The post GMAT Tip of the Week: The Song Remains the Same appeared first on Veritas Prep Blog.

]]>Biggie’s “Hypnotize” samples directly from “La Di Da Di” (originally by Doug E. Fresh – yep, he’s the one who inspired “The Dougie” that Cali Swag District wants to teach you – and Slick Rick). “Biggie Biggie Biggie, can’t you see, sometimes your words just hypnotize me…” was originally “Ricky, Ricky, Ricky…” And right around the same time, Snoop Dogg and 2Pac just redid the entire song just about verbatim, save for a few brand names.

The “East Coast edit” of Chris Brown’s “Loyal”? French Montana starts his verse straight quoting Jay-Z’s “I Just Wanna Love U” (“I’m a pimp by blood, not relation, I don’t chase ’em, I replace ’em…”), which (probably) borrowed the line “I don’t chase ’em I replace ’em” from a Biggie track, which probably got it from something else. And these are just songs we heard on the radio this morning driving to work…

The point? Hip hop is a constant variation on the same themes, one of the greatest recycling centers the world has ever known.

And so is the GMAT.

Good test-takers – like veteran hip hop heads – train themselves to see the familiar within what looks (or sounds) unique. A hip hop fan often says, “Wait, where I have heard that before?” and similarly, a good test-taker sees a unique, challenging problem and says, “Wait, where have I seen that before?”

And just like you might recite a lyric back and forth in your mind trying to determine where you’ve heard it before, on test day you should recite the operative parts of the problem or the rule to jog your memory and to remind yourself that you’ve seen this concept before.

Is it a remainder problem? Flip through the concepts that you’ve seen during your GMAT prep about working with remainders (“the remainder divided by the divisor gives you the decimals; when the numerator is smaller then the denominator the whole numerator is the remainder…”).

Is it a geometry problem? Think of the rules and relationships that showed up on tricky geometry problems you have studied (“I can always draw a diagonal of a rectangle and create a right triangle; I can calculate arc length from an inscribed angle on a circle by doubling the measure of that angle and treating it like a central angle…”).

Is it a problem that asks for a seemingly-incalculable number? Run through the strategies you’ve used to perform estimates or determine strange number properties on similar practice problems in the past.

The GMAT is a lot like hip hop – just when you think they’ve created something incredibly unique and innovative, you dig back into your memory bank (or click to a jazz or funk station) and realize that they’ve basically re-released the same thing a few times a decade, just under a slightly different name or with a slightly different rhythm.

The lesson?

You won’t see anything truly unique on the GMAT. So when you find yourself stumped, act like the old guy at work when you tell him to listen to a new hip hop song: “Oh I’ve heard this before…and actually when I heard it before in the ’90s, my neighbor told me that she had heard it before in the ’80s…” As you study, train yourself to see the similarities in seemingly-unique problems and see though the GMAT’s rampant plagiarism of itself.

The repetitive nature of the GMAT and of hip hop will likely mean that you’re no longer so impressed by Tyga, but you can use that recognition to be much more impressive to Fuqua.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Big Sean Says Your GMAT Score Will Bounce Back appeared first on Veritas Prep Blog.

]]>If you have a car stereo or Pandora account, you’ve undoubtedly heard Big Sean talking about bouncing back this month. “Bounce Back” is a great anthem for anyone hitting a rough patch – at work, in a relationship, after a rough day for your brackets during next week’s NCAA tournament – but this isn’t a self-help, “it’s always darkest before dawn,” feel-good article. Big Sean has some direct insight into the GMAT scoring algorithm with Bounce Back, and if you pay attention, you can leverage Bounce Back (off the album “I Decided” – that’ll be important, too) to game-plan your test day strategy and increase your score.

So, what’s Big Sean’s big insight?

The GMAT scoring (and question delivery) algorithm is designed specifically so that you can “take an L” and bounce back. And if you understand that, you can budget your time and focus appropriately. The test is designed so that just about everybody misses multiple questions – the adaptive system serves you problems that should test your upper threshold of ability, and can also test your lower limit if you’re not careful.

What does that mean? Say you, as Big Sean would say, “take an L” (or a loss) on a question. That’s perfectly fine…everyone does it. The next question should be a bit easier, providing you with a chance to bounce back. The delivery system is designed to use the test’s current estimate of your ability to deliver you questions that will help it refine that estimate, meaning that it’s serving you questions that lie in a difficulty range within a few percentile points of where it thinks you’re scoring.

If you “take an L” on a problem that’s even a bit below your true ability, missing a question or two there is fine as long as it’s an outlier. No one question is a perfect predictor of ability, so any single missed question isn’t that big of a deal…if you bounce back and get another few questions right in and around that range, the system will continue to test your upper threshold of ability and give you chances to prove that the outlier was a fluke.

The problem comes when you don’t bounce back. This doesn’t mean that you have to get the next question right, but it does mean that you can’t afford big rough patches – a run of 3 out of 4 wrong or 4 out of 5 wrong, for example. At that point, the system’s estimate of you has to change (your occasional miss isn’t an outlier anymore) and while you can still bounce back, you now run the risk of running out of problems to prove yourself. As the test serves you questions closer to its new estimate of you, you’re not using the problems to “prove how good you are,” but instead having to spend a few problems proving you’re “not that bad, I promise!”

So, okay. Great advice – “don’t get a lot of problems wrong.” Where’s the real insight? It can be found in the lyrics to “Bounce Back”:

*Everything I do is righteous
Betting on me is the right risk
Even in a ***** crisis…*

During the test you have to manage your time and effort wisely, and that means looking at hard questions and determining whether betting on that question is the right risk. You **will** get questions wrong, but you also control how much you let any one question affect your ability to answer the others correctly. A single question can hurt your chances at the others if you:

- Spend too much time on a problem that you weren’t going to get right, anyway
- Let a problem get in your head and distract you from giving the next one your full attention and confidence

Most test-takers would be comfortable on section pacing if they had something like 3-5 fewer questions to answer, but when they’re faced with the full 37 Quant and 41 Verbal problems they feel the need to rush, and rushing leads to silly mistakes (or just blindly guessing on the last few problems). And when those silly mistakes pile up and become closer to the norm than to the outlier, that’s when your score is in trouble.

You can avoid that spiral by determining when a question is not the right risk! If you recognize in 30-40 seconds (or less) that you’re probably going to take an L, then take that L quickly (put in a guess and move on) and bank the time so that you can guarantee you’ll bounce back. You know you’re taking at least 5 Ls on each section (for most test-takers, even in the 700s that number is probably closer to 10) so let yourself be comfortable with choosing to take 3-4 Ls consciously, and strategically bank the time to ensure that you can thoroughly get right the problems that you know you should get right.

Guessing on the GMAT doesn’t have to be a panic move – when you know that the name of the game is giving yourself the time and patience to bounce back, a guess can summon Big Sean’s album title, “I Decided,” as opposed to “I screwed up.” (And if you need proof that even statistics PhDs who wrote the GMAT scoring algorithm need some coaching with regard to taking the L and bouncing back, watch the last ~90 seconds of this video.)

So, what action items can you take to maximize your opportunity to bounce back?

**Right now:** pay attention to the concepts, question types, and common problem setups that you tend to waste time on and get wrong. Have a plan in mind for test day that “if it’s *this* type of problem and I don’t see a path to the finish line quickly, I’m better off taking the L and making sure I bounce back on the next one.”

Also, as you review those types of problems in your homework and practice tests, look for techniques you can use to guess intelligently. For many, combinatorics with restrictions is one of those categories for which they often cannot see a path to a correct answer. Those problems are easy to guess on, however! Often you can eliminate a choice or two by looking at the number of possibilities that would exist without the restriction (e.g. if Remy and Nicki would just patch up their beef and stand next to each other, there would be 120 ways to arrange the photo, but since they won’t the number has to be less than 120…). And you can also use that total to ask yourself, “Does the restriction take away a lot of possibilities or just a few?” and get a better estimate of the remaining choices.

**On test day:** Give yourself 3-4 “I Decided” guesses and don’t feel bad about them. If your experience tells you that betting your time and energy on a question is not the right risk, take the L and use the extra time to make sure you bounce back.

The GMAT, like life, guarantees that you’ll get knocked down a few times, but what you can control is how you respond. Accept the fact that you’re going to take your fair share of Ls, but if you’re a real one you know how to bounce back.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Evolving Your GMAT Quant Score with Help from The Evolution Of Rap appeared first on Veritas Prep Blog.

]]>The video below (which is absolutely worth a watch during a designated study break) explores the way that rap has evolved from simple rhyme schemes (yada yada yada Bat, yada yada yada Hat, yada yada yada Rat, yada yada yada Cat…) to the more complex “wait did he just say what I thought he said?” inside-out rhyme schemes that make you rewind an Eminem or Kendrick Lamar track because your ears must be playing tricks on you.

And if you don’t have the study break time right now, we’ll summarize. While a standard rhyme might have a one-syllable rhyme at the end of each bar (do you like green eggs and HAM, yes I like them Sam I AM), rappers have continued to evolve to the point where nowadays each bar can contain multiple rhyme schemes. Consider Eminem’s “Lose Yourself”:

*Snap back to reality, oh there goes gravity*

* Oh there goes Rabbit he choked, he’s so mad but he won’t*

* Give up that easy, nope, he won’t have it he knows*

* His whole back’s to these ropes, it don’t matter he’s dope*

* He knows that but he’s broke, he’s so stagnant he knows…*

Where “gravity,” “Rabbit, he,” “mad but he,” “that easy,” “have it he,” “back’s to these,” “matter he’s,” “that but he’s,” and “stagnant, he” all rhyme with one another, the list of goes/goes/choked/so/won’t/knows/whole/ropes/don’t/dope… keeps that hard “O” sound rhyming consistently throughout, too. And that was 15 years ago…since them, Eminem, Kendrick, and others have continued to build elaborate rhyme schemes that reward those listeners who don’t just listen for the simple rhyme at the end of each bar, but pick up the subtle rhyme flows that sometimes don’t come back until a few lines later.

So what does this have to do with your GMAT score?

One of the most common study mistakes that test-takers make is that they study skills as individual, standalone entities, and don’t look for the subtle ways that the GMAT testmaker can layer in those sophisticated Andre-3000-style combinations. Consider an example of an important GMAT skill, the “Difference of Squares” rule that (x + y)(x – y) = x^2 – y^2. A standard (think early 1980s Sugarhill Gang or Grandmaster Flash) GMAT question might test it in a relatively “obvious” way:

*What is the value of (x + y)?*

*(1) x^2 – y^2 = 0*

*(2) x does not equal y*

Here if you factor Statement 1 you’ll get (x + y)(x – y) = 0, and then Statement 2 tells you that it’s not (x – y) that equals zero, so it must be x + y. This Data Sufficiency answer is C, and the test is essentially just rewarding you for knowing the Difference of Squares.

*The GMAT it cares
’bout the Difference of Squares
When there’s squares and subtraction
Put this rule into action*

A slightly more sophisticated question (think late 1980s/early 1990s Rob Bass or Run DMC) won’t so obviously show you the Difference of Squares. It might “hide” that behind a square that few people tend to see as a square, the number 1:

*If y = 2^(16) – 1, the greatest prime factor of y is:*

*(A) Less than 6*

* (B) Between 6 and 10*

* (C) Between 10 and 14*

* (D) Between 14 and 18*

* (E) Greater than 18*

Here, many people don’t recognize 1 as a perfect square, so they don’t see that the setup is 2^(16) – 1^(2), which can be factored as:

(2^8 + 1)(2^8 – 1)

And that 2^8 – 1 can be factored again, since 1 remains 1^2:

(2^8 + 1)(2^4 + 1)(2^4 – 1)

And that ultimately you could do it again with 2^4 – 1 if you wanted, but you should know that 2^4 is 16 so you can now get to work on smaller numbers. 2^8 is 256 and 2^4 is 16, so you have:

257 * 17 * 15

And what really happens now is that you have to factor out 257 to see if you can break it into anything smaller than 17 as a factor (since, if not, you can select “greater than 18”). Since you can’t, you know that 257 must have a prime factor greater than 18 (it turns out that it’s prime) and correctly select E.

The lesson here? This problem directly tests the Difference of Squares (you don’t want to try to calculate 2^16, then subtract 1, then try to factor out that massive number) but it does so more subtly, layering it inside the obvious “prime factor” problem like a rapper might embed a secondary rhyme scheme in the middle of each bar.

But in really hard problems, the testmaker goes full-on Greatest of All Time rapper, testing several things at the same time and rewarding only the really astute for recognizing the game being played. Consider:

*The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?*

*(A) 2*

* (B) 4*

* (C) 16*

* (D) 38*

* (E) 40*

Now here you KNOW you’re dealing with a geometry problem, and it also looks like a word problem given the television backstory. As you start calculating, you’ll know that you have to take the diagonal of each square TV and use that to determine the length of each side, using the 45-45-90 triangle ratio, where the diagonal = x√2. So the length of a side of the smaller TV is 19/√2 and the length of a side of the larger TV is 21/√2.

Then you have to calculate the area, which is the side squared, so the area of the smaller TV is (19/√2)^2 and the area of the larger TV is (21/√2)^2. This is starting to look messy (Who knows the squares for 21 and 19 offhand? And radicals in denominators never look fun…) UNTIL you realize that you have to subtract the two areas. Which means that your calculation is:

(21/√2)^2 – (19/√2)^2

This fits perfectly in the Difference of Squares formula, meaning that you can express x^2 – y^2 as (x + y)(x – y). Doing that, you have:

[(21 + 19)/√2][(21-19)/√2]

Which is really convenient because the math in the numerators is easy and leaves you with:

(40/√2) * (2/√2)

And when you multiply them, the √2 terms in the denominators square out to 2, which factors with the 2 in the numerator of the right-side fraction, and everything simplifies to 40. And then, in classic “oh this guy’s effing GOOD” hip-hop style (like in the Eminem lyric “you’re witnessing a massacre like you’re watching a church gathering take place” and you realize that he’s using “massacre” and “mass occur” – the church gathering taking place – simultaneously), you realize that you should have seen it coming all along. Because when you subtract the area of one square minus the area of another square you’re LITERALLY taking the DIFFERENCE of two SQUARES.

So what’s the point?

Too often people study for the GMAT like they’d listen to 1980s rap. They expect the Difference of Squares to pair nicely at the end of an Algebra-with-Exponents bar, and the Isosceles Right Triangle formula to pair nicely with a Triangle question. They learn skills in distinct silos, memorize their flashcards in nice, tidy sets, and then go into the test and realize that they’re up against an exam that looks a lot more like a 2017 mixtape with layers of rhyme schemes and motives.

You need to be prepared to use skills where they don’t seem to obviously belong, to jot down and rearrange your scratchwork, label your unknowns, etc., looking for how you might reposition the math you’re given to help you bring in a skill or concept that you’ve used countless times, just in totally different contexts. The GMAT testmaker has a much more sophisticated flow than the one you’re likely studying for, so pay attention to that nuance when you study and you’ll have a much better chance of keeping your score 800.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

The post GMAT Tip of the Week: Evolving Your GMAT Quant Score with Help from The Evolution Of Rap appeared first on Veritas Prep Blog.

]]>The post GMAT Tip of the Week: Keep Your GMAT Score Safe from the Bowling Green Massacre appeared first on Veritas Prep Blog.

]]>Whatever Ms. Conway’s intentions (or lack thereof; again we’ll let you decide) with the quote, she is certainly guilty of inadvertently doing one thing: she didn’t likely intend to help you avoid a disaster on the GMAT, but if you’re paying attention she did.

Your GMAT test day does not have to be a Bowling Green Massacre!

Here’s the thing about the Bowling Green Massacre: it never happened. But by now, it’s lodged deeply enough in the psyche of millions of Americans that, to them, it did. And the same thing happens to GMAT test-takers all the time. They think they’ve seen something on the test that isn’t there, and then they act on something that never happened in the first place. And then, sadly, their GMAT hopes and dreams suffer the same fate as those poor souls at Bowling Green (#thoughtsandprayers).

Here’s how it works:

**The Quant Section’s Bowling Green Massacre**

On the Quant section, particularly with Data Sufficiency, your mind will quickly leap to conclusions or jump to use a rule that seems relevant. Consider the example:

*What is the perimeter of isosceles triangle LMN?*

*(1) Side LM = 4*

* (2) Side LN = 4√2*

*A. Statement (1) ALONE is sufficient, but statement (2) alone is insufficient*

* B. Statement (2) ALONE is sufficient, but statement (1) alone is insufficient*

* C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient*

* D. EACH statement ALONE is sufficient*

* E. Statements (1) and (2) TOGETHER are NOT sufficient*

When people see that square root of 2, their minds quickly drift back to all those flash cards they studied – flash cards that include the side ratio for an isosceles right triangle: x, x, x√2. And so they then leap to use that rule, inferring that if one side is 4 and the other is 4√2, the other side must also be 4 to fit the ratio and they can then calculate the perimeter. With both statements together, they figure, they can derive that perimeter and select choice C.

But think about where that side ratio comes from: an isosceles **right** triangle. You’re told in the given information that this triangle is, indeed, isosceles. But you’re never told that it’s a right triangle. Much like the Bowling Green Massacre, “right” never happened. But the mere suggestion of it – the appearance of the √2 term that is directly associated with an isosceles, right triangle – baits approximately half of all test-takers to choose C here instead of the correct E (explanation: “isosceles” means only that two sides match, so the third side could be either 4, matching side LM, or 4√2, matching side LN).

Your mind does this to you often on Data Sufficiency problems: you’ll limit the realm of possible numbers to integers, when that wasn’t defined, or to positive numbers, when that wasn’t defined either. You’ll see symptoms of a rule or concept (like √2 leads to the isosceles right triangle side ratio) and assume that the entire rule is in play. The GMAT preys on your mind’s propensity for creating its own story when in reality, only part of that story really exists.

**The Verbal Section’s Bowling Green Massacre**

This same phenomenon appears on the Verbal section, too – most notably in Critical Reasoning. Much like what many allege that Kellyanne Conway did, your mind wants to ascribe particular significance to events or declarations, and it will often exaggerate on you. Consider the example:

*About two million years ago, lava dammed up a river in western Asia and caused a small lake to form. The lake existed for about half a million years. Bones of an early human ancestor were recently found in the ancient lake-bottom sediments that lie on top of the layer of lava. Therefore, ancestors of modern humans lived in Western Asia between two million and one-and-a-half million years ago.*

*Which one of the following is an assumption required by the argument?*

*A. There were not other lakes in the immediate area before the lava dammed up the river.*

* B. The lake contained fish that the human ancestors could have used for food.*

* C. The lava that lay under the lake-bottom sediments did not contain any human fossil remains.*

* D. The lake was deep enough that a person could drown in it.*

* E. The bones were already in the sediments by the time the lake disappeared.*

The key to most Critical Reasoning problems is finding the conclusion and knowing EXACTLY what the conclusion says – nothing more and nothing less. Here the conclusion is the last sentence, that “ancestors of modern humans lived” in this region at this time. When people answer this problem incorrectly, however, it’s almost always for the same reason. They read the conclusion as “the FIRST/EARLIEST ancestors of modern humans lived…” And in doing so, they choose choice C, which protects against humans having come before the ones related to the bones we have.

“First/earliest” is a classic Bowling Green Massacre – it’s a much more noteworthy event (“scientists have discovered human ancestors” is pretty tame, but “scientists have discovered the FIRST human ancestors” is a big deal) that your brain wants to see. But it’s not actually there! It’s just that, in day to day life, you’d rarely ever read about a run-of-the-mill archaeological discovery; it would only pop up in your social media stream if it were particularly noteworthy, so your mind may very well assume that that notoriety is present even when it’s not.

In order to succeed on the GMAT, you need to become aware of those leaps that your mind likes to take. We’re all susceptible to:

- Assuming that variables represent integers, and that they represent positive numbers
- Seeing the symptoms of a rule and then jumping to apply it
- Applying our own extra superlatives or limits to conclusions

So when you make these mistakes, commit them to memory – they’re not one-off, silly mistakes. Our minds are vulnerable to Bowling Green Massacres, so on test day #staywoke so that your score isn’t among those that are, sadly, massacred.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Taking the Least Amount of Time to Solve “At Least” Probability Problems appeared first on Veritas Prep Blog.

]]>Fortunately, and contrary to popular belief, the GMAT isn’t “pure evil.” Wherever it provides opportunities for less-savvy examinees to waste their time, it also provides a shortcut for those who have put in the study time to learn it or who have the patience to look for the elevator, so to speak, before slogging up the stairs. And one classic example of that comes with the “at least one” type of probability question.

To illustrate, let’s consider an example:

*In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random and at the same time, what is the probability that at least one of the marbles will be yellow?*

*(A) 5/17*

* (B) 12/17*

* (C) 25/81*

* (D) 56/81*

* (E) 4/9*

Here, you can first streamline the process along the lines of one of those “There are two types of people in the world: those who _______ and those who don’t _______” memes. Your goal is to determine whether you get a yellow marble, so you don’t care as much about “blue” and “black”…those can be grouped into “not yellow,” thereby giving you only two groups: 8 yellow marbles and 10 not-yellow marbles. Fewer groups means less ugly math!

But even so, trying to calculate the probability of every sequence that gives you one or two yellow marbles is labor intensive. You could accomplish that “not yellow” goal several ways:

First marble: Yellow; Second: Not Yellow

First: Not Yellow; Second: Yellow

First: Yellow; Second: Yellow

That’s three different math problems each involving fractions and requiring attention to detail. There ought to be an easier way…and there is. When a probability problem asks you for the probability of “at least one,” consider the only situation in which you WOULDN’T get at least one: if you got none. That’s a single calculation, and helpful because if the probability of drawing two marbles is 100% (that’s what the problem says you’re doing), then 100% minus the probability of the unfavorable outcome (no yellow) has to equal the probability of the favorable outcome. So if you determine “the probability of no yellow” and subtract from 1, you’re finished. That means that your problem should actually look like:

PROBABILITY OF NO YELLOW, FIRST DRAW: 10 non-yellow / 18 total

PROBABILITY OF NO YELLOW, SECOND DRAW: 9 remaining non-yellow / 17 remaining total

10/18 * 9/17 reduces to 10/2 * 1/17 = 5/17. Now here’s the only tricky part of using this technique: 5/17 is the probability of what you DON’T want, so you need to subtract that from 1 to get the probability you do want. So the answer then is 12/17, or B.

More important than this problem is the lesson: when you see an “at least one” probability problem, recognize that the probability of “at least one” equals 100% minus the probability of “none.” Since “none” is always a single calculation, you’ll always be able to save time with this technique. Had the question asked about three marbles, the number of favorable sequences for “at least one yellow” would be:

Yellow Yellow Yellow

Yellow Not-Yellow Not-Yellow

Yellow Not-Yellow Yellow

Yellow Yellow Not-Yellow

Not-Yellow Yellow Yellow

…

(And note here – this list is not yet exhaustive, so under time pressure you may very well forget one sequence entirely and then still get the problem wrong even if you’ve done the math right.)

Whereas the probability of No Yellow is much more straightforward: Not-Yellow, Not-Yellow, Not-Yellow would be 10/18 * 9/17 * 8/16 (and look how nicely that last fraction slots in, reducing quickly to 1/2). What would otherwise be a terrifying slog, the “long way” becomes quite quick the shorter way.

So, remember, when you see “at least one” probability on the GMAT, employ the “100% minus probability of none” strategy and you’ll save valuable time on at least one Quant problem on test day.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: 3 Guiding Principles for Exponent Problems appeared first on Veritas Prep Blog.

]]>But as thoroughly and quickly as you know those rules, this exponent-based problem in front of you has you stumped. You know what you need to KNOW, but you’re not quite sure what you need to DO. And that’s an ever-important part about taking the GMAT – it’s necessary to know the core rules, facts, and formulas, but it’s also every bit as important to have action items for how you’ll apply that knowledge to tricky problems.

For exponents, there are three “guiding principles” that you should keep in mind as your action items. Any time you’re stuck on an exponent-based problem, look to do one (or more) of these things:

**1) Find Common Bases**

Most of the exponent rules you know only apply when you’re dealing with two exponents of the same base. When you multiply same-base exponents, you add the exponents; when you divide two same-base exponents, you subtract. And if two exponents of the same base are set equal, then you know that the exponents are equal. But keep in mind – these major rules all require you to be using exponents with the same base! If the GMAT gives you a problem with different bases, you have to find ways to make them common, usually by factoring them into their prime bases.

So for example, you might see a problem that says that:

*2^x * 4^2x = 8^y. Which of the following must be true?*

*(A) 3x = y*

* (B) x = 3y*

* (C) y = (3/5)x*

* (D) x = (3/5)y*

* (E) 2x^2 = y*

In order to apply any rules that you know, you must get the bases in a position where they’ll talk to each other. Since 2, 4, and 8 are all powers of 2, you should factor them all in to base 2, rewriting as:

2^x * (2^2)^2x = (2^3)^y

Which simplifies to:

2^x * 2^4x = 2^3y

Now you can add together the exponents on the left:

2^5x = 2^3y

And since you have the same base set equal with two different exponents, you know that the exponents are equal:

5x = 3y

This means that you can divide both sides by 5 to get x = (3/5)y, making answer choice D correct. But more importantly in a larger context, heed this lesson – when you see an exponent problem with different bases for multiple exponents, try to find ways to get the bases the same, usually by prime-factoring the bases.

**2) Factor to Create Multiplication**

Another important thing about exponents is that they represent recurring multiplication. x^5, for example, is x * x * x * x * x…it’s a lot of x’s multiplied together. Naturally, then, pretty much all exponent rules apply in cases of multiplication, division, or more exponents – you don’t have rules that directly apply to addition or subtraction. For that reason, when you see addition or subtraction in an exponent problem, one of your core instincts should be to factor common terms to create multiplication or division so that you’re in a better position to leverage the rules you know. So, for example, if you’re given the problem:

*2^x + 2^(x + 3) = (6^2)(2^18). What is the value of x?*

*(A) 18*

* (B) 20*

* (C) 21*

* (D) 22*

* (E) 24*

You should see that in order to do anything with the left-hand side of the equation, you’ll need to factor the common 2^x in order to create multiplication and be in a position to divide and cancel terms from the right. Doing so leaves you with:

2^x(1 + 2^3) = (6^2)(2^18)

Here, you can simplify the 1 + 2^3 parenthetical: 2^3 = 8, so that term becomes 9, leaving you with:

9(2^x) = (6^2)(2^18)

And here, you should heed the wisdom from above and find common bases. The 9 on the left is 3^2, and the 6^2 on the right can be broken into 3^2 * 2^2. This gives you:

(3^2)(2^x) = (3^2)(2^2)(2^18)

Now the 3^2 terms will cancel, and you can add the exponents of the base-2 exponents on the right. That means that 2^x = 2^20, so you know that x = 20. And a huge key to solving this one was factoring the addition into multiplication, a crucial exponent-based action item on test day.

**3) Test Small Numbers and Look For Patterns**

Remember: exponents are a way to denote repetitive, recurring multiplication. And when you do the same thing over and over again, you tend to get similar results. So exponents lend themselves well to finding and extrapolating patterns. When in doubt – when a problem involves too much abstraction or too large of numbers for you to get your head around – see what would happen if you replaced the large or abstract terms with smaller ones, and if you find a pattern, then look to extrapolate it. With this in mind, consider the problem:

*What is the tens digit of 11^13?*

*(A) 1*

* (B) 2*

* (C) 3*

* (D) 4*

* (E) 5*

Naturally, calculating 11^13 without a calculator is a fool’s errand, but you can start by taking the first few steps and seeing if you establish a pattern:

11^1 = 11 –> tens digit of 1

11^2 = 121 –> tens digit of 2

11^3 = 1331 –> tens digit of 3

And depending on how much time you have you could continue:

11^4 = 14641 –> tens digit of 4

But generally feel pretty good that you’ve established a recurring pattern: the tens digit increases by 1 each time, so by 11^13 it will be back at 3. So even though you’ll never know exactly what 11^13 is, you can be confident in your answer.

Remember: the GMAT is a test of how well you apply knowledge, not just of how well you can memorize it. So for any concept, don’t just know the rules, but also give yourself action items for what you’ll do when problems get tricky. For exponent problems, you have three guiding principles:

1) Find Common Bases

2) Factor to Create Multiplication

3) Test Small Numbers to Find a Pattern

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>How?

The main feature of the Switch (and the driving factor behind its name) is its flexibility. It can be an in-home gaming system attached to a fixed TV set, but then immediately Switch to a hand-held portable system that allows you to continue your game on the go. Nintendo’s business plan is primarily based on offering flexibility…and on the GMAT, your plan should be to prove to business schools that you can offer the same.

The GMAT, of course, tests algebra skills and critical thinking skills and grammar skills, but beneath the surface it also has a preference for testing flexibility. Many problems will punish those with pure tunnel vision, but reward those who can identify that their first course of action isn’t working and who can then Switch to another plan. This often manifests itself in:

- Math problems that seem to require algebra…but halfway through beg to be back-solved using answer choices.
- Sentence Correction problems that seem to ask you to make a decision about one major difference…but for which the natural choices leave you with clearer-cut errors elsewhere.
- Critical Reasoning answer choices that seem out of scope at first, but reward those who read farther and then see their relevance.
- Data Sufficiency problems for which you’ve made a clear, confident decision on one statement…but then the other statement shows you something you hadn’t considered before and forces you to reconsider.
- The overall concept that if you’re a one-trick pony – you’re a master of plugging in answer choices, for example – you’ll find questions that just won’t reward that strategy and will force you to do something else.

Flexibility matters on the GMAT! As an example, consider the following Data Sufficiency question:

*Is x/y > 3? *

*1) 3x > 9y*

*2) y > 3y*

If you’re like many, you’ll confidently address the algebra in Statement 1, divide both sides by 3 to get x > 3y, and then see that if you divide both sides by y, you can make it look exactly like the question stem: x/y > 3. And you may very well say, “Statement 1 is sufficient!” and confidently move on to Statement 2.

But when you look at Statement 2 – either conceptually or algebraically – something should stand out. For one, there’s no way that it’s sufficient because it doesn’t help you determine anything about x. And secondly, it brings up the point that “y is negative” (algebraically you’d subtract y from both sides to get 0 > 2y, then divide by 2 to get 0 > y). And here’s where, if it hasn’t already, your mind should Switch to “positive/negative number properties” mode. If you weren’t thinking about positive vs. negative properties when you considered Statement 1, this one gives you a chance to Switch your thinking and reconsider – what if y were negative? Algebraically, you’d then have to flip the sign when you divide both sides by y:

3x > 9y : Divide both sides by 3

x > 3y : Now divide both sides by y, but remember that if y is positive you keep the sign (x/y > 3), and if y is negative you flip the sign (x/y < 3).

With this in mind, Statement 1 doesn’t really tell you anything. x/y can be greater than 3 or less than 3, so all Statement 1 does is eliminate that x/y could be exactly 3. Now you have the evidence to Switch your answer. If you initially thought Statement 1 was sufficient, Statement 2 has given you a chance to reassess (thereby demonstrating flexibility in thinking) and realize that it’s not, until you know whether y is negative or positive.

Statement 2 supplies that missing piece, and the answer is thus C. But more important is the lesson – because the GMAT so values mental flexibility, it will often provide you with clues that can help you change your mind if you’re paying attention. So on the GMAT, take a lesson from Nintendo Switch: flexibility is an incredibly marketable skill, so look for clues and opportunities to Switch your line of thinking and save yourself from trap answers.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>It’s no surprise that candidate approval ratings are low for the same reason that far too many GMAT scores are lower than candidates would hope. Why?

People don’t directly answer the question.

This is incredibly common in the debates, where the poor moderators are helpless against the talking points and stump speeches of the candidates. The public then suffers because people cannot get direct answers to the questions that matter. This is also very common on the GMAT, where students will invest the time in critical thought and calculation, and then levy an answer that just doesn’t hit the mark. Consider the example:

*Donald has $520,000 in campaign money available to spend on advertising for the month of October, and his advisers are telling him that he should spend a minimum of $360,000 in the battleground states of Ohio, Florida, Virginia, and North Carolina. If he plans to spend the minimum amount in battleground states to appease his advisers, plus impress his friends by a big ad spend specific to New York City (and then he will skip advertising in the rest of the country), how much money will he have remaining if he wants 20% of his ad spend to take place in New York City?*

*(A) $45,000*

* (B) $52,000*

* (C) $70,000*

* (D) $90,000*

* (E) $104,000*

As people begin to calculate, it’s common to try to determine all of the facets of Donald’s ad spend. If he’s spending only the $360,000 in battleground states plus the 20% he’ll spend in New York City, then $360,000 will represent 80% of his total ad spend. If $360,000 = 0.8(Total), then the total will be $450,000. That means that he’ll spend $90,000 in New York City. Which is answer choice D…but that’s not the question!

The question asked for how much of his campaign money would be left over, so the calculation you need to focus on is the $520,000 he started with minus the $450,000 he spent for a total of $70,000, answer choice C. And in a larger context, you can learn a major lesson from Wharton’s most famous alumnus: it’s not enough for your answer to be related to the question. On the GMAT, you must answer the question directly! So make sure that you:

- Double check which portion of a word problem the question asked for. Don’t be relieved when your algebra spits out “a” number. Make sure it’s “the” number.
- Be careful with Strengthen/Weaken Critical Reasoning problems. A well-written Strengthen problem will likely have a good Weaken answer choice, and vice-versa.
- In algebra problems, make sure to identify the proper variable (or combination of variables if they ask, for example “What is 6x – y?”).
- With Data Sufficiency problems, pay attention to the exact values being asked for. One of the most common mistakes that people make is saying that a statement is insufficient because they’re looking to fill in all variables, when actually it is sufficient to answer the exact combination that the test asked for.

As you watch the debate this weekend, notice (How could you not?) how absurd it is that the candidates just about never directly answer the question…and then vow to not make the same mistake on your GMAT exam.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>In pressure situations, it’s not uncommon for your brain to fail you as you “blank” on a concept you know (or should know). So it’s important to have strategies ready for that moment that very well may come to you. To paraphrase the Morning Joe question to Johnson:

What would you do about “Aleppo?”

Meaning: what would you do if your mind were to go blank on an important GMAT rule or formula?

There are four major strategies that should be in your toolkit for such a situation:

**1) Test Small Numbers**

You should absolutely know formulas like exponent rules or relationships like that between dividend, divisor, and remainder in division, but sometimes your mind just goes blank. In those cases, remember that math rules are logically-derived, not arbitrarily ordained! Math rules will hold for all possible values, so if you’re unsure, test numbers. For example, if you’re forced to solve something like:

*(x^15)(x^9) =*

And you’ve blanked on what to do with exponents, try testing small numbers like (2^2)(2^3). Here, that’s (4)(8) = 32, which is 2^5. So if you’re unsure, “Do I add or multiply the exponents?” you should see from the small example that you definitely don’t multiply, and that your hunch that, “Maybe I add?” works in this case, so you can more confidently make that decision.

Similarly, if a problem asked:

*When integer y is divided by integer z, the quotient is equal to x. Which of the following represents the remainder in terms of x, y, and z?*

*(A) x – yz*

* (B) zy – x*

* (C) y – zx*

* (D) zy – x*

* (E) zx – y*

Many students memorize equations to organize dividend, divisor, quotient, and remainder, but in the fog of war on test day it can even be difficult to remember which element of the division problem is the dividend (it’s the number you start with) and which is the divisor (it’s the one you divide by). So if your mind has blanked on any part of the equation or on which element is which, just test it with small numbers to remind yourself how the concept works:

11 divided by 4 is 2 with a remainder of 3. How do you get to the remainder? You take the 11 you started with and subtract the 8 that you get from taking the divisor of 4 and multiplying it by the quotient of 2. So the answer is y (what you started with) minus zx (the divisor times the quotient), or answer choice C.

Simply put, if you blank on a rule or concept, you can test small numbers to remind yourself how it works.

**2) Use Process of Elimination and Work Backwards From the Answer Choices**

One beautiful thing about the GMAT is that, while in “the real world” if you need to know the Pythagorean Theorem and blank on it, you’re out of luck (well, unless you have a Google-enabled Smartphone in your pocket which you almost certainly do…), on the GMAT you have answer choices as assets. So if your own work stalls in progress, you can look to the answer choices to eliminate options you know for sure you wouldn’t get with that math:

What is x^5 + x^6? You know you don’t add or multiply those exponents, so even if you don’t see to factor out the common x^5, you could eliminate answer choices like x^11 and x^30.

Or you can look to the answer choices to see if they help you determine how you’d apply a rule. For example, if a problem forces you to employ the side ratios for a 45-45-90 triangle and you’ve forgotten them, the presence of some square roots of 2 in the answer choices can help you remember. The square root of 2 is greater than 1, and two sides must match, so if someone spots you “the rule includes a square root of 2” the only thing it can really be is the ratio x : x : x(√2)

Gary Johnson should have been so lucky – had the question been posed as, “What would you do about Aleppo, which is either a DJ on the new Drake album; the epicenter of the Syrian crisis; or a new restaurant in the Garment District?” he would get that question right every single time. Answer choices are your friends…when you blank, consult them!

**3) Think Logically**

Similar to that 45-45-90 “what else could it be?” logic, many times when you blank on a rule, you can work your way to either the rule itself or just to the answer by thinking logically about it. For example, if you end up with math that includes a radical sign in the denominator and can’t quite remember the steps for rationalizing the denominator:

*What is 1/(1 – √2)?*

*(A) √2*

* (B) 1 – √2*

* (C) 1 + √2*

* (D) -1 – √2*

* (E) √2 – 1*

Not all is lost! Sure, algebraically you should multiply the numerator and the denominator by the conjugate (1 + *√*2) but you can also logically work with this one. The numerator is 1, and the denominator is 1 – the square root of 2. You know that *√*2 is between 1 and 2, so what do you know about the denominator? It’s negative, and it’s a fraction (or decimal), so once you’ve taken 1 divided by that, your answer must be a negative number to the left of -1 – only answer choice D would work. So, yeah, you blanked on the steps, but you can still employ logic to back into the answer.

**4) Write Down Everything You Know**

Blanking is particularly troublesome because it’s that moment of panic. You’re trying to retrace your mental steps and the answer is elusive; it’s a moment you’re not in control of at that point. So take control! The more you’re actively working – jotting down other related formulas or facts you know, working on other facets of the diagram or problem and saving that step for last, etc. – the more you’re controlling, or at least actively managing, the situation.

Gary Johnson couldn’t get away with a “Who Wants to Be a Millionaire?” style talk-through-it (“Um, I know it’s not the name of any congressmen; it’s not Zika, it’s not…”) without looking dumb, but no one is going to audit your scratchwork and release it to *Huffington Post*, so you’re free to jot down half-baked thoughts and trial calculations to your heart’s content. Actively manage the situation, and you can work your way through that dreaded “my mind is blank” moment.

So learn from Gary Johnson. No matter how much you’ve prepared for your GMAT, there’s a chance that your mind will go blank on something you know that you know, but just can’t recall in the moment. But you have options, so heed the wisdom above, and let Trump or Clinton handle the gaffes for the day while you move on confidently to the next question.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>What does that mean?

On a timed test like the GMAT, one of the biggest drains on your score can be a combination of undue time and undue energy spent on problems that could be done much simpler. “The long way is the wrong way” as a famous GMAT instructor puts it – those seconds you waste, those extra steps that could lead to error or distraction, they’ll add up over the test and pull your score much lower than you’d like it to be. With that in mind, here are six ways to help you avoid too much labor on test day:

QUANTITATIVE SECTION

**1) Do the math in your order, only when necessary.**

Because the GMAT doesn’t allow a calculator, it heavily rewards candidates who can find efficient ways to avoid the kind of math for which you’d need a calculator. Very frequently this means that the GMAT will tempt you with calculations that you’d ordinarily just plug-and-chug with a calculator, but that can be horribly time-consuming once you start.

For example, a question might require you to take an initial number like 15, then multiply by 51, then divide by 17. On a calculator or in Excel, you’d do exactly that. But on the GMAT, that calculation gets messy. 15*51 = 765 – a calculation that isn’t awful but that will take most people a few steps and maybe 20 seconds. But then you have to do some long division with 17 going into 765. Or do you? If you’re comfortable using factors, multiples, and reducing fractions, you can see those two steps (multiply by 51, divide by 17) as one: multiply by 51/17, and since 51/17 reduces to 3, then you’re really just doing the calculation 15*3, which is easily 45.

The lesson? For one, don’t start doing ugly math until you absolutely know you have to perform that step. Save ugly math for later, because the GMAT is notorious for “rescuing” those who are patient enough to wait for future steps that will simplify the process. And, secondly, get really, really comfortable with factors and divisibility. Quickly recognizing how to break a number into its factors (51 = 3*17; 65 = 5*13; etc.) allows you to streamline calculations and do much of the GMAT math in your head. Getting to that level of comfort may take some labor, but it will save you plenty of workload on test day.

**2) Recognize that “Answers Are Assets.”**

Another way to avoid or shortcut messy math is to look at the answer choices first. Some problems might look like they involve messy algebra, but can be made much easier by plugging in answer choices and doing the simpler arithmetic. Other times, the answer choices will lead themselves to process of elimination, whether because some choices do not have the proper units digit, or are clearly too small.

Still others will provide you with clues as to how you have to attack the math. For example, if the answer choices are something like: A) 0.0024; B) 0.0246; C) 0.246; D) 2.46; E) 24.6, they’re not really testing you on your ability to arrive at the digits 246, but rather on where the decimal point should go (how many times should that number be multiplied/divided by 10). You can then set your sights on the number of decimal places while not stressing other details of the calculation.

Whatever you do, always scan the answer choices first to see if there are easier ways to do the problem than to simply slog through the math. The answers are assets – they’re there for a reason, and often, they’ll provide you with clues that will help you save valuable time.

**3) Question the Question – Know where the game is being played.**

Very often, particularly in Data Sufficiency, the GMAT Testmaker will subtly provide a clue as to what’s really being tested. And those who recognize that can very quickly focus on what matters and not get lost in other elements of the problem.

For example, if the question stem includes an inequality with zero (x > 0 or xy < 0), there’s a very high likelihood that you’re being tested on positive/negative number properties. So, when a statement then says something like “1) x^3 = 1331”, you can hold off on trying to take the cube root of 1331 and simply say, “Odd exponent = positive value, so I know that x is positive,” and see if that helps you answer the question without much calculation. Or if the problem asks for the value of 6x – y, you can say to yourself, “I may not be able to solve for x and y individually, but if not, let’s try to isolate exactly that 6x – y term,” and set up your algebra accordingly so that you’re efficiently working toward that specific goal.

Good test-takers tend to see “where the game is being played” by recognizing what the Testmaker is testing. When you can see that a question is about number properties (and not exact values) or a combination of values (and not the individual values themselves) or a comparison of values (again, not the actual values themselves), you can structure your work to directly attack the question and not fall victim to a slog of unnecessary calculations.

VERBAL SECTION

**4) Focus on keywords in Critical Reasoning conclusions.**

The Verbal section simply *looks* time-consuming because there’s so much to read, so it pays to know where to spend your time and focus. The single most efficient place to spend time (and the most disastrous if you don’t) is in the conclusion of a Strengthen or Weaken question. To your advantage, noticing a crucial detail in a conclusion can tell you exactly “where the game is being played” (Oh, it’s not how much iron, it’s iron PER CALORIE; it’s not that Company X needs to reduce costs overall, it’s that it needs to reduce SHIPPING costs; etc.) and help you quickly search for the answer choices that deal with that particular gap in logic.

On the downside, if you don’t spend time emphasizing the conclusion, you’re in trouble – burying a conclusion-limiting word or phrase (like “per calorie” or “shipping”) in a long paragraph can be like hiding a needle in a haystack. The Testmaker knows that the untrained are likely to miss these details, and have created trap answers (and just the opportunity to waste time re-reading things that don’t really matter) for those who fall in that group.

**5) Scan the Sentence Correction answer choices before you dive into the sentence.**

Much like “Answers are Assets” above, a huge help on Sentence Correction problems is to scan the answer choices quickly to see if you can determine where the game is being played (Are they testing pronouns? Verb tenses?). Simply reading a sentence about a strange topic (old excavation sites, a kind of tree that only grows on the leeward slopes of certain mountains…) and looking for anything that strikes you as odd or ungrammatical, that takes time and saps your focus and energy.

However, the GMAT primarily tests a handful of concepts over and over, so if you recognize what is being tested, you can read proactively and look for the words/phrases that directly control that decision you’re being asked to make. Do different answers have different verb tenses? Look for words that signal time (before, since, etc.). Do they involve different pronouns? Read to identify the noun in question and determine which pronoun it needs. You’re not really being tasked with “editing the sentence” as much as your job is to make the proper decision with the choices they’ve already given you. They’ve already narrowed the scope of items you can edit, so identify that scope before you take out the red marking pen across the whole sentence.

**6) STOP and avoid rereading.**

As the Veritas Prep Reading Comprehension lesson teaches, stop at the end of each paragraph of a reading passage to ask yourself whether you understand Scope, Tone, Organization, and Purpose. The top two time-killers on Reading Comprehension passages/problems are re-reading (you get to the end and realize you don’t really know what you just read) and over-reading (you took several minutes absorbing a lot of details, but now the clock is ticking louder and you haven’t looked at the questions yet).

STOP will help you avoid re-reading (if you weren’t locked in on the first paragraph, you can reread that in 30 seconds and not wait to the end to realize you need to reread the whole thing) and will give you a quick checklist of, “Do I understand just enough to move on?” Details are only important if you’re asked about them, so focus on the major themes (Do you know what the paragraph was about – a quick 5-7 word synopsis is perfect – and why it was written? Good.) and save the details for later.

It may seem ironic that the GMAT is set up to punish hard-workers, but in business, efficiency is everything – the test needs to reward those who work smarter and not just harder, so an effective test day simply cannot be a Labor Day. Use this Labor Day weekend to study effectively so that test day is one on which you prioritize efficiency, not labor.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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