 50%, 100%.
So you got to make sure you understand that math. If nothing else, for your investments. So negative net growth here, and you definitely, Josh, good point, you definitely want a calculator for this. They chose numbers that are not rigged. You got to multiply these things together on the calculator, so you definitely want to do it that way.
All right. Here’s a statistics interlude that comes up on this section that doesn’t really show up anywhere else on the GMAT, so it’s one of these weird little guys. In particular, applicable to scatter plots, and also to the tables. It’s called correlation.
So this is an example of a stats topic that is kind of unique to IR. And they make you learn it. This is all you got to learn about it, though. Positive correlation, two numbers go together, like peanut butter and chocolate. One goes up, the other one goes up. You see it looking like you put a line that slopes up to the right. Doesn’t have to be exact, in fact, it probably won’t be.
And if you sorted the table, you’d see, in rough numbers, this kind of thing, where they both get bigger together. Do they get bigger exactly together? Maybe not, but they both got to get bigger, roughly together.
Negative correlation, opposite scenario. You have a decline as you move to the right. “X” gets bigger, “Y” gets smaller. So they get big in opposite directions. And then the zero or no correlation, no significant correlation, this is the shotgun blast to the chest, baby. It’s all over the map. So, if you sort by one column, it’s all mixed up in the other.
So we’ve seen that show up, and that’s all you go to do, is be able to identify positive, negative, or none. Notice some of these pull down menus have just as few as three choices. Ain’t that nice? So take your shot and move on. You get some weird graphs in here.
Let me…oh, first, scatter plot takeaways. Same things we’ve seen. Understand the prompt. Ask what and so what. If you need to, imagine the source table. Focus in on a particular case if it helps. When you look to understand the question, translate to concrete terms. You might get the question in terms of the world, and you translate over to the graph, like count these points. That’s concrete.
Or it might be in the world of graph. Hey, here’s a point up here. If it were plotted there, what would it mean in the world? And you go the other way. But either way, you are translating to concrete terms.
Good question, Becky. Can you skip and come back to questions? You can’t. So you just take your shot and move on, that’s all. And lastly, plan your approach, your point and count, know your percent math.
Even weird graphs are organized, so you’ve got lions, and columns, and bears, oh my! You’ve got columns, and lines, and pies, and bubble charts, where it’s like scatter plots on steroids, pumped up like muscles. Like the size of the dot means something, too. You might even have a non-numeric chart, like an org chart or something.
Don’t stress. All you got to do is ask what and so what step by step. Just read it. Read the text. Read the titles. Try to figure out what the labels mean. If you don’t recognize the kind of graph, just study a piece at a time. And then generalize.
The question’s always going to be translatable to concrete terms, like how many boxes, or which box is connected to this one I care about? So that’s all. So that is what you really need to know about graphs. I do want to do one other little statistics interlude before going on to the next type.
Here you go. You’ve got a table that involves ages, and reading scores, various percentiles of them. So let’s think about what percentiles mean. And we’re doing this because the GMAT IR has asked some questions in its samples. They get pretty hardcore into percentiles so we thought it would be worthwhile teaching this a little bit more extensively.
So 85th percentile, that just means, for some group, what’s the score that 85% of the scores fall below? And that means 15% fall at it or above it. That’s all. And you can definitely think about this in terms of the GMAT and all that, right? Like a 760 is a 99th percentile score. That’s what our instructors have. Plug for Manhattan GMAT, sorry.
So 85th percentile read on your reading score some score below which a certain number, in this case 85% of scores. So answer me this, Batman. For 6-year-olds, 85th percentile score is what? What is it? Type it in.
Bam, you got it. So 14.7. That means 85% of 6-year-olds scored below that. And think of it as you give me the age and you give me the percentile you want, and I spit you back a score. In fact, you can graph this whole dang table. You just got to do it a column at a time. So the age is going to be your x-axis, and reading scores is your y-axis, and you’re going to have three sort of jagged lines.
I’m not going to draw them jagged, I’m just going to draw them as if they were straight, but they’d probably jag all over the place. So, the first one is 15th percentile, there’s 50th percentile, and the top one would be 85th percentile. They’re never going to intersect because the 85th percentile’s always got to be higher. In theory, they could touch, but they can’t cross.
So once you have something like that, here’s the dastardly devil of the GMAT, the Beelzebub of the standardized test trying to tempt you into something. Can you work backwards? Oh, I have crass. I’m going from the x-axis, and I’m reading up to the y-axis. Can I go from the y-axis and go back to the x-axis? And the answer is that is a sin against nature.
Do not do it. You can’t take a score and figure back out the percentile ages. Can’t do it. The GMAT is trying to trick you into doing so. Only interpret percentiles in the given direction. Why is that? Because you don’t know how many kids are at different ages. But you don’t have to really think about why, just realize, they give you percentiles in the direction percentiles of scores for given ages, never try to work your way backwards to the ages from scores.
In fact, what they even do is give you like a two link chain, where you go from age to reading score, then from reading score to school GPA, and you can go in that direction. For instance, Billy is 6 years old. He reads at the 85th percentile for his age, but for his reading score, his GPA is only at the 50th percentile. Poor Billy.
So we take his age, and we start with his age, and his percentile. Type in for me what his reading score is. Give me his reading score. It’s something like 15, about what we had before. So cool. And now what’s his GPA? Six-year-olds should not have a GPA but here we are.
We had 14.7 from the previous thing, so I just left it in there. And then I say okay, 14.7, or 15, and I’m going to go up to the 50th percentile. Bang, 2.0. But never go backwards. All right? That’s the deal. Only interpret percentiles in the given direction. That’s all you need.
All right. On to MSRs. We got about 20 minutes. We’re going to do an MSR, a couple problems in there, touch on two parts, maybe go over just a couple minutes. Hope that’s okay. Power through.
So, here it’s tables and graphs. It’s just you got a couple of things. And you’ve got seven and a half minutes in all. We’re not going to take that much time on it, but realize you can take your time to interpret the tabs. So let’s take a look here.
Here’s the first tab. Read it and give me a check mark, a green check, at the bottom of the window, when you’ve read through this. All right, good. So, often in these things, the first sentence is the topic sentence. Pay attention to that. So, it says hey, China’s the biggest export market. Pay attention expletives, extremes. Biggest.
And it gives you some data, some percent of exports that went to China, and there’s a preview of the other tabs, tables one and two. So let’s go on to those. Oh, question on slide availability. You’ll be able to…you’ll get the recording, we’re not giving the slides out, per se, but you will have access to this recording, be able to go back through it at your leisure.
Second tab. Glance over this. What do we got? Type it in. Yeah, it’s GDPs of a bunch of the countries we just talked about. And these GDPs are in dollars. So, I might say oh, okay, so that’s what that is. By the way, these tables aren’t sortable, but you never need to do them. And billion, as they define it here, they don’t define it as 10 to the 9th, it is what they mean, but it doesn’t matter.
And then the next table. What’s this? Tell me. Yeah, so this is exports to China as a percent of G.D.P. Hm. Also notice this is a bunch of countries or regions, and it’s more than in the other table. So we’re going to cheat for a moment, and we’re going to put all these things on one screen.
You don’t have that option. You would actually be tabbing back and forth, and so forth. I’ll come back to that in a moment, how to deal with the fact you have to tab, but for right now, imagine that they’re all together in your mind and sort of floating before you. As you read these things, I want you to notice connections.
Down to the same labels. Tell me what countries do you have a lot of data for? From different tabs. Text them in. Yeah, I got a lot of repeats across the tables, and then some of those even echo into that first tab. And there’s Japan and Russia, so you don’t have to ever make an exhaustive list, but just notice connections that way.
And then look at ways the data could combine. So for instance, in one table, in that middle table, the smaller one on the left, you’ve got G.D.P. in bucks, and in that bigger table, you got exports to China as a percent of G.D.P. So what can we figure out from these two numbers? You tell me. Type it in. What can I figure out, y’all?
You know it, Andrew. I’m seeing it come in from other folks. Exports to China in dollars, by multiplying those two. So, that’s important. See how you can combine the data, and when you have a percent of something, and you also have that something, that’s your bottom dollar, and twice on Sundays, they’re going to make you put those things together.
So, go to it. Now, you might also notice, hey, Australia’s up there in the 21.8% in the text. So I got 21.8% up there, and over here, I got 3.4%. What gives? I got a couple of different percentages. So draw distinctions such as percent of what?
Australian exports to China are 21.8% of its exports to China, but 3.4% of G.D.P. So those are different ofs. It means different things. So don’t be afraid to draw distinctions, as well. They’re going to be critical.
So, let’s address the issue of aren’t we cheating? So, for instance, you might say to yourself, it’s all on different tabs. Well, use the little tape loop in your head. Of course you can jot things down, but you have a tape loop in your head. Tape loop is how you memorize phone numbers. My phone number growing up was 302-478-4579. You can memorize quickly little stuff.
And so there’s you, little dude, or little dudette, looking and saying oh, 21.8% of exports went to China, muttering under your breath. Oh, it’s of G.D.P. over there. So that’s how you carry between. Of course you jot things down, but you don’t want to be copying this whole dang thing down. You’d go crazy.
So, you just use the fact that you also have what’s, you want the technical name? Okay, you asked for it, the phonological loop. It’s just a little tape loop. It’s like a little tape recorder that just can handle a few seconds of data. Use that to carry stuff between and make connections.
All right, here’s your first question. Give me an answer when you can. Go ahead and text it in. All right, seeing a mix of answers. A little bias towards one. We’ll see what they are. All right. If you get stuck on something like this, focus on the concrete stuff like dollars, Japan, exports. Just go grab it.
Okay, I need dollars, Japan, and exports to all countries. Notice I’m not focusing on the 2009 because there ain’t no change here, folks. Nothing in all this stuff changes. It’s all 2009 snapshots. So I stick with that. All right, so, I say to myself, Japan. Tell me, type it in folks, what do I have, if I want dollars, what do I have that’s in dollars?
And I know I got to get an answer, so I got to start from dollars. What do I have that’s in dollars? G.D.P. is in bucks, so if I only had a brain, if I only had a way to connect exports directly to G.D.P., I’d be done, but I don’t, because they don’t list the percent of all exports as a percent of G.D.P., but we don’t have a percent of G.D.P.
Oh, I got exports to China. Hm. we talked about this before. So if I go through and connect G.D.P. to exports to China here with Japan, and I already got the G.D.P., can I connect exports to China back to exports? And yes I can. Cue that 18.9%.
So I think 2.2% and 18.9%, and round that, round that sucker. And I say okay, the G.D.P.’s about 5 thousand billion, 5 trillion. Five-thousand, two percent of that. That’s, 1% would be 50, so 2%, 100. Twenty-percent of what is 100? Twenty-percent of 500. Here are my answer choices. I go for “C” and I get the wrong answer. Oh, snap. Oh, snap.
You got to be really careful with rounding here. This is why you have a calculator, y’all. They actually want you to use it. So, don’t round away the stuff. Say okay, they gave me 5,069, use 5,069. It doesn’t cost you much to type that in, times .022, that gives me 111.5, and now, that’s 18.9% of what? What I would do is I would leave the 111.5 in the calculator, divide by .189, and guess what I get?
I get 590. Oh yeah, that’s the answer. So use that there calculator. All right? It’s what you want to do. It doesn’t mean use it mindlessly, use it all the time, we already saw that, right? What, what? Snap.
So, be really careful here. Compute the number pretty precisely. Try this question. For each of the following countries or regions, determine whether it’s 2009 exports to China can be shown to have exceeded 100 billion in 2009 U.S. dollars. Indicate yes if exports can be shown, you can prove it, and no if you can’t.
Notice what no means here. Either you can prove it’s less than 100 billion, or less than or equal to 100 billion, or you can’t, you simply don’t know what it is. So, here are the counties or regions. Can you prove greater than 100 billion? If so, yes, if not, no. Go ahead and work on it.
Now what I want to point out is, again, use that little friend of yours, say on the European Union, 16.415 times .007, that’s .7% gives you this number. Notice how close that is to 100. It’s just above 100. Do you want to sit there and try to estimate that that’s above 100? Yeah, you can do it if you know 16 times 6 is 96. And why are you doing that?
Yeah, it’s cool to be able to do it, but you got to save your mental energy for the main event. Go ahead and use the calculator. In fact, here, like the Japan, yes, you can figure out that hey, if this were 5,000, and this were 2, then it would be exactly 100. This is bigger, that’s bigger, this means this must be…why are you doing that?
Sure, it’s great. Hey, I’m a big believer in estimation. But also use the calculator. Feel free to. There’s no shame in that game. Nigeria, you don’t have the G.D.P., so you can’t do it. So, mental math is like, if you go crazy with it, yeah, it’s not for the…you got to estimate on the real part of the GMAT where they don’t give you a calculator, but they give you a calculator here so go ahead and use it.
So, yes, question [said Chris] on could you use the data from the last question for Japan? That would save you a little bit of time, it’s true. It’s kind of rare that they do something like that, but they went ahead and did it here. So Nigeria is the no because they don’t have G.D.P. So, you do need to calculate what the exports are because if they do exceed it, it’s not just whether or not they could, if this number came in at 90, I bet there’s some numbers in here that come in just below 100, and then you’d have a no.
So there is sort of a D.S. question, but notice the no would, is not the same thing as insufficient. No would mean less than 100, or you are, you don’t know. Less than 100 or you don’t know, because you can’t show it to exceed 100 billion. So it’s less than or equal to 100, or you don’t know, is what no is there.
And it would be just like them. So, takeaways…Oh, by the way, when you watch the recording, you’re going to see this whole thing. You’re not going to hear just my voice on its own, you’re going to see everything here. So, MSR takeaways, what and so what, use that tape loop. Draw the connections and draw distinctions.
Pay attention to specific language, and of course use that easy language for you. Use that easy path. Sometimes you’re just looking it up. One that we didn’t do involves just literally look something up. And you’re looking up hey, is the Australian number bigger than one-fifth? Is this number bigger than 20%?
And the answer is yes, it is. So sometimes that’s all you got to do. It’s not even that computation. Be ready to just look it up. All right. Last type. Variations on MSRs. You could just have two tabs, so what? Could contain graphs, so what? You just apply all that. The thing that is interesting is occasionally, there are no numbers here, and what they have is they have some kind of little dialog between a couple of people.
It doesn’t look like that. They actually, it’s like an email from “A” to “B” and back to “A.” You just read the dialog and you make some inferences about what they care about, what they think, what they believe, what they’re willing to do.
All right. Two-parts. Reason why we didn’t leave a whole lot of time for this is because these are actually pretty close to the rest of the GMAT. We’re going to do one problem here. Because the Quant problems, it’s pretty much just open season, and it’s just you’re asked to solve for two things instead of one. So solve for “X” and “Y.”
So this is where you might see a divisibility and primes problem. For Verbal, it’s really critical reasoning in disguise. So, those disguises can be very thin. You’ll asked what would strengthen, what would weaken this argument? There can be some variations, though, where you’re asked, okay, about cause and effect, or cost and benefit.
And the weirdest little one, what we’re going to try right now, is a little logic game. You know what? That little logic game, as scary as it’s going to be, you’re going to have a little fright in the next minute or two. It relies on standard logical reasoning, and understand/plan/solve still works. All right.
Last problem of the night. You ready? Here it is. It’s scary. Okay. Take a moment and read through this. Give me a check when you’re done reading. And there you go. All right, most of you are not done, and that’s fine. There’s a lot here. If you encounter one of these, and you might not encounter one at all, there are a lot of constraints.
What I want you to notice is you’re playing a little logic game, which just means you are trying to follow some inferences and solve a puzzle. This is really a puzzle. Hey, I got four writers on this day, and four writers on that day, and I got an open slot. There are five writers on each day.
And then they give me a bunch of constraints about which writers could go on which day. And I got to find who’s on either day, and who could go on neither day. So tell me, tell me in the chat window, what’s going to be true about the four writers we don’t pick? Notice there are six writers down there. What’s true about the four writers we don’t pick?
What must be true about them? Yeah, Becky, that’s right. If one of them is able to go on either day, the other one that we’re going to pick is going to go on neither day, then the four we don’t pick go on exactly one day. They’ll either go one day one and not day two, or they’ll go on day two and not day one.
So here’s the game. What you’re going to do is keep thinking of that open slot. And we’re going to take all those constraints and draw some inferences about those open slots. Those are all going to be reducible to simpler things. Think what if and just sometimes it’s literally counting. So let’s go through it.
I’m going to start from where I just bracketed in blue. To reflect the department’s strength, the majority of writers, okay, majority, that means majority select for one of the days of three or more will be writers whose primary language is not English. I look at this thing and I say okay, I’ve already got two people whose primary language is English.
So, not English, right? Oh, wait a second, it’s just one of the days. I don’t know which day, and here I got two people speaking English. Maybe it’s this day I can’t put someone speaking English on. Hm. So, let me keep going. When in doubt, keep going. On the other day of the festival, at least four writers will be women, because that’s a really big constraint.
At least four writers out of five. That means it can’t be this day, because I already got two males. This person can’t be double female. So, I got to have a female writer on day one, which means that that first constraint we looked at must apply to day two, not English.
Next I have neither day should have more than two writers from the same country. Okay, so I glance down and I say oops, day one can’t have another France person, and day two can’t have another U.K. person. Now apply slot by slot.
And I say, okay, day one, who can I pick for day one? Got to be female, not from France. Type them in. Who can I pick for day one? And just give me checks and x’s. You can pick LeGuin and Murasaki. How about day two? Who can I pick? Not English, not U.K.
And I think it’s actually faster to scan this vertically. I can pick any of the last four people, because I’m knocking out the first two. Good. So now, answer the question carefully. I did one of these things all this way and managed to reverse my answers. Such a pain. Sometimes you do that on the GMAT.
So either day. Oh, that’s Murasaki. Either day, that’s Longfellow. And that’s your answer. This is as hard as one of these gets, the most complicated. And that’s it for the two-parts that we’re going to talk about.
Let me just give you a couple of themes. Thanks for sticking with a few minutes over. I’m seeing it’s 11:35 now here on the East Coast of the United States. Let me just state some themes.
So IR tests the same core skills. Once again, understand/plan/solve is going to work for you. Do not less this mess up the rest of your test. You’ve already put in a good deal of preparation simply by being here. Of course, I want you to practice, including full exams. It could be ours, it could be Manhattan, or mba.com exam, the new GMATPrep. Or somebody else’s exam that’s got IR on it. Just practice.
Be sure to guess and move on. Drink that half a Gatorade, or Powerade, or sugar water, and focus on that main event. Couple points on timing, simple benchmarks. Thirty minutes, 12 questions, that’s two and a half minutes a question. That’s 4 questions in 10 minutes. Something like that.
So for that crazy logic game we just did, you’d have two and a half minutes. That’s cool. That’s probably enough to do it. Do not please use those benchmarks anywhere else. Do not carry over to the Quant section. Oh yeah, I’ve got two and a half minutes per question, it’s like loosey-goosey. Don’t be like that.
Now, what are the additional resources? Let me mention what does GMAC have? GMAC has mba.com, 15 practice problems. We’ve done a couple tonight. GMATPrep 2.0 has those 15 practices plus 12 in an actual section. And then there’s this Quant pack 1, which has 24 refills, and OG 13, which has 50 online.
We have our IR book, which has principles and some practice inside it. Question banks associated with that book, which will give you more practice online, those should get posted in the next few days. And CATs with IR are also coming very soon. Got the questions and just got to post them up, make sure everything is nice and tight, and so, latest at some point next week.
Let me leave it on this slide around do not let IR mess up the rest of your test. You’ve already done a bunch of rehearsal for it. I really want to emphasize, you’re preparing for this thing by preparing for the regular part of the GMAT. Just treat this as a warm-up. You’re going to use understand/plan/solve the same way.
It’s just bells and whistles that are a little bit different. More junk you got to wade through. And with that, I’d like to pause here. Again, my apologies for running a little bit over. Thanks for sticking with, and I hope you’ve found this helpful. I’m going to stick around and answer additional questions, and thank you so much for your time, and best of luck on your whole process of preparing for the GMAT.
Best of luck. Thank you.