I. Roman numeral Quant problems aren’t a whole lot of fun.
II. A lot of my students choose to skip them entirely, which is much smarter than wasting five minutes wondering what to do!
III. However, it’s possible to turn this rare and tricky problem type into an opportunity.
Read on, and learn why many GMAT high-scorers love Roman numeral problems. Read more
There are really only a dozen different Critical Reasoning problems in the Official Guide to the GMAT. The test writers recycle the same basic argument structures over and over, and they use the same right answers over and over, too. Even though the topics change — an argument might be about school funding the first time you see it, and industrial efficiency the next — you can sometimes recognize the underlying structure, outsmart the test, and earn some well-deserved points on the Verbal section. Read more
Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.
In our previous article, we divided the logical errors that test-takers make on Data Sufficiency questions into two types:
Type 1: You thought that something was sufficient, but it was actually insufficient.
Type 2: You thought that something was insufficient, but it was actually sufficient.
We already covered the most common reasons for Type 1 errors to occur and a few good ways to avoid them; now, let’s cover Type 2 errors. Read more
Most second-round deadlines are in early January, so around now, a lot of people are asking me how to eke out the last 30 to 80 points they need to reach their goal.
Let’s talk about what to do to try to lift your score that last bit in the final 2 months of your study.
Is this article for me?
If you’re going to do a great job on the GMAT, then you’ve got to know how to Test Cases. This strategy will help you on countless quant problems.
This technique is especially useful for Data Sufficiency problems, but you can also use it on some Problem Solving problems, like the GMATPrep® problem below. Give yourself about 2 minutes. Go!
* “For which of the following functions f is f(x) = f(1 – x) for all x?
|(A)||f(x) = 1 – x|
|(B)||f(x) = 1 – x2|
|(C)||f(x) = x2 – (1 – x)2|
|(D)||f(x) = x2(1 – x)2|
|(E)||f(x) = x / (1 – x)”|
Testing Cases is mostly what it sounds like: you will test various possible scenarios in order to narrow down the answer choices until you get to the one right answer. What’s the common characteristic that signals you can use this technique on problem solving?
The most common language will be something like “Which of the following must be true?” (or “could be true”).
The above problem doesn’t have that language, but it does have a variation: you need to find the answer choice for which the given equation is true “for all x,” which is the equivalent of asking for which answer choice the given equation is always, or must be, true.
Welcome to our third and final installment dedicated to those pesky maximize / minimize quant problems. If you haven’t yet reviewed the earlier installments, start with part 1 and work your way back up to this post.
I’d originally intended to do just a two-part series, but I found another GMATPrep® problem (from the free tests) covering this topic, so here you go:
“A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?
Here’s the general process for answering quant questions—a process designed to make sure that you understand what’s going on and come up with the best plan before you dive in and solve:
Fifteen integers…that’s a little annoying because I don’t literally want to draw 15 blanks for 15 numbers. How can I shortcut this while still making sure that I’m not missing anything or causing myself to make a careless mistake?
Hmm. I could just work backwards: start from the answers and see what works. In this case, I’d want to start with answer (E), 50, since the problem asks for the greatest possible integer.
We’re going to kill two birds with one stone in this week’s article.
Inference questions pop up on both Critical Reasoning (CR) and Reading Comprehension (RC), so you definitely want to master these. Good news: the kind of thinking the test-writers want is the same for both question types. Learn how to do Inference questions on one type and you’ll know what you need to do for the other!
That’s actually only one bird. Here’s the second: both CR and RC can give you science-based text, and that science-y text can get pretty confusing. How can you avoid getting sucked into the technical detail, yet still be able to answer the question asked? Read on.
Try this GMATPrep® CR problem out (it’s from the free practice tests) and then we’ll talk about it. Give yourself about 2 minutes (though it’s okay to stretch to 2.5 minutes on a CR as long as you are making progress.)
“Increases in the level of high-density lipoprotein (HDL) in the human bloodstream lower bloodstream cholesterol levels by increasing the body’s capacity to rid itself of excess cholesterol. Levels of HDL in the bloodstream of some individuals are significantly increased by a program of regular exercise and weight reduction.
“Which of the following can be correctly inferred from the statements above?
“(A) Individuals who are underweight do not run any risk of developing high levels of cholesterol in the bloodstream.
“(B) Individuals who do not exercise regularly have a high risk of developing high levels of cholesterol in the bloodstream late in life.
“(C) Exercise and weight reduction are the most effective methods of lowering bloodstream cholesterol levels in humans.
“(D) A program of regular exercise and weight reduction lowers cholesterol levels in the bloodstream of some individuals.
“(E) Only regular exercise is necessary to decrease cholesterol levels in the bloodstream of individuals of average weight.”
Got an answer? (If not, pick one anyway. Pretend it’s the real test and just make a guess.) Before we dive into the solution, let’s talk a little bit about what Inference questions are asking us to do.
Inference questions are sometimes also called Draw a Conclusion questions. I don’t like that title, though, because it can be misleading. Think about a typical CR argument: they usually include a conclusion that is…well…not a solid conclusion. There are holes in the argument, and then they ask you to Strengthen it or Weaken it or something like that.
Last time, we discussed two GMATPrep® problems that simultaneously tested statistics and the concept of maximizing or minimizing a value. The GMAT could ask you to maximize or minimize just about anything, so the latter skill crosses many topics. Learn how to handle the nuances on these statistics problems and you’ll learn how to handle any max/min problem they might throw at you.
Feel comfortable with the two problems from the first part of this article? Then let’s kick it up a notch! The problem below was written by us (Manhattan Prep) and it’s complicated—possibly harder than anything you’ll see on the real GMAT. This problem, then, is for those who are looking for a really high quant score—or who subscribe to the philosophy that mastery includes trying stuff that’s harder than what you might see on the real test, so that you’re ready for anything.
Ready? Here you go:
“Both the average (arithmetic mean) and the median of a set of 7 numbers equal 20. If the smallest number in the set is 5 less than half the largest number, what is the largest possible number in the set?
Out of the letters A through E, which one is your favorite?
You may be thinking, “Huh? What a weird question. I don’t have a favorite.”
I don’t have one in the real world either, but I do for the GMAT, and you should, too. When you get stuck, you’re going to need to be able to let go, guess, and move on. If you haven’t been able to narrow down the answers at all, then you’ll have to make a random guess—in which case, you want to have your favorite letter ready to go.
If you have to think about what your favorite letter is, then you don’t have one yet. Pick it right now.
I’m serious. I’m not going to continue until you pick your favorite letter. Got it?
From now on, when you realize that you’re lost and you need to let go, pick your favorite letter immediately and move on. Don’t even think about it.
Blast from the past! I first discussed the problems in this series way back in 2009. I’m reviving the series now because too many people just aren’t comfortable handling the weird maximize / minimize problem variations that the GMAT sometimes tosses at us.
In this installment, we’re going to tackle two GMATPrep® questions. Next time, I’ll give you a super hard one from our own archives—just to see whether you learned the material as well as you thought you did. 🙂
Here’s your first GMATPrep problem. Go for it!
“*Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the maximum possible weight, in kilograms, of the lightest box?
When you see the word maximum (or a synonym), sit up and take notice. This one word is going to be the determining factor in setting up this problem efficiently right from the beginning. (The word minimum or a synonym would also apply.)
When you’re asked to maximize (or minimize) one thing, you are going to have one or more decision points throughout the problem in which you are going to have to maximize or minimize some other variables. Good decisions at these points will ultimately lead to the desired maximum (or minimum) quantity.
This time, they want to maximize the lightest box. Step back from the problem a sec and picture three boxes sitting in front of you. You’re about to ship them off to a friend. Wrap your head around the dilemma: if you want to maximize the lightest box, what should you do to the other two boxes?
Note also that the problem provides some constraints. There are three boxes and the median weight is 9 kg. No variability there: the middle box must weigh 9 kg.
The three items also have an average weight of 7. The total weight, then, must be (7)(3) = 21 kg.
Subtract the middle box from the total to get the combined weight of the heaviest and lightest boxes: 21 – 9 = 12 kg.
The heaviest box has to be equal to or greater than 9 (because it is to the right of the median). Likewise, the lightest box has to be equal to or smaller than 9. In order to maximize the weight of the lightest box, what should you do to the heaviest box?
Minimize the weight of the heaviest box in order to maximize the weight of the lightest box. The smallest possible weight for the heaviest box is 9.
If the heaviest box is minimized to 9, and the heaviest and lightest must add up to 12, then the maximum weight for the lightest box is 3.
The correct answer is (C).
Make sense? If you’ve got it, try this harder GMATPrep problem. Set your timer for 2 minutes!
“*A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
Hmm. There are 11 voting districts, each with some number of people. We’re asked to find the minimum possible population in the least populated district—that is, the smallest population that any one district could possibly have.
Let’s say that District 1 has the minimum population. Because all 11 districts have to add up to 132,000 people, you’d need to maximize the population in Districts 2 through 10. How? Now, you need more information from the problem:
“no district is to have a population that is more than 10 percent greater than the population of any other district”
So, if the smallest district has 100 people, then the largest district could have up to 10% more, or 110 people, but it can’t have any more than that. If the smallest district has 500 people, then the largest district could have up to 550 people but that’s it.
How can you use that to figure out how to split up the 132,000 people?
In the given problem, the number of people in the smallest district is unknown, so let’s call that x. If the smallest district is x, then calculate 10% and add that figure to x: x + 0.1x = 1.1x. The largest district could be 1.1x but can’t be any larger than that.
Since you need to maximize the 10 remaining districts, set all 10 districts equal to 1.1x. As a result, there are (1.1x)(10) = 11x people in the 10 maximized districts (Districts 2 through 10), as well as the original x people in the minimized district (District 1).
The problem indicated that all 11 districts add up to 132,000, so write that out mathematically:
11x + x = 132,000
12x = 132,000
x = 11,000
The correct answer is (D).
Practice this process with any max/min problems you’ve seen recently and join me next time, when we’ll tackle a super hard problem.
Key Takeaways for Max/Min Problems:
(1) Figure out what variables are “in play”: what can you manipulate in the problem? Some of those variables will need to be maximized and some minimized in order to get to the desired answer. Figure out which is which at each step along the way.
(2) Did you make a mistake—maximize when you should have minimized or vice versa? Go through the logic again, step by step, to figure out where you were led astray and why you should have done the opposite of what you did. (This is a good process in general whenever you make a mistake: figure out why you made the mistake you made, as well as how to do the work correctly next time.)
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
The newest GMAT Strategy Guides have hit the shelves! We’re really excited about these new books, the perfect stocking stuffers to make all of your dreams come true. (Well…your GMAT-related dreams, anyway.)
Yesterday, we talked about the Quant Guides and today I’ve got the Verbal scoop for you. Let’s start with Sentence Correction.
The SC Guide begins with a new strategy chapter that discusses our 4-Step SC Process and lays out drills that you can do to get better at such skills as the First Glance and Finding a Starting Point. We’ve also significantly expanded the Subject-Verb Agreement chapter to include a full treatment of Sentence Structure, an area that has been becoming much more commonly tested on the GMAT.
We’ve added important segments to Modifiers, Parallelism, and Verbs and we’ve woven relevant Meaning topics into every chapter in the book.
Finally, we’ve streamlined the Idioms material. The main chapter contains a strategy for tackling idioms as well as the most commonly tested idioms found on the GMAT. A separate appendix contains the less-commonly-tested idioms. We recommend taking the time to memorize the ones listed in the main chapter, but to use the appendix more as a resource to look up the correct idiom when you struggle with a particular problem. (It’s impossible to memorize every idiom in a language; there are thousands, if not tens of thousands!)
What about RC and CR?
Glad you asked! Our Reading Comprehension Guide was re-written from scratch. We’ve streamlined the process for reading passages and added lessons designed to help you wade through these dense passages and extract the kernels you need to answer questions. We’ve also expanded our lessons for each question type and provided you with end-of-chapter cheat sheets that summarize what to do for each question type and what common traps to avoid. (I’m most excited about this book; students often complain that RC is hard to study, and I’m hoping that this book will change your minds!)
Of all of the books, Critical Reasoning has changed the least, although we did add more information about Fill-In-The-Blank question types. This Guide also provides you with end-of-chapter cheat sheets that summarize how to recognize each type of question, what to look for in the argument, what kind of characteristics the right answer needs to possess, and how to spot the most common trap answers.
What is the best way to use the books?
Here’s how we typically study each topic in class:
First, we learn how to use the SC Process and we discuss the main topics being tested (grammar and meaning); these correspond to chapters 1 and 2 of the book. Then, we work through one new chapter a week, starting with Chapter 3 (Sentence Structure). The order of chapters in the book is the same order we use in class.
You can use the same approach mentioned for quant (in the first half of this article): do some end-of-chapter problems first to see what your skills are. If you know that you don’t really know this material, then you can also skip this step. After you’ve finished a chapter, try some of those end-of-chapter problems to ensure that you did actually internalize the concepts that you just learned. Then, if you have the OG books, follow up with some questions from the OG Problem Sets, located in your Manhattan Prep Student Center.
The class contains three RC lessons. First, we learn how to read. Bet you thought you already knew how, didn’t you?
Of course you do know how to read, but the way you read in the real world may not work very well on the GMAT. You’ll learn a new way to deal with the short timeframe we’re given on the test. After that, you’ll learn how to handle General questions, the ones for which you need to wrap your brain around the main ideas of the passage.
Then, you’ll move on to Specific Questions, including Detail, Inference, and Purpose questions. The test writers are asking us to do something a bit different for each one, so you’ll need to learn how to recognize each type in the first place and then how to handle it.
In class, we finish off with a Challenging RC lesson. You can create something similar for yourself by tackling harder and harder OG passages.
Critical Reasoning begins with a thorough treatment of argument building blocks and the 4-Step CR Process. After that, you’ll learn about each question type (do actually use the order presented in the book). Pay attention to what the book says about frequency of each type; some types are much more common than others (and those types should obviously get more of your attention).
For both CR and RC, tear out or photo-copy the cheat sheets and use them to quiz yourself. Alternatively, put the material onto flash cards yourself (the act of rewriting the material will help you to remember it better!) and drill while you’re sitting on the subway or waiting for that meeting to start.
Is that all I need to do?
That will certainly keep you busy for a while. As you get further into your studies, note that you also need to lift yourself to the 2nd Level of GMAT Study. Yes, of course, there are lots of facts, formulas, and rules to memorize, and your brain will be focused on those areas at first. It’s crucial, however, for you to learn the various strategies presented in our Guides, as well as your own decision-making strategies based on your own strengths and weaknesses, and timing strategies.
In short, get ready to make a commitment. Think of studying for the GMAT as a university-level course: you’re going to spend hours every week for about 3 to 4 months to get ready for this test. With a solid plan, you’ll achieve your goals.
Studying for the GMAT? Take our free GMAT practice exam or sign up for a free GMAT trial class running all the time near you, or online. And, be sure to find us on Facebook and Google+,LinkedIn, and follow us on Twitter!