Articles published in How to Study

ADVANCED CRITICAL REASONING, Part II: Deductive Logic

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gmat-advanced-critical-reasoning-2
My last article discussed the difference between inductive and deductive arguments. Today’s article will focus mostly on the rules of deductive arguments. I promise to nerd out on inductive reasoning in later articles.

Here’s a quick quiz on the difference between inductive and deductive logic: //www.thatquiz.org/tq/previewtest?F/Z/J/V/O3UL1355243858

To review: In a deductively “valid” argument, if all the premises are true, the conclusion must also be true, with 100% certainty. Luckily, on the GMAT, we should usually act as if the premises of an argument are true, especially when the question specifies, “the statements above are true.”

Deductive reasoning shows up most often on inference (aka “draw a conclusion”) questions and “mimic the reasoning” questions, but it often appears on other types of questions, and even on reading comprehension!

On inference questions, the correct answer will usually be deductively valid (or very very strong, inductively). An incorrect answer will be deductively invalid, with some significant probability that it could be false.

What follows are most of the formal rules of deductive reasoning (from a stack of logic textbooks I have on my shelf), with examples from the GMAT. For shorthand, I’ll label the arguments with a “P” for premise and a “C” for conclusion:

P) premise
P) premise
C) conclusion

Remember: these are not the same kind of conclusions (opinions) you’ll see on strengthen and weaken questions. Deductive conclusions are deductively “valid” facts that you can derive with 100% certainty from given premises.

EASY STUFF: Simplification/conjunction (“and” statements)

This is kind of a “duh” conclusion, but here goes: If two things are linked with an “and,” then you know each of them exist. Conversely, if two things exist, you can link them with an “and.”

Simplification:

P) A and B
C) Therefore, A

Conjunction:

P) A
P) B
C) Therefore, A and B

P) Bill is tall and was born in Texas.
P) Bill rides a motorcycle.
C) Therefore, Bill was born in Texas (simplification).
C) Therefore, at least one tall person named Bill was born in Texas and rides a motorcycle (conjunction).

CAUTION: Fallacies ahead!!

Don’t confuse “and” with “or.” (More about this later.) More importantly, don’t confuse “and” with causality, condition, or representativeness. Bill’s tallness probably has nothing to do with Texas, so keep an eye out for wrong answers that say, “Bill is tall because he was born in Texas” or “Most people from Texas ride motorcycles.”

MEDIUM STUFF: Disjunctive syllogism (“or” statements)

With “or” statements, if one thing is missing, the other must be true.

Valid conclusions:

P) A or B
P) not B (shorthand: ~B)
C) Therefore, A

P) We will go to the truck rally or to a Shakespeare play
P) We won’t go to the Shakespeare play.
C) Therefore, we will go to the truck rally.

CAUTION: Fallacies ahead!!

Unlike in the real world, “or” statements do not always imply mutual exclusivity, unless the argument explicitly says so. For example, in the above arguments, A and B might both be true; we might go to a play and go to the movies. Yes, really. A wrong answer might say “We went to a play, so we won’t go to the movies.” This error is called “affirming the disjunct.”

Invalid:

P) A or B
P) B
C) Not A

GMAT example:

To see this in action, check out your The Official Guide for GMAT Review 13th Edition, by GMAC®*, question 41. This argument opens with an implied “or” statement:

“Installing scrubbers in smokestacks and switching to cleaner-burning fuel are the two methods available to Northern Power…”

The author here incorrectly assumes that by using one method, Northern Power can’t use both methods at the same time. Question 51 does the same thing; discuss it in the comments below?

TOUGH STUFF: Fun with conditional statements

This is important! Keep a sharp eye out for statements that can be expressed conditionally and practice diagramming them. Look for key words such as “if,” “when,” “only,” and “require.”

I use the symbol “–>” to express an if/then relationship, and a “~” to express the word “not.” Use single letters or abbreviations to stand in for your elements.
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Want a 51 on Quant? Can you answer this problem?

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GMAT-problemSequence problems aren’t incredibly common on the test, but if you’re doing well on the quant section, be prepared to see one. Now, you’ve got a choice: do you want to guess quickly and save time for other, easier topics? Do you want to learn some “test savvy” techniques that will help you with some sequence questions but possibly not all of them? Or do you want to learn how to do these every single time, no matter what?

That isn’t a trick question. Every good business person knows that there’s a point of diminishing returns: if you don’t actually need a 51, then you may study for a lower (but still good!) score and re-allocate your valuable time elsewhere.

Try this GMATPrep® problem from the free test. After, we’ll talk about how to do it in the “textbook” way and in the “back of the envelope” way.

* ”For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by Screen Shot 2014-01-28 at 12.32.37 PM. If T is the sum of the first 10 terms in the sequence, then T is

“(A) greater than 2

“(B) between 1 and 2

“(C) between 1/2 and 1

“(D) between 1/4 and 1/2

“(E) less than 1/4”

First, let’s talk about how to do this thing in the “textbook math” way. If you don’t want to do this the textbook math way, feel free to skip to the second method below.

Textbook Method

If you’ve really studied sequences, then you may recognize the sequence as a particular kind called a Geometric Progression. If not, you would start to find the terms and see whether you can spot a pattern.

Plug in k = 1, 2, 3. What’s going on?

Screen Shot 2014-01-28 at 12.36.33 PM

What’s going on here? Each time, the term gets multiplied by -1/2 in order to get to the next one. When you keep multiplying by the same number in order to get to the next term, then you have a geometric progression.

This next part gets into some serious math. Unless you really just love math, I wouldn’t bother learning this part for the GMAT, because there’s a very good chance you’ll never need to use it. But, if you want to, go for it!

When you have a geometric progression, you can calculate the sum in the following way:

Screen Shot 2014-01-28 at 12.38.03 PM

Next, you’re going to multiply every term in the sum by the common ratio. What’s the common ratio? It’s the constant number that you keep multiplying each term by to get the next one. In this case, you’ve already figured this out: it’s – 1/2.

If you multiply this through all of the terms on both sides of the equation, you’ll get this:

Screen Shot 2014-01-28 at 12.40.36 PM

Does anything look familiar? It’s basically the same list of numbers as in the first sum equation, except it’s missing the first number, 1/2. All of the others are identical!

Subtract this second equation from the first:

Screen Shot 2014-01-28 at 12.41.31 PM

The right-hand side of the equation is always going to be just the first term of the original sum. The rest of the terms on the right-hand side of the two equations are identical, so when you subtract, they become zero and disappear.

Solve for s:

Screen Shot 2014-01-28 at 12.42.07 PM

This value falls between 1/4 and 1/2, so the answer is (D).

Back of the Envelope Method

There is another way to tackle this one. At the same time, this problem is really tricky—so this solution is still not an “easy” solution. Your best choice might be just to guess and move on.

Before you start reading the text, take a First Glance at the whole thing. It’s a problem-solving problem. The answers are… weird. They’re not exact. What does that mean?

Read the problem, but keep that answer weirdness in mind. The first sentence has a crazy sequence. The question asks you to sum up the first 10 terms of this sequence. And the answers aren’t exact… so apparently you don’t need to find the exact sum.

Take a closer look at the form of the answers. Notice anything about them?

They don’t overlap! They cover adjacent ranges. If you can figure out that, for example, the sum is about 3/4, then you know the answer must be (C). In other words, you can actually estimate here—you don’t have to do an exact calculation.

That completely changes the way you can approach this problem! Here’s the sequence:

Screen Shot 2014-01-28 at 12.42.54 PM

According to the problem, the 10 terms are from k = 1 to k = 10. Calculating all 10 of those and then adding them up is way too much work (another clue that there’s got to be a better way to do this one). So what is that better way?

Since you know you can estimate, try to find a pattern. Calculate the first two terms (we had to do this in the first solution, too).

Screen Shot 2014-01-28 at 12.43.57 PM

What’s going on? The first answer is positive and the second one is negative. Why? Ah, because the first part of the calculation is -1 raised to a power. That will just keep switching back and forth between 1 and -1, depending on whether the power is odd or even. It won’t change the size of the final answer, but it will change the sign.

Okay, and what about that second part? it went from 1/2 to 1/4. What will happen next time? Try just that part of the calculation. If k = 3, then just that part will become Screen Shot 2014-01-28 at 12.44.39 PM.

Interesting! So the denominator will keep increasing by a factor of 2: 2, 4, 8, 16 and so on.

Great, now you can write out the 10 numbers!

Screen Shot 2014-01-28 at 12.45.21 PM… ugh. The denominator’s getting pretty big. That means the fraction itself is getting pretty small. Do I need to keep writing these out?

What was the problem asking again?

Right, find the sum of these 10 numbers. Let’s see. The first number in the sequence is 1/2 and the second is -1/4, so the pair adds up to 1/4.

Screen Shot 2014-01-28 at 12.46.11 PM

Right now, the answer would be right between D and E. Does the sum go up or down from here?

The third number will add 1/8, so it goes up:

Screen Shot 2014-01-28 at 12.46.39 PM

But the fourth will subtract 1/16 (don’t forget that every other term is negative!), pulling it back down again:

Screen Shot 2014-01-28 at 12.47.15 PM

Hmm. In the third step, it went up but not enough to get all the way to 1/2. Then, it went down again, but by an even smaller amount, so it didn’t get all the way back down to 1/4.

The fifth step would go up by an even smaller amount (1/32), and then it would go back down again by yet a smaller number (1/64). What can you conclude?

First, the sum is always growing a little bit, because each positive number is a bit bigger than the following negative number. The sum is never going to drop below 1/4, so cross off answer (E).

You keep adding smaller and smaller amounts, though, so if the first jump of 1/8 wasn’t enough to get you up to 1/2, then none of the later, smaller jumps will get you there either, especially because you also keep subtracting small amounts. You’re never going to cross over to 1/2, so the sum has to be between 1/4 and 1/2.

The correct answer is (D).

As I mentioned above, you may decide that you don’t want to do this problem at all. These aren’t that common—many people won’t see one like this on the test. Also, you don’t have to get everything right to get a top score. Just last week, I spoke with a student who outright guessed on 4 quant problems, and she still scored a 51 (the top score).

Key Takeaways for Advanced Sequence Problems

(1) Do you even want to learn how to do these? Don’t listen to your pride. Listen to your practical side. This might not be the best use of your time.

(2) All of these math problems do have a textbook solution method—but you’d have to learn a lot of math that you might never use if you try to learn all of the textbook methods. That’s not a problem if you’re great at math and have a great memory for this stuff. If not…

(3) … then think about alternate methods that can work just as well. Certain clues will indicate when you can estimate on a problem, rather than solving for the “real” number. You may already be familiar with some of these, for instance when you see the word “approximately” in the problem or answer choices that are spread pretty far apart. Now, you’ve got a new clue to add to your list: answers that offer a range of numbers and the different answer ranges don’t overlap.

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

New Year’s Resolution: Get Your GMAT Score! (Part 2)

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gmat-blog-post

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.


How do you study? More importantly, how do you know that the way in which you’re studying is effective—that is, that you’re learning what you need to learn to improve your GMAT score? Read on! Read more

New Year’s Resolution: Get Your GMAT Score! (Part 1)

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gmat-New-year-2014

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.


Whether you’ve been studying for a while or are just getting started, let’s use the New Year as an opportunity to establish or renew your commitment to getting your desired GMAT score. Read more

The 4 Math Strategies Everyone Must Master, part 2

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Math-strategies-gmatLast time, we talked about the first 2 of 4 quant strategies that everyone must master: Test Cases and Choose Smart Numbers.

Today, we’re going to cover the 3rd and 4th strategies. First up, we have Work Backwards. Let’s try a problem first: open up your Official Guide, 13th edition (OG13), and try problem solving #15 on page 192. (Give yourself about 2 minutes.)

I found this one by popping open my copy of OG13 and looking for a certain characteristic that meant I knew I could use the Work Backwards technique. Can you figure out how I knew, with just a quick glance, that this problem qualified for the Work Backwards strategy? (I’ll tell you at the end of the solution.)

For copyright reasons, I can’t reproduce the entire problem, but here’s a summary: John spends 1/2 his money on fruits and vegetables, 1/3 on meat, and 1/10 on treats from the bakery. He also spends $6 on candy. By the time he’s done, he’s spent all his money. The problem asks how much money he started out with in the first place.

Here are the answer choices:

“(A) $60

“(B) $80

“(C) $90

“(D) $120

“(E) $180”

Work Backwards literally means to start with the answers and do all of the math in the reverse order described in the problem. You’re essentially plugging the answers into the problem to see which one works. This strategy is very closely tied to the first two we discussed last time—except, in this instance, you’re not picking your own numbers. Instead, you’re using the numbers given in the answers.

In general, when using this technique, start with answer (B) or (D), your choice. If one looks like an easier number, start there. If (C) looks a lot easier than (B) or (D), start with (C) instead.

This time, the numbers are all equally “hard,” so start with answer (B). Here’s what you’re going to do:

(B) $80

 

F + V (1/2)

M (1/3)

B (1/10)

C $6

Add?

(B) $80

$40

…?

$6

Set up a table to calculate each piece. If John starts with $80, then he spends $40 on fruits and vegetables. He spends… wait a second! $80 doesn’t go into 1/3 in a way that would give a dollar-and-cents amount. It would be $26.66666 repeating forever. This can’t be the right answer!

Interesting. Cross off answer (B), and glance at the other answers. They’re all divisible by 3, so we can’t cross off any others for this same reason.

Try answer (D) next.

 

F + V (1/2)

M (1/3)

B (1/10)

C $6

Add to?

(B) $80

$40

…?

$6

?

(D) $120

$60

$40

$12

$6

$118

 

In order for (D) to be the correct answer, the individual calculations would have to add back up to $120, but they don’t. They add up to $118.

Okay, so (D) isn’t the correct answer either. Now what? Think about what you know so far. Answer (D) didn’t work, but the calculations also fell short—$118 wasn’t large enough to reach the starting point. As a result, try a smaller starting point next.

 

F + V (1/2)

M (1/3)

B (1/10)

C $6

Add?

(B) $80

$40

…?

$6

?

(D) $120

$60

$40

$12

$6

$118

(C) $90

$45

$30

$9

$6

$90

 

It’s a match! The correct answer is (C).

Now, why would you want to do the problem this way, instead of the “straightforward,” normal math way? The textbook math solution on this one involves finding common denominators for three fractions—somewhat annoying but not horribly so. If you dislike manipulating fractions, or know that you’re more likely to make mistakes with that kind of math, then you may prefer to work backwards.

Note, though, that the above problem is a lower-numbered problem. On harder problems, this Work Backwards technique can become far easier than the textbook math. Try PS #203 in OG13. I would far rather Work Backwards on this problem than do the textbook math!

So, have you figured out how to tell, at a glance, that a problem might qualify for this strategy?

It has to do with the form of the answer choices. First, they need to be numeric. Second, the numbers should be what we consider “easy” numbers. These could be integers similar to the ones we saw in the above two problems. They could also be smaller “easy” fractions, such as 1/2, 1/3, 3/2, and so on.

Further, the question should ask about a single variable or unknown. If it asks for x, or for the amount of money that John had to start, then Work Backwards may be a great solution technique. If, on the other hand, the problem asks for xy, or some other combination of unknowns, then the technique may not work as well.

(Drumroll, please) We’re now up to our fourth, and final, Quant Strategy that Everyone Must Master. Any guesses as to what it is? Try this GMATPrep© problem.

 

geometry

“In the figure above, the radius of the circle with center O is 1 and BC = 1. What is the area of triangular region ABC?

Screen Shot 2013-12-29 at 3.26.36 PM

If the radius is 1, then the bottom line (the hypotenuse) of the triangle is 2. If you drop a line from point B to that bottom line, or base, you’ll have a height and can calculate the area of the triangle, since A = (1/2)bh.

You don’t know what that height is, yet, but you do know that it’s smaller than the length of BC. If BC were the height of the triangle, then the area would be A = (1/2)(2)(1) = 1. Because the height is smaller than BC, the area has to be smaller than 1. Eliminate answers (C), (D), and (E).

Now, decide whether you want to go through the effort of figuring out that height, so that you can calculate the precise area, or whether you’re fine with guessing between 2 answer choices. (Remember, unless you’re going for a top score on quant, you only have to answer about 60% of the questions correctly, so a 50/50 guess with about 30 seconds’ worth of work may be your best strategic move at this point on the test!)

The technique we just used to narrow down the answers is one I’m sure you’ve used before: Estimation. Everybody already knows to estimate when the problem asks you for an approximate answer. When else can (and should) you estimate?

Glance at the answers. Notice anything? They can be divided into 3 “categories” of numbers: less than 1, 1, and greater than 1.

Whenever you have a division like this (greater or less than 1, positive or negative, really big vs. really small), then you can estimate to get rid of some answers. In many cases, you can get rid of 3 and sometimes even all 4 wrong answers. Given the annoyingly complicated math that sometimes needs to take place in order to get to the final answer, your best decision just might be to narrow down to 2 answers quickly and then guess.

Want to know how to get to the actual answer for this problem, which is (B)? Take a look at the full solution here.

The 4 Quant Strategies Everyone Must Master

Here’s a summary of our four strategies.

(1) Test Cases.

–      Especially useful on Data Sufficiency with variables / unknowns. Pick numbers that fit the constraints given and test the statement. That will give you a particular answer, either a value (on Value DS) or a yes or no (on Yes/No DS). Then test another case, choosing numbers that differ from the first set in a mathematically appropriate way (e.g., positive vs. negative, odd vs. even, integer vs. fraction). If you get an “always” answer (you keep getting the same value or you get always yes or always no), then the statement is sufficient. If you find a different answer (a different value, or a yes plus a no), then that statement is not sufficient.

–      Also useful on “theory” Problem Solving questions, particularly ones that ask what must be true or could be true. Test the answers using your own real numbers and cross off any answers that don’t work with the given constraints. Keep testing, using different sets of numbers, till you have only one answer left (or you think you’ve spent too much time).

(2) Choose Smart Numbers.

–      Used on Problem Solving questions that don’t require you to find something that must or could be true. In this case, you need to select just one set of numbers to work through the math in the problem, then pick the one answer that works.

–      Look for variable expressions (no equals or inequalities signs) in the answer choices. Will also work with fraction or percent answers.

(3) Work Backwards.

–      Used on Problem Solving questions with numerical answers. Most useful when the answers are “easy”—small integers, easy fractions, and so on—and the problem asks for a single variable. Instead of selecting your own numbers to try in the problem, use the given answer choices.

–      Start with answer (B) or (D). If a choice doesn’t work, cross it off but examine the math to see whether you should try a larger or smaller choice next.

(4) Estimate.

–      You’re likely already doing this whenever the problem actually asks you to find an approximate answer, but look for more opportunities to save yourself time and mental energy. When the answers are numerical and either very far apart or split across a “divide” (e.g., greater or less than 0, greater or less than 1), you can often estimate to get rid of 2 or 3 answers, sometimes even all 4 wrong answers.

The biggest takeaway here is very simple: these strategies are just as valid as any textbook math strategies you know, and they also require just as much practice as those textbook strategies. Make these techniques a part of your practice: master how and when to use them, and you will be well on your way to mastering the Quant portion of the GMAT!

Read The 4 Math Strategies Everyone Must Master, Part 1.

The 4 Math Strategies Everyone Must Master, Part 1

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We need to know a lot of different facts, rules, formulas, and techniques for the Quant portion of the test, but there are 4 math strategies that can be used over and over again, across any type of math—algebra, geometry, word problems, and so on.

Do you know what they are?

Try this GMATPrep® problem and then we’ll talk about the first of the 4 math strategies.

*If mv < pv < 0, is v > 0?

(1) m < p

(2) m < 0

All set? Read more

Turn Up the Volume & Get Ready to Study with Manhattan Prep

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Music can do a lot for us, but the word is still out on whether it can enhance our ability to stay focused and sharpen our memories during long study sessions. On the one hand, we have a report from the University of Toronto suggesting that fast and loud background music can hinder our performance on reading comprehension. On the other, there’s the recentMusic to help you study GMAT research from the digital music service, Spotify, and Clinical Psychologist Dr. Emma Gray, which proclaims that pop hits from artists like Justin Timberlake, Katy Perry, and Miley Cyrus can actually enhance our cognitive abilities.

“Music has a positive effect on the mind, and listening to the right type of music can actually improve studying and learning,” says Dr. Gray. She even suggests that students who listen to music while studying can perform better than those who do not.

We also cannot leave out the so-called “Mozart Effect,” which alleges that listening to classical music provides short-term enhancement of mental tasks, like memorization. We’ve heard students swear by this tactic, while others say that silence is golden.
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GMAT INTERACT™ for Integrated Reasoning

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gmat-integrated-reasoning-study-logoINTERACT FOR IR - Available on iPadWe have some exciting news for you today! We have launched GMAT INTERACT™ for Integrated Reasoning, a truly interactive, video-based digital learning platform that engages you in all facets of learning.

INTERACT is our dynamic digital learning platform, and it’s unlike anything you’ve used to study online. It’s designed to engage your whole brain, keeping the student-teacher connection at the core of every lesson. It’s been called “the best self study method out right now.” Our full GMAT INTERACT program will be launching in 2014, but we’re bringing you all five IR lessons now, for free, so you can kick off your studies.

INTERACT prepares you for the newest section of the GMAT, Integrated Reasoning, which is the most significant overhaul of the GMAT in its 60 year history. The feature component of INTERACT for IR is an expert, on-screen instructor who engages with you as if you were actually receiving private tutoring. The INTERACT program, unlike simple video tutorials, actually receives answers from you and responds to them.

INTERACT has been a two year process of technological innovation, in which Manhattan Prep designers, coders, instructors, and videographers meticulously worked together to create the most interactive student-teacher focused experience available online.

Happy studying: //www.manhattanprep.com/gmat/INTERACT/

Be the Tiger Woods of Testing: Expert Performance and Deliberate Practice

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Consistently and overwhelmingly, the evidence showed that experts are always made, not born. (“The Making of an Expert” by K. Anders Ericsson, Michael J. Prietula, and Edward T. Cokely, Harvard Business Review, July-August 2007)

gmat deliberate practiceStandardized test-taking is a skill–like winning a chess game, swinging a golf club, or playing a Bach concerto. And to master a skill, you need high-quality practice. Of course, the more content you know the better, but no matter how much you study for the GMAT, you won’t improve without practice. (I tried reading a book about snowboarding before my first time on the slopes, with predictably laughable results.) According to the scientific research, the most efficient and most effective kind of practice-the way Tiger Woods become the golfer he is today–is called “Deliberate Practice.”

If you spend time reading motivational blogs such as LifeHacker you’ll see many articles about “Deliberate Practice.” You may have even heard of whole books–Talent is Overrated by Geoffrey Colvin or Outliers by Malcolm Gladwell–about exceptional individuals such as Bobby Fischer and Tiger Woods. All those blogs, as well as Colvin and Gladwell, base their ideas on the research of K. Anders Ericsson, a Professor of Psychology at Florida State University and probably the world’s number-one expert on expertise. His good-news thesis can be summed up as follows:

New research shows that outstanding performance is the product of years of deliberate practice and coaching, not of any innate talent or skill. (Ericsson et al., “The Making of an Expert”)

First of all, relax. You may have heard about Ericsson’s 10,000 hour rule. Apparently, it takes about 10 years and 10,000 hours of “deliberate practice” to achieve true mastery. Yes, Tiger Woods, Bobby Fischer, Mozart, and other one-in-a-million people needed 10,000 hours to get to where they are. Luckily, the GMAT is much less difficult to master than golf, chess, or composition. Also, you’re not looking to be one in a million–at best 1 in 100 (a score of 760-800)–so you don’t need 10,000 hours. Maybe a few hundred hours, depending on how much you want to improve.

But what is “Deliberate Practice?”  And how do you apply it to the GMAT? At the end of this article, I’ve given you a few links, but to save you time, I’ve pulled my favorite Ericsson quotes and applied them to the GMAT:

1) Get motivated.

The most cited condition concerns the subjects’ motivation to attend to the task and exert effort to improve their performance. (“The Role of Deliberate Practice in the Acquisition of Expert Performance” by K. Anders Ericsson, Ralf Th. Krampe, and Clemens Tesch-Romer. Psychological Review. 1993, Vol. 100. No. 3)

Moving outside your traditional comfort zone of achievement requires substantial motivation and sacrifice, but it’s a necessary discipline. (Ericsson et al., “The Making of an Expert”)

If you’re reading this, you want a higher GMAT score. You’re already motivated. If you need more motivation, research schools. Take a diagnostic test and see how far you are from your dream school’s median. After that, the best way to get motivated is to sign up for the real GMAT a few months from now. (How many people don’t lose weight until they schedule the wedding or high school reunion?) Read more

Test your Critical Reasoning Skills: Are Top GMAT Scorers Less Ethical?

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Some interesting —and alarming—articles have been making the rounds lately, following on the heels of an academic study published by professors at the University of Akron and Cleveland State University. The more reputable articles report such sweeping conclusions that I actually wondered whether the journalists got it wrong, so I went to the source (I can link only to the abstract here, but I did read the full study).

When I read the study’s methodology, I knew I had my next article topic. We’re going to test our Critical Reasoning (CR) skills on an actual academic study! You might have to do something similar in business school (admittedly with a business case, not an academic study), so let’s test your b-school readiness now!gmat correlation causation

(Note: I refer to the “more reputable articles” because some blogs have picked this up and publishing under headlines such as “Is the GMAT the root of all evil?” As much as you may hate studying for this test, I think we can agree that this characterization is a bit over the top. : ) )

Correlation vs. Causation

We need to define a couple of terms first. You may already have learned about correlation and causation in your CR studies; here’s a refresher.

Correlation: two phenomena tend to occur or appear at the same time or in conjunction with one another

Causation: one phenomenon causes another phenomenon

Correlation does not imply causation. One of two correlated phenomena could cause the other but those two things could also have absolutely no causation between them. Alternatively, the two things could both be caused by a third thing. The two things could even cause each other! (Predator-prey dynamics are an example of this kind of two-way dependency.)

For example, have you ever noticed how, when the ground is wet, people often seem to be carrying around umbrellas? Those two phenomena are correlated. Which one causes the other? Read more