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2-12-MinMaxP3

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?

“(A) 32

“(B) 37

“(C) 40

“(D) 43

“(E) 50”

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:

gmat1

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.
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2-11-ScienceWe’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.
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minLast 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?

“(A) 40

“(B) 38

“(C) 33

“(D) 32

“(E) 30”

 

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.
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2-6-HabitsDistractions are bad. Routine, concentration, and hard work are good. These all seem like common-sense rules for studying, right? Surprisingly (for many people, at least), learning science tells us that these “good habits” may actually be hurting your learning process!

When you were in college, your study process probably looked something like this: for a given class, you’d attend a lecture each week, do the readings (or at least most of them), and maybe turn in an assignment or problem set. Then, at the end of the semester, you’d spend a week furiously cramming all of that information to prepare for the test.

Since this is the way you’ve always studied, it’s probably how you’re approaching the GMAT, too. But I have bad news: this is not an effective approach for the GMAT!

Taking notes then cramming the night before the test is beneficial for tests that ask you to recite knowledge: “what were the major consequences of the Hawley-Smoot tariff” or “explain Heisenberg’s uncertainty principle.” You can hold a lot of facts  -for a brief time – in your short-term memory when cramming. You memorize facts, you spit them out for the test… and then, if you’re like me, you find that you’ve forgotten half of what you memorized by the next semester.

Why the GMAT is Different

The GMAT doesn’t reward this style of studying because it’s not simply a test of facts or knowledge. The GMAT requires you to know a lot of rules, of course, but the main thing that it’s testing is your ability to apply those concepts to new problems, to adapt familiar patterns, and to use strategic decision-making. You’ll never see the same problem twice.

Shallow memorization is not nearly enough. You need deep conceptual understanding.

In How We Learn*, science writer Benedict Carey outlines decades of research about how this kind of learning happens. Many of the findings go against what you probably thought were “good” study habits.
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1-20-StatisticsBlast 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?

“(A) 1

“(B) 2

“(C) 3

“(D) 4

“(E) 5”

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?
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The Graduate Management Admission Test, better known as the GMAT®, is a standardized test used in the admissions process for business school and other specialized Master’s programs. The exam measures certain skills that the business schools care about, most notably Executive Reasoning skills. It does not test any specific business knowledge.

When is the GMAT given?

You can take the GMAT year-round, nearly any day of the week (though they limit you to 5 sittings in a 12-month period and require a wait of 31 days between tests). The exam is given on a computer and is known as a “CAT.”

What is a CAT?

A CAT is a computer-adaptive test: the test actually adapts itself to you while you’re taking it! Two of the four sections on the GMAT, the Quantitative and Verbal sections, are adaptive. Each of these two sections begins with a random, approximately medium-level question. The computer chooses each subsequent question based upon your collective performance to that point in the section.

The practical implications are important. First, every test taker will take a different exam with a different mix of questions, but the test feels hard for everyone, since the test will just keep getting harder until it finds a particular person’s limit. Second, the scoring is pretty peculiar; it’s important to understand how the scoring works.

Want to try your hand at a practice test? Take our free, full-length practice exam here.

How is the GMAT Scored?

Tests you took in school were generally based on the percentage of questions answered correctly: the more you got right, the higher the score you received. As a result, you have been trained to take your time and try to get everything right when you take a test. This general strategy does not work on computer-adaptive sections of the GMAT because, strangely enough, the quant and verbal scores are not based on the percentage of questions answered correctly. On the GMAT, most people answer similar percentages of questions correctly, typically in the 50% to 70% range (even at higher scoring levels!).

How is that possible? The first thing to know: the GMAT is not a school test. The quant section is not really a math test, and the verbal section is not really a grammar test. Of course, you do need to know how to handle those topics. The test writers are really interested, however, in knowing how good you are at making decisions and managing scarce resources. (That’s the second time we’ve linked to that same article. Go read it!)
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GMAT_ChartThe 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:

Sentence Correction

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.

Reading Comprehension

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

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.

Visit our store and be the first to own the full set of our brand new Strategy Guides. Happy studying!

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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!

DS StrategyIf you’re going to do a great job on Data Sufficiency, then you’ve got to know how to Test Cases. This strategy will help you on countless DS problems.

 

Try this GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “On the number line, if the number k is to the left of the number t, is the product kt to the right of t?

“(1) t < 0

“(2) k < 1”

 

If visualizing things helps you wrap your brain around the math (it certainly helps me), sketch out a number line:

GMAT_Chart

k is somewhere to the left of t, but the two actual values could be anything. Both could be positive or both negative, or k could be negative and t positive. One of the two could even be zero.

The question asks whether kt is to the right of t. That is, is the product kt greater than t by itself?

There are a million possibilities for the values of k and t, so this question is what we call a theory question: are there certain characteristics of various numbers that would produce a consistent answer? Common characteristics tested on theory problems include positive, negative, zero, simple fractions, odds, evens, primes—basically, number properties.

“(1) t < 0

This problem appears to be testing positive and negative, since the statement specifies that one of the values must be negative. Test some real numbers, always making sure that t is negative.

Case #1:

t k Valid case? Is kt > t?
-1 -2 Valid: t < 0 and k < t 2 > -1? Yes.

Testing Cases involves three consistent steps:

First, choose numbers to test in the problem

Second, make sure that you have selected a valid case. All of the givens must be true using your selected numbers.

Third, answer the question.

In this case, the answer is Yes. Now, your next strategy comes into play: try to prove the statement insufficient.

How? Ask yourself what numbers you could try that would give you the opposite answer. The first time, you got a Yes. Can you get a No?

Case #2:

t k Valid case? Is kt > t?
-1 2 Invalid! k is not less than t!

 

Careful: this is where you might make a mistake. In trying to find the opposite case, you might try a mix of numbers that is invalid. Always make sure that you have a valid case before you actually try to answer the question. Discard case 2.

Case #3:

t k Valid case? Is kt > t?
-1 -5 Valid: t < 0 and k < t 5 > -1? Yes.

Hmm. We got another Yes answer. What does this mean? If you can’t come up with the opposite answer, see if you can understand why. According to this statement, t is always negative. Since k must be smaller than t, k will also always be negative.

The product kt, then, will be the product of two negative numbers, which is always positive. As a result, kt must always be larger than t, since kt is positive and t is negative.

Okay, statement (1) is sufficient. Cross off answers BCE and check out statement (2):

“(2) k < 1”

You know the drill. Test cases again!

Case #1:

k t Valid case? Is kt > t?
0 1 Valid: k < 1 and k < t 0 > 1? No.

 

You’ve got a No answer. Try to find a Yes.

Case #2:

k t Valid case? Is kt > t?
-1 1 Valid: k < 1 and k < t -1 > 1? No.

 

Hmm. I got another No. What needs to happen to make kt > t? Remember what happened when you were testing statement (1): try making them both negative!

In fact, when you’re testing statement (2), see whether any of the cases you already tested for statement (1) are still valid for statement (2). If so, you can save yourself some work. Ideally, the below would be your path for statement (2), not what I first showed above:

“(2) k < 1”

Case #1:

k t Valid case? Is kt > t?
-2 -1 Valid: k < 1 and k < t Same case, still Yes.

All you have to do is make sure that the case is valid. If so, you’ve already done the math, so you know that the answer is the same (in this case, Yes).

Now, try to find your opposite answer: can you get a No?

Case #2: Try something I couldn’t try before. k could be positive or even 0…

k t Valid case? Is kt > t?
0 1 Valid: k < 1 and k < t 0 > 1? No.

 

A Yes and a No add up to an insufficient answer. Eliminate answer (D).

The correct answer is (A).

Guess what? The technique can also work on some Problem Solving problems. Try it out on the following GMATPrep problem, then join me next week to discuss the answer:

* “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) prob

Key Takeaways: Test Cases on Data Sufficiency

(1) When DS asks you a “theory” question, test cases. Theory questions allow multiple possible scenarios, or cases. Your goal is to see whether the given information provides a consistent answer.

(2) Specifically, try to disprove the statement: if you can find one Yes and one No answer, then you’re done with that statement. You know it’s insufficient. If you keep trying different kinds of numbers but getting the same answer, see whether you can think through the theory to prove to yourself that the statement really does always work. (If you can’t, but the numbers you try keep giving you one consistent answer, just go ahead and assume that the statement is sufficient. If you’ve made a mistake, you can learn from it later.)

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

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The GMAT Review Game

Céilidh Erickson —  November 19, 2014 — 2 Comments

GMAT_ChartSo you’ve just taken a practice test. Chances are, you didn’t get a perfect 800. (If you did, stop studying and come work for us!). You probably didn’t even get a score that you like yet. That doesn’t mean that you’ve failed, though. In fact, you’ve barely started, because…

REVIEWING IS THE MOST IMPORTANT PART OF THE PROCESS!!

Most people take tests, then look at the score, then click on the explanations to the ones they got wrong. Their review process takes about 15 minutes, and just involves “oh, I did that wrong. Oh, that’s the right answer.” This kind of review process teaches you next to nothing about how to do better on the next one.

So here’s what you need to do. The test gave you a score from 200-800 on accuracy, but you need to give yourself your own score on your review process. Here’s how it works…

For every single question – not just the ones you got wrong! – you should be going back and re-solving. Take yourself through this checklist for quant problems:

GMAT_Chart

1) Did I fully understand the concept and the rules behind it? +1
Give yourself a point if you could tell that a question was asking about DIVISIBILITY, or understood the RATE x TIME = DISTANCE relationship.

2) Did I understand what the question was asking for? +1
Did you rephrase DS questions to pinpoint what they were really asking for? Did you notice that it asked for “Amy’s age in 5 years,” and wrote down A + 5 instead of just A? Did you understand what it means when they ask for “x in terms of y and z”?

3) Did you solve it correctly? up to +5
Give yourself up to 5 points if you solved correctly the first time and got the right answer. Subtract a point or two if you took longer than you should have, or made a mistake before ultimately correcting it. Only give yourself +1 for a random lucky guess and +2 for an educated guess.

4) … or if you didn’t solve correctly, did you make a good decision to skip? +2
You’re not going to be able to solve every question on the GMAT, because you’re always going to run into questions that are above your ability level – that’s how the test is designed! So you should pat yourself on the back whenever you recognize that a question is too hard to solve, and you make the decision not to attempt it. Lock in an educated guess and save that extra time for a problem that is doable for you.
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11-12-ReviewAs we discussed in the first half of this series, Building Your Game Plan, during the last 7 to 14 days before you take the real test, your entire study focus changes. In this article, we’re going to discuss the second half of this process: how to review. (If you haven’t already read the first half, do so before you continue with this part.)

What to Review

Part of the game planning process is determining your strengths and weaknesses. Map these against the frequency with which various topics or question types tend to be tested on the real exam. You want to spend the bulk of your time reviewing the material that is most likely to appear on the test.

If an infrequently-tested area is also a weakness (I’m looking at you, combinatorics), drop it entirely. If you get an easier one on the test, try it for up to 2 minutes. If you get a hard one, call that one of your freebies: guess quickly and use that time elsewhere.

If you’re not sure how frequently a particular type of content or question appears on the exam, ask on the forums. I’m not going to provide a list in this article because these frequencies can change over time; I don’t want people reading this in future to be misled when things do change. The General GMAT Strategy folder in our own forums has a bookmarked thread—it always sits at the top—that discusses this very issue. If I’ve commented on the topic or question type mix within (at least) the past 6 months, then you’re up to date.

How to Review

How you review is going to vary somewhat depending upon whether you’re reviewing a strength or a weakness. You do NOT want to do the same kind of review for everything, but you DO want to review both strengths and weaknesses. I’m going to make a distinction between the following categories:

Easier-for-you: you find the question fairly straightforward and you expect to answer it correctly without needing extra time, though you may sometimes make a careless mistake.

Harder-for-you: this question is more of a struggle, though you still will answer some of these correctly.
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