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2-17-HighSchool-2If you have two equations, you can solve for two variables.

This rule is a cornerstone of algebra. It’s how we solve for values when we’re given a relationship between two unknowns:

If I can buy 2 kumquats and 3 rutabagas for $16, and 3 kumquats and 1 rutabaga for $9, how much does 1 kumquat cost?

We set up two equations:

2k + 4r = 16

3k + r = 9

Then we can use either substitution or elimination to solve. (Try it out yourself; answer* below).

On the GMAT, you’ll be using the “2 equations à 2 variables” rule to solve for a lot of word problems like the one above, especially in Problem Solving. Be careful, though! On the GMAT this rule doesn’t always apply, especially in Data Sufficiency. Here are some sneaky exceptions to the rule…

2 Equations aren’t always 2 equations
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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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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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Decision

Manhattan Prep is holding a two one-day auditions for new GMAT, GRE, and LSAT instructors in Dallas and Fort Worth! Come join us February 7th  in Dallas or February 8th in Fort Worth at 10:00 AM and transform your passion for teaching into a lucrative and fulfilling part-time or full-time career.

Manhattan Prep offers instructors flexible hours and great pay ($100/hour for all teaching and $116/hour on all tutoring). In addition to teaching classes, instructors can work on other projects such as curriculum development.

Our regular instructor audition process, which includes a series of video, online, and in-person mock lessons, usually takes weeks, even months, to complete. However, we are offering one-day events on February 7th and on 8th for teachers interested in working with us. All candidates who attend will receive a decision that day.

The events will take place in Dallas and Fort Worth at the locations listed below. It is open to candidates who live in the area, who have teaching experience, and who are GMAT, LSAT, or GRE experts.

The audition will include several rounds of lessons, as well as other activities. Each round will be pass/ fail. The day will begin at 10 AM and may last as late as 5:30 PM for those who make it to the final round. Candidates will need to prepare lessons for some rounds; we will send a more detailed instruction packet to those who sign up for the event.

Dallas, TX (Saturday, February 7, 2015)

Meridian Business Center
3010 LBJ Freeway, Suite 1200
Dallas, TX 75234
 

Fort Worth, TX (Sunday, February 8, 2015)

Courtyard Fort Worth at University
3150 Riverfront Drive
Fort Worth, TX 76107

To register, please email Rina at auditions@manhattanprep.com. Make sure to include in your full name, an attachment of your resume detailing your teaching experience, and an official GRE, GMAT, or LSAT score report. We look forward to meeting you in February!

modifierRecently, I was discussing sentence structure with one of my classes and we practiced a crucial but difficult GMAT skill: how to strip an SC sentence to its core components. Multiple OG problems can be solved just by eliminating faulty sentence cores—and the real GMAT is testing this skill today more than we see in the published materials.

So I’m going to write a series of articles on just this topic; welcome to part 1 (and props to my Wednesday evening GMAT Fall AA class for inspiring this series!).

Try out this GMATPrep® problem from the free exams. (Note: in the solution, I’m going to discuss aspects of our SC Process; if you haven’t learned it already, go read about it right now, then come back and try this problem.)

* “With surface temperatures estimated at minus 230 degrees Fahrenheit, Jupiter’s moon Europa has long been considered far too cold to support life, and with 60 square miles of water thought to be frozen from top to bottom.

“(A) Europa has long been considered far too cold to support life, and with

“(B) Europa has long been considered far too cold to support life, its

“(C) Europa has long been considered as far too cold to support life and has

“(D) Europa, long considered as far too cold to support life, and its

“(E) Europa, long considered to be far too cold to support life, and to have”

The First Glance does help on this one, but only if you have studied sentence structure explicitly. Before I did so, I used to think: “Oh, they started with Europa because they added a comma in some answers, but that doesn’t really tell me anything.”

But I’ve learned better! What is that comma replacing? Check it out: the first three answers all have a verb following Europa. The final two don’t; that is, the verb disappears. That immediately makes me suspect sentence structure, because a sentence does have to have a verb. If you remove the main verb from one location, you have to put one in someplace else. I’ll be watching out for that when I read the sentence.

And now it’s time to do just that. As I read the sentence, I strip it down to what we call the “sentence core” in my mind. It took me a long time to develop this skill. I’ll show you the result, first, and then I’ll tell you how I learned to do it.

The “sentence core” refers to the stuff that has to be there in order to have a complete sentence. Everything else is “extra”: it may be important later, but right now, I’m ignoring it.

modifier

I greyed out the portions that are not part of the core. How does the sentence look to you?

Notice something weird: I didn’t just strip it down to a completely correct sentence. There’s something wrong with the core. In other words, the goal is not to create a correct sentence; rather, you’re using certain rules to strip to the core even when that core is incorrect.

Using this skill requires you to develop two abilities: the ability to tell what is core vs. extra and the ability to keep things that are wrong, despite the fact that they’ll make your core sound funny. The core of the sentence above is:

Europa has long been considered too cold to support life, and.

Clearly, that’s not a good sentence! So why did I strip out what I stripped out, and yet leave that “comma and” in there? Here was my thought process:

Text of sentence My thoughts:
“With…” Preposition. Introduces a modifier. Can’t be the core.
With surface temperatures estimated at minus 230 degrees Fahrenheit,” Each word I’ve italicized introduces a new noun modifier. Nothing here is a subject or main verb. *
“Jupiter’s moon Europa” The main noun is Europa; ignore the earlier words.
“Europa has long been considered far too cold to support life,” That’s a complete sentence. Yay.
“, and” A complete sentence followed by “comma and”? I’m expecting another complete sentence to follow. **
with 60 square miles of water thought to be frozen from top to bottom.” Same deal as the beginning of the sentence! Each word I’ve italicized introduces a new modifier. Nothing here that can function as a subject or main verb.

 

* Why isn’t estimated a verb?

Estimated is a past participle and can be part of a verb form, but you can’t say “Temperatures estimated at minus 230 degrees Fahrenheit.” You’d have to say “Temperatures are estimated at…” (Note: you could say “She estimated her commute to be 45 minutes from door to door.” In other words, estimated by itself can be the main verb of a sentence. In my example, though, the subject is actually doing the estimating. In the GMATPrep problem above, the temperatures can’t estimate anything!)

** Why is it that I expected another complete sentence to follow the “comma and”?

The word and is a parallelism marker; it signals that two parts of the sentence need to be made parallel. When you have one complete sentence, and you follow that with “comma and,” you need to set up another complete sentence to be parallel to that first complete sentence.

For example:

She studied all day, and she went to dinner with friends that night.

The portion before the and is a complete sentence, as is the portion after the and.

(Note: the word and can connect other things besides two complete sentences. It can connect other segments of a sentence as well, such as: She likes to eat pizza, pasta, and steak. In this case, although there is a “comma and” in the sentence, the part before the comma is not a complete sentence by itself. Rather, it is the start of a list.)

Okay, so my core is:

Europa has long been considered too cold to support life, and.

And that’s incorrect. Eliminate answer (A). Either that and needs to go away or, if it stays, I need to have a second complete sentence. Since you know the sentence core is at issue here, check the cores using the other answer choices:

modifier

Here are the cores written out:

“(B) Europa has long been considered too cold to support life.

“(C) Europa has long been considered as too cold to support life and has 60 square miles of water.

“(D) Europa and its 60 square miles of water.

“(E) Europa.”

(On the real test, you wouldn’t have time to write that out, but you may want to in practice in order to build expertise with this technique.)

Answers (D) and (E) don’t even have main verbs! Eliminate both. Answers (B) and (C) both contain complete sentences, but there’s something else wrong with one of them. Did you spot it?

The correct idiom is consider X Y: I consider her intelligent. There are some rare circumstances in which you can use consider as, but on the GMAT, go with consider X Y. Answers (C), (D), and (E) all use incorrect forms of the idiom.

Answer (C) also loses some meaning. The second piece of information, about the water, is meant to emphasize the fact that the moon is very cold. When you separate the two pieces of information with an and, however, they appear to be unrelated (except that they’re both facts about Europa): the moon is too cold to support life and, by the way, it also has a lot of frozen water. Still, that’s something of a judgment call; the idiom is definitive.

The correct answer is (B).

Go get some practice with this and join me next time, when we’ll try another GMATPrep problem and talk about some additional aspects of this technique.

Key Takeaways: Strip the sentence to the Core

(1) Generally, this is a process of elimination: you’re removing the things that cannot be part of the core sentence. With rare exceptions, prepositional phrases typically aren’t part of the core. I left the prepositional phrase of water in answers (C) and (D) because 60 square miles by itself doesn’t make any sense. In any case, prepositional phrases never contain the subject of the sentence.

(2) Other non-core-sentence clues: phrases or clauses set off by two commas, relative pronouns such as which and who, comma + -ed or comma + ing modifiers, -ed or –ing words that cannot function as the main verb (try them in a simple sentence with the same subject from the SC problem, as I did with temperatures estimated…)

(3) A complete sentence on the GMAT must have a subject and a working verb, at a minimum. You may have multiple subjects or working verbs. You could also have two complete sentences connected by a comma and conjunction (such as comma and) or a semi-colon. We’ll talk about some additional complete sentence structures next time.

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

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!

11-20-BF-GMATOne of the biggest shopping days of the year has arrived–Happy Black Friday! In case you’re too full of turkey and stuffing to make your way out to the shops today, we’re serving up something extra special.

Today through December 15th, we’re offering $200 off all of our Complete GMATLSAT, and GRE courses*! This deal includes all Complete Courses– in-person as well as Live-Online. To receive this limited-time discount, register for a course that starts in December and enter the code Holiday200 at checkout.

This is only the beginning of the holiday season, which means we have many more amazing things coming your way, including our BRAND NEW 6th Edition GMAT Strategy Guides. You can pre-order your copies now and be the first to experience the best!

*Offer is valid for courses starting in the month of December only. Not valid for students currently registered for courses, or with any additional offers. Offer expires 12/15/2013 for GMAT courses

 

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.

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!