### GMAT Problem Solving Strategy: Test Cases

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 – x^{2} |

(C) | f(x) = x^{2} – (1 – x)^{2} |

(D) | f(x) = x^{2}(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.

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### How to Switch from the GRE to the GMAT

Lately, we’ve been talking about how to decide which test to take, as well as what to do if . What if you decide to switch from the GRE to the GMAT? That’s what we’ll tackle today! (We have also talked about what to do if you want to switch from the GMAT to the GRE.)

### How do I study?

The overall *way* that you want to study doesn’t actually change that much; rather, you’ll just need to change *what* you are studying, as discussed later in this article.

First, you’ll need to determine whether the way that you’ve already been studying is actually the optimal way. If not, then you’ll need to make some changes, regardless of whether you stick with the GRE or switch to the GMAT.

The GRE and the GMAT are both executive reasoning tests; that is, the test makers want to know how you think and make decisions. You of course need to know content (certain facts, rules, formulas) in order to do well on either test, but that level of study is not enough; you also need to lift yourself to a second level of understanding that allows you to think your way through these sometimes bizarrely-worded problems as effectively and efficiently as possible.

Follow the two links I put in the last paragraph. Take some time to just think about the concepts presented there. Has this been your approach to studying so far? If so, great. Keep thinking and working in that way.

If not, however, recognize that you’re going to need to start studying with this new mindset, regardless of whether you take the GRE or the GMAT.

### What are my strengths and weaknesses?

Any time you’re developing or revising a study plan, you’ll want to put together a solid analysis of your strengths and weaknesses.

If you have been studying for the GRE for a while, then you should have some practice CAT data. (If not, or if it has been more than 6 weeks since you last took a CAT, then you’ll need to take one to get the data. Make sure to take the test under official conditions, including the essays, length of breaks, and so on.)

Analyze your most recent two CATs (this link tells you how to analyze Manhattan Prep CATs). If you haven’t taken MPrep CATs, you can still read through that link to get an idea of how you want to analyze your data from another test. Your goal is to split all question types and content into one of three buckets:

*Bucket 1:* Strengths. I’ll still study and practice these but not as heavily as other areas.

*Bucket 2:* Low-hanging Fruit: These are my easiest opportunities for improvement. Careless mistakes. Things that I get wrong fast. Things that I get right but just a little too slowly.

*Bucket 3:* Weaknesses. These are areas that I’ll ignore until I’ve worked out my Bucket 2 issues. Things that I’m likely to get wrong even if I give myself unlimited time. Things that I get right but *way* too slowly. Things that use up way too much mental energy, even if I get them right.

Your primary focus until your next practice test will be working a lot to improve Bucket 2, while maintaining Bucket 1 skills and getting Bucket 3 questions wrong fast (yes, seriously!).

[Aside: there are certain things that will stay in Bucket 3 forever. I’m terrible at combinatorics and I’m pretty bad at 3D geometry. That’s been true since my very first practice GRE, more than 10 years ago! When I see these, I’ll give it a look in case the problem is very similar to one that I do remember how to do, but otherwise, I pick my favorite letter and move on.]

Okay, now that you know what your strengths and weaknesses are, you need to familiarize yourself with the differences between the GRE and the GMAT.

### What *new* things do I have to learn?

*The Essays and Integrated Reasoning*

You won’t care as much about one difference, so let’s get it out of the way. At the beginning of the GRE, you write two essays. The GMAT also asks you to write an essay but in place of the second essay you’ll have to do the Integrated Reasoning section, a multiple-choice section that mixes quant and verbal skills.

This section is different enough from the others that you will have to study how to answer these questions and how to manage your time during the section. At the time of this publication (in March 2015), schools aren’t using IR scores much, so this section is less important, though this could change in the future.

*Quant*

Next, for the quant section of the test, you’re going to need to learn about one different question type contained on the GMAT: Data Sufficiency (DS).

The GMAT dives more deeply into number properties, story problems, and some algebra concepts, so you may need to get GMAT books for these topics versus continuing to use your GRE books.

The timing on the two tests is also quite different, so you’ll have to learn how to handle 37 questions in 75 minutes on the GMAT, or about 2 minutes per question on average.

*Verbal*

Most of your new efforts on verbal will be geared towards the grammar question type, Sentence Correction (SC). You’ll definitely need to get some materials that teach you the grammar and meaning issues that are tested on SC.

Again, if you are already using Manhattan Prep materials, you can use what you already have for Reading Comprehension (RC), but you will need to get new materials for Critical Reasoning (CR). The CR question types on the GRE are also tested on the GMAT, but the GMAT contains additional CR question types that don’t appear on the GRE.

Again, the timing will be different on the GMAT. You’ll need to answer 41 verbal questions in 75 minutes, spending about 1 minute 20 seconds on SC, 2 minutes on CR, and about 6 to 8 minutes total for RC passages and questions.

### How do I make a study plan?

We’ve already talked about part of the process (analyzing your strengths and weaknesses). You may decide to take a class or work with a tutor, in which case your teacher will give you specific assignments . If not, you’ll need to develop your own study plan.

### Takeaways for switching from GRE to GMAT

(1) Make sure that you’re going into your studies with the right overall mindset (executive reasoning!) and that you know how to lift yourself to the “second level” of study.

(2) Begin your studies by concentrating on the aspects that are new to you: the different question types and topics that are tested on the GMAT. Once you build those skills up to a competent level, you’ll review all aspects and question types.

### How to Switch from the GMAT to the GRE

Lately, we’ve been talking about how to decide which test to take, as well as what to do if you decide to stick with the GMAT. What if you decide to switch from the GMAT to the GRE? That’s what we’ll tackle today! (Next time, we’ll talk about what to do if you want to switch from the GRE to the GMAT.)

### How do I study?

The overall *way* that you want to study doesn’t actually change that much; rather, you’ll just need to change *what* you are studying, as discussed later in this article.

First, you’ll need to determine whether the way that you’ve already been studying is actually the optimal way. If not, then you’ll need to make some changes, regardless of whether you stick with the GMAT or switch to the GRE.

The GMAT and the GRE are both executive reasoning tests; that is, the test makers want to know how you think and make decisions. You of course need to know content (certain facts, rules, formulas) in order to do well on either test, but that level of study is not enough; you also need to lift yourself to a second level of understanding that allows you to think your way through these sometimes bizarrely-worded problems as effectively and efficiently as possible.

Follow the two links I put in the last paragraph. Take some time to just think about the concepts presented there. Has this been your approach to studying so far? If so, great. Keep thinking and working in that way.

If not, however, recognize that you’re going to need to start studying with this new mindset, regardless of whether you take the GMAT or the GRE.

### What are my strengths and weaknesses?

Any time you’re developing or revising a study plan, you’ll want to put together a solid analysis of your strengths and weaknesses.

If you have been studying for the GMAT for a while, then you should have some practice CAT data. (If not, or if it has been more than 6 weeks since you last took a CAT, then you’ll need to take one to get the data. Make sure to take the test under official conditions, including the essay and IR sections, length of breaks, and so on.)

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### When Your High School Algebra is Wrong: How the GMAT Breaks Systems of Equations Rules

*If 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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### Tackling Max/Min Statistics on the GMAT (part 3)

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*:

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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### Tackling Max/Min Statistics on the GMAT (Part 2)

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?

“(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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### Break Your “Good” GMAT Study Habits! What Learning Science Can Teach Us About Effective GMAT Studying

*Distractions 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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### Round 3 Application Deadlines for the Top 25 B-Schools

The round three deadlines for business schools are right around the corner! Are you still working to hit your target GMAT score? Use the chart below to check the deadlines for the top 25 business schools, and evaluate whether you have enough time to prep and retake the official exam.

Looking for some guidance to maximize your study time? Our upcoming February GMAT Boot Camps are designed to prep you in just two weeks. Be prepared for intensive in-class work paired with hours of one-on-one coaching that will get you ready for the exam quickly, without sacrificing content knowledge.

We’re running a special promotion for our February Boot Camps only. **Get $500 off with code CAMP500**—but hurry, this promotion is only valid this month! There are still a few spots left in our upcoming boot camps (New York City and Live Online). Check out the full schedule and see all that’s included!

School |
Round 3 Deadline |

Harvard University | April 6, 2015 |

Stanford University | April 1, 2015 |

University of Pennsylvania (Wharton) | March 26, 2015 |

University of Chicago (Booth) | April 7, 2015 |

Massachusetts Institute of Technology (Sloan) | N/A |

Northwestern University (Kellogg) | April 1, 2015 |

University of California–Berkeley (Haas) | March 11, 2015 |

Columbia University | April 15, 2015 |

Dartmouth College (Tuck) | April 1, 2015 |

New York University (Stern) | March 15, 2015 |

University of Michigan–Ann Arbor (Ross) | March 23, 2015 |

University of Virginia (Darden) | April 1, 2015 |

Yale University | April 23, 2015 |

Duke University (Fuqua) | March 19, 2015 |

University of Texas–Austin (McCombs) | March 24, 2015 |

University of California–Los Angeles (Anderson) | April 15, 2015 |

Cornell University (Johnson) | March 11, 2015 |

Carnegie Mellon University (Tepper) | March 15, 2015 |

University of North Carolina–Chapel Hill (Kenan-Flager) | March 13, 2015 |

Emory University (Goizueta) | March 13, 2015 |

Indiana University–Bloomington (Kelley) | March 01, 2015 |

Washington University in St. Louis (Olin) | February 15, 2015 (Next: April 1) |

Georgetown University (McDonough) | April 1, 2015 |

University of Notre Dame (Mendoza) | February 23, 2015 |

University of Washington (Foster) | March 15, 2015 |

### Tackling Max/Min Statistics on the GMAT (Part 1)

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?

“(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?

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?

“(A) 10,700

“(B) 10,800

“(C) 10,900

“(D) 11,000

“(E) 11,100”

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* + 0.1*x* = 1.1*x*. The largest district could be 1.1*x* but can’t be any larger than that.

Since you need to maximize the 10 remaining districts, set all 10 districts equal to 1.1*x*. As a result, there are (1.1*x*)(10) = 11*x* 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:

11*x* + *x* = 132,000

12*x* = 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.

### GMAT Sentence Correction: How To Find the Core Sentence (Part 4)

It’s here at last: the fourth and final installment of our series on core sentence structure! I recommend reading all of the installments in order, starting with part 1.

Try out this GMATPrep® problem from the free exams.

* “The greatest road system built in the Americas prior to the arrival of Christopher Columbus was the Incan highway, which, over 2,500 miles long and extending from northern Ecuador through Peru to southern Chile.

“(A) Columbus was the Incan highway, which, over 2,500 miles long and extending

“(B) Columbus was the Incan highway, over 2,500 miles in length, and extended

“(C) Columbus, the Incan highway, which was over 2,500 miles in length and extended

“(D) Columbus, the Incan highway, being over 2,500 miles in length, was extended

“(E) Columbus, the Incan highway, was over 2,500 miles long, extending”

The First Glance in this question is similar to the one from the second problem in the series. Here, the first two answers start with a noun and verb, but the next three insert a comma after the subject. Once again, this is a clue to check the core subject-verb sentence structure.

First, strip down the original sentence:

Here’s the core:

The greatest road system was the Incan highway.

(Technically, *greatest* is a modifier, but I’m leaving it in because it conveys important meaning. We’re not just talking about any road system. We’re talking about the *greatest* one in a certain era.)

The noun at the beginning of the underline, *Columbus*, is not the subject of the sentence but the verb *was* does turn out to be the main verb in the sentence. The First Glance revealed that some answers removed that verb, so check the remaining cores.

“(B) The greatest road system was the Incan highway and extended from Ecuador to Chile.

“(C) The greatest road system.

“(D) The greatest road system was extended from Ecuador to Chile.

“(E) The greatest road system was over 2,500 miles long.”

Answer (C) is a sentence fragment; it doesn’t contain a main verb. The other choices do contain valid core sentences, though answers (B) and (D) have funny meanings. Let’s tackle (B) first.

“(B) The greatest road system was the Incan highway and extended from Ecuador to Chile.

When two parts of a sentence are connected by the word *and*, those two parallel pieces of information are not required to have a direct connection:

Yesterday, I worked for 8 hours and had dinner with my family.

Those things did not happen simultaneously. One did not lead to the other. They are both things that I did yesterday, but other than that, they don’t have anything to do with each other.

In the Columbus sentence, though, it doesn’t make sense for the two pieces of information to be separated in this way. The road system was the greatest system built to that point in time *because* it was so long. The fact that it extended across all of these countries is part of the point. As a result, we don’t want to present these as separate facts that have nothing to do with each other. Eliminate answer (B).

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