# GMAT Tip of the Week: Trick or Treat

One of the most dreaded things about the GMAT is the time-honored “Testmaker Trick” – the device that the GMAT question author uses to sucker you into a trap answer on a question. You’ve done all the math right, but forgot to consider negative numbers or submitted the answer for x when the question really asks for y. The “Testmaker Tricks” are enough to make you resent the test and to see it in a derogatory light. This is a grad school test, not Simon Says! Why should it matter that Simon didn’t say “positive”?

But as we head into Halloween weekend, it’s an appropriate time for you to think back to the phrase that earned you pounds and pounds of candy (and maybe tons if you followed Jim Harbaugh’s double-costume strategy): Trick or Treat.

In a GMAT context, that means that on these challenging questions, what tricks one examinee is the “treat” or reward for those who buy into the critical thinking mindset that the GMAT is set up to reward. The GMAT testmakers themselves are defensive about the idea of the “trap” answer, preferring to see it as a reward system; the intent isn’t to “trick” people as much as it is to “treat” higher-order thinking and critical reasoning. Consider the Data Sufficiency example:

Is x > 3z?

(1) x/z > 3

(2) z > 0

Here the “trick” that the testmaker employs is that of negative numbers. Many people will say that Statement 1 is sufficient (just multiply both sides by z and Statement 1 directly answers the questions, x > 3z), but it’s important to remember that z could be negative, and if it were negative you’d have to flip the sign, as you do in an inequality problem when you multiply or divide by a negative. In that case x < 3z and the answer is an emphatic no.

Now, those test takers who lament the trick after getting it wrong are somewhat justified in their complaint that “you forgot about negatives!” is a pretty cheap trick. But that’s not the entire question: Statement 2 exists, too, and it’s a total throwaway when you consider it alone. Why is it there? It’s there to “treat” those who are able to leverage that hint: why would it matter if z is greater than 0? That statement provides a very important clue as to how you should have been thinking when you looked at Statement 1.

If your initial read of Statement 1 – under timed pressure in the middle of a test, mind you – had you doing that quick algebra and making the mistake of saying that it’s sufficient, that’s understandable. But if you blew right past the clear hint in the second statement, you missed a very important opportunity to seize the treat. To some degree this problem is about the math, but the GMAT often adds that larger degree of leveraging hints – after all, much of business success comes down to your ability to find an asset that others have overlooked, or to get more value out of an asset than anyone else could.

So as you study for the GMAT, keep that Halloween spirit close by. When you miss a problem because of a dirty “trick,” take a second to also go back and see if you missed a potential treat – a reward that the GMAT was dangling just out of reach so that only the most critical thinkers could find it and take advantage. GMAT problems aren’t all ghosts, goblins, and ghouls out to frighten and trick you; often they include very friendly pieces of information just disguised or camouflaged enough that you have to train yourself to spot the treat.

By Brian Galvin.

# How to Solve Tough GMAT Quant Problems by Blending Strategies

I wrote a post a few weeks ago in which I discussed the importance of blending strategies on certain questions. It’s a mistake to pigeonhole a complex problem as one in which a single tool will be most effective. By test day you will have cultivated a veritable Swiss army knife of strategies and you want to be able to switch from one to another seamlessly.

This philosophy came to mind the other day when a student sent me the following official problem:

For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was \$10 and the price of a student ticket was \$6. If on one day 3 times as man regular admissions tickets were sold as student tickets, was the total revenue from ticket sales that day?

A) 24,960

B) 25,920

C) 28,080

D) 28,500

E) 29,160

Oh boy. There’s a lot going on here. So let’s start by simply finding the total number of tickets sold. We know that every 5 minutes, 30 tickets are sold. We know that there are twelve 5-minute increments each hour, so 12*30 = 360 tickets are sold each hour. We see that the museum will be open for a total of 9 hours, so a total of 9*360 = 3240 tickets are sold during that time.

We’ve got two different kinds of tickets – general and student. The general tickets were \$10 and the student tickets were \$6. And we know that 3 times as many general tickets were sold as student tickets. So the tickets were overwhelmingly for general admission. If they were all for general admissions tickets, we know that the revenue would have been 3240*10 = 32,400. Because 25% of the tickets were sold for \$6, we know that the correct answer will be a bit below this value. If we were short on time, E would be a pretty reasonable guess.

But say we’ve achieved a level of mastery where we don’t need to guess. Hopefully, you recognized that if the ratio of general tickets to student tickets is 3:1, we’re dealing with a kind of weighted average, meaning we can use a number line to find the average overall ticket price, which will be much closer to \$10 than to \$6. So we know the average price is greater than \$8, as this would be the average price if the same number of both kinds of tickets were sold. What about \$9? On the number line, we’ll have the following: 6——–9—-10.

9 is three units away from 6 and one unit away from 10, thus yielding our desired 3:1 ratio. Now we know that the average price is \$9 per ticket.

So all we have to do is calculate 3240 * 9, as 3240 tickets were sold for an average of \$9 each, and we have our answer. That math isn’t too bad, but we can incorporate a couple more useful strategies to save some time. We know that 3000*9 = 27,000, so clearly 3240*9 is greater than 27,000. Now we can eliminate A and B from contention.  Next, we can see that going from right to left, the first non-zero digit of 3240*9 will be 6, as 4*9 = 36. Among C, D, and E, the only answer choice that has a 6 in the tens place is E, which is our answer.

Takeaway: In a single question, we ended up doing a bit of estimation, using the answer choices, employing some rudimentary logic, and using the number line to simplify a weighted average. Just as important as what we did do, is what we avoided doing – a lot of grinding calculation.

We cannot emphasize this enough: the Quant section is not a math test. It’s an opportunity to demonstrate fluid thinking under pressure. So when you’re doing practice questions, work on employing every tool in your Swiss army knife of strategies. By the day of the test, the more fluidly you can switch from one tool to another, the better you’ll be able to handle even the most challenging problems.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

As a social media user, you’re probably very away that today – October 21, 2015 – is “The Future,” the day from Back to the Future II when Marty McFly and Doc Brown (along with a sleeping Jennifer) visit Hill Valley 30 years in the future. And while we don’t yet have hoverboards and while the bold prediction that the Cubs will have just won the World Series seems to be slipping away, the Back to the Future trilogy does offer some incredibly valuable GMAT lessons. How can Marty McFly help you better understand the GMAT and increase your score?

1) The Space-Time Continuum

Throughout the Back to the Future series, Doc Brown was keenly aware of the impacts that any slight alteration to the past would have on the future (as it turns out, stopping your parents from meeting or allowing the scores of all future sporting events to fall into the hands of your family’s mortal enemy could have disastrous results!). The GMAT works on a similar premise: because the GMAT is adaptive, each question impacts the future questions you will see – the events are connected and sequential. Which means:

A) You can’t go back and change your answers. That would violate the “Space-Time Continuum” nature of the GMAT (changing #5 would mean that questions 6-37 would all be different, so it’s just not an option). And THAT means that you have to make good decisions in real-time – you need to double-check for careless errors before you submit, because if you realize later that you blew it, that question is gone.

B) You can’t afford a disastrous start. It’s not that the first 10 questions matter exponentially more (as the old myth goes), but they are slightly more important if only for this reason: a strong early performance means that you’re seeing harder questions once you’re in your groove, and a poor early performance means that you’re seeing easier questions and have a much lower margin for error. Throughout each section you’ll make a few mistakes and you’ll hit a lucky guess or two.

If you’ve done well and avoided careless mistakes early, then your mistakes and lucky guesses will be on harder questions. If you haven’t, then those mistakes come on easier questions and pull down your score all the more. It *is* possible to recover from a poor start…it just requires you to be a lot closer to perfect and that can be hard to do on test day. Please note: you don’t need to get all 10 right to consider it a good start!  6 or 7 will probably put you on a track you’re happy with; the key is to just make sure you’re not making too many silly mistakes early and missing the questions that you should get right.

2) Save the Clock Tower!

Back to the Future taught a generation the importance of timeline, and that’s critical on the GMAT. You need to be mindful of time and ensure that you have enough to finish each section. Just like in the movies, where mismanagement of time and unforeseen events created precarious situations (would Doc get the wire connected before lightning struck? Would Marty get to that point at the proper time? Would Doc reach Clara before the train tumbled off the cliff?), the GMAT offers you plenty of opportunities to waste time and get off schedule (and maybe your score falls off a cliff, or you’re the one stuck in the past…an era when master’s degrees were far from the norm).

You need to conserve time on the test so that you don’t find a catastrophe waiting at the end. Which means that sometimes you have to let a hard problem go so that it doesn’t suck up several minutes of your time (even if the hard problem seems to be calling you “chicken”!). Like Marty should have done in most time-travel situations, have a plan for how you’ll address events in a timely fashion and stick to it. If you want to have 53 minutes left after 10 questions and you have 51, know that you’ll probably have to guess soon to get back on track.

1985 was easy for Marty, like a 400-500 level GMAT problem. If he needed to quickly get from one place to another, he’d hop on his skateboard and grab the back of a truck. But 1955 and 2015 were quite different – there weren’t conventional skateboards for him to use, so he had to improvise either by breaking a scooter in two or learning how to handle a hoverboard.

The GMAT is similar: the tools you’ll use to solve problems (find skateboard, let a Tannen chase you, veer off at the last second leaving him to crash into a pile of manure) are extremely similar, but just different enough that it may not be obvious what to do at first. Your job as you study is to learn how to look for that “skateboard.”

On exponent problems, for example, the key is almost always getting the given information to a point where you can perform the rules you know. And since those rules are almost always requiring you to deal with exponents with the same base and that the terms are being multiplied or divided, your “finding the skateboard” process usually involves factoring non-prime bases into prime factors and factoring addition and subtraction into multiplication. Much like Marty McFly in a new decade, you’ll find yourself seeing slightly-familiar, but yet totally different situations on the test – your job is to focus more on the similarity and seek out a couple steps to get it to where the rest is rote.

4) Be a Man (or Woman) of Action

In the original Back to the Future, you saw how the entire future changed with just one action: the ever analytical and incredibly intelligent George McFly just wasn’t a confident or action-oriented man, and so despite Marty’s best efforts to talk him up to Lorraine and to get him to be a bit more debonair, the McFly family future was fading quickly. Until…George had the opportunity to stop analyzing and just “do,” telling Biff to “get your damn hands off” Lorraine and ultimately punching Biff in the mouth. From that point on, the George-and-Lorraine romance was on (again?) and the future was just a matter of density. I mean…destiny.

If you’re reading a blog post about the GMAT you’re certainly not the type that Principal Strickland would call a slacker, but there’s a good likelihood that you’ll perform on test day like the “old” George McFly: intelligent and capable, but timid and over-analytical. Particularly with the timed nature of the GMAT, you often just have to go with an instinct and try it out, whether that means writing down an equation and then double checking that you like your math (as opposed to reading the question again and again) or testing your theory that you’re allowed to cross-multiply there (test it with small numbers and see if you get the answer you should).

The biggest mistake that the truly-capable make on the GMAT is one of paralysis by analysis; they’re afraid to put pen to paper to “try something” and then they become acutely aware of the time ticking past them and panic all the more. Avoid that trap! Be willing to try, to take action, and you’ll find that – like the owner of  DeLorean time machine – you have plenty of time.

On this 30th anniversary of Marty’s journey to the future, plan for your future 30 years down the road. The way you study for the GMAT, the way you manage your time and confidence on the test – they could have a major impact on what your future looks like. Heed the lessons that Doc and Marty taught you, and you could leave the test center saying, “Roads? Where I’m going, we don’t need roads,” of course because most elite b-school campuses are all about sidewalks.

By Brian Galvin.

# GMAT Tip of the Week: Your GMAT Verbal (Donald) Trump Card

The general consensus coming out of this week’s Democratic debate for the 2016 U.S. Presidency was this: the Democrats were quick to defend and agree with each other, particularly in contrast to the recent Republican debates in which the candidates were much more apt to attack each other.

The Democrats discussed, but the Republicans DEBATED, fiercely and critically. And – putting politics aside – one of the main issues on which those Republican candidates have attacked each other is “who is the more successful CEO/entrepreneur?” (And the answer to that? Likely Wharton’s finest: Donald “You’re Fired” Trump.)

So as you watch the political debates in between GMAT study sessions, keep this in mind: on the GMAT verbal section, you want to think more like a Republican candidate, and if possible you want to think like The Donald. Trump thinking is your Trump card: on GMAT verbal, you should attack, not defend.

Why?

Because incorrect answers are very easy to defend if that’s your mindset. They’re wrong because of a small (but significant) technicality, but to the “I see the good in all answer choices” eye, they’ll often look correct. You want to be in attack mode, critically eliminating answer choices and enjoying the process of doing so. Consider an example:

From 1998 to 2008, the amount of oil exported from the nation of Livonia increased by nearly 20% as the world’s demand soared. Yet over the same period, Livonia lost over 8,000 jobs in oil drilling and refinement, representing a 25% increase in the nation’s unemployment rate.

Which of the following, if true, would best explain the discrepancy outlined above?

A) Because of a slumping local economy, Livonia also lost 5,000 service jobs and 7,500 manufacturing jobs.

B) Several other countries in the region reported similar percentages of jobs lost in the oil industry over the same period.

C) Because of Livonia’s overvalued currency, most of the nation’s crude oil is now being refined after it has been exported.

D) Technological advancements in oil drilling techniques have allowed for a greater percentage of the world’s oil to be obtained from underneath the ocean floor.

E) Many former oil employees have found more lucrative work in the Livonia’s burgeoning precious metals mining industry.

The paradox/discrepancy here is that oil exports are up, but that jobs in oil drilling and refinement are down. What’s a Wharton-bound Trump to do here? Donald certainly wouldn’t overlook the word “Critical” in “Critical Reasoning.” Almost immediately, he’d be attacking the two-part job loss – it’s not that “oil jobs” are down, it’s that oil jobs in “drilling AND refinement” are down. Divide and conquer, he’d think, one of those items (either drilling or refinement) is bound to be a “lightweight” ready to be attacked.

Choice A is something that you could talk yourself into. “Hey, the economy overall is down, so it only makes sense that oil jobs would be down, too.” But think critically – you ALREADY know that the oil sector is not down. Oil exports are up 20% and global demand is soaring, so these oil jobs should be different. Critical thinking shows you that the general economy and this particular segment are on different tracks. Choice A does not explain the discrepancy.

Choice B is similar: if you’re looking for a reason to make it right, you might think, “See, it’s just part of what’s going on in the world.” But again, be critical. This is a bad answer, because it overlooks information you already have. Livonia’s oil exports are up, so absent a major reason that those exports are occurring without human labor, we don’t have a sound explanation.

Choice C hits on Trump’s “divide and conquer” attack strategy outlined above: if a conclusion to a Critical Reasoning problem includes the word “AND” there’s a very high likelihood that one of the two portions is the weak link. So fixate on that “and” and try to find which is the lightweight. Here you see that the oil is being exported from Livonia, but no longer being REFINED there. Those are the jobs that are leaving the country, and that explains why exports could be up with employment going down.

Choice D is tempting (statistically the most popular incorrect answer choice to this problem, with Trump-like polling numbers in the ~25% range). Why? Because you’re conditioned to think, “Oh, they’re losing jobs to technology.” So if you’re looking to find a correct answer without much critical thought and effort, this one shines like a beacon. But get more critical on the second half of the sentence: it’s not that technology makes it easier to obtain oil without human labor, it’s that technology is allowing for more drilling from the ocean. But that’s irrelevant, because, again, Livonia’s exports are up! So whether it’s Livonia getting that seafloor oil or other countries doing so, the fact remains that with oil exports up, you’d think that Livonia would have more jobs in oil, and this answer doesn’t explain why that’s not the case.

Here it pays to be critical all the way through the sentence: just because the first few words match what you think you might want to hear, that doesn’t mean that the entire statement is true. Think of this in Trump terms: Megyn Kelly might start a sentence with, “Mr. Trump, you’re arguably the most successful businessman of your generation,” (and you know Trump will love that) but if she follows that with, “But many would argue that your success was largely a result of your father’s money and that your manipulation of bankruptcy laws is unbefitting of an American president,” you know he’d be in attack mode immediately thereafter. Don’t fall in love with the first few words of an answer choice – stay ready to attack at a moment’s notice!

And choice E is similarly vulnerable to attack: yes some oil employees may have taken other jobs, but someone has to be doing the oil work. And if unemployment is up overall (as you know from the stimulus) then people are waiting to take those jobs, so the fact that some employees have left doesn’t explain why no one has filled those spots. When Donald Trump had to surrender his post as the star of The Apprentice, Arnold Schwarzenegger was ready to take his place; so, too, should unemployed members of the labor pool in Livonia be ready to take those oil jobs, absent a major reason why they wouldn’t, and choice E fails to present one.

Overall, your job on GMAT Verbal is to be as critical as possible. You’re there to debate the answer choices, not to defend or discuss them. As you read the conclusion of a Critical Reasoning problem, you want to be scanning for a “lightweight” word or phrase that makes it all the more vulnerable to attack. And as you read each answer choice, you shouldn’t be quick to see the good in the sentence, but instead you should be probing it to see where it’s weak and vulnerable to attack.

Let the answer choices view you as a bully – you’re not at the GMAT test center to make friends. Always be attacking, always be looking for words, phrases, or ideas that are an answer choice’s undoing. Trump logic is your Trump card, take joy from telling four of five answer choices “You’re Fired.”

By Brian Galvin.

# Read the Last Piece First on the GMAT!

When I was in grad school, I had a writing teacher who insisted on reading the last page of a novel before she read the first. Her reasoning was that she was starting a kind of journey, and she was curious to know where she’d be going before she could decide whether she wished to embark. Now, as a devoted reader, I couldn’t find this strategy more abhorrent. Uncertainty and mystery are integral parts of the pleasure of reading fiction. Why ruin it?

However, when it comes to the GMAT, I am quite content to ruin the suspense of a question in favor of deriving a more convenient and efficient means of solving it. Interestingly, it turns out that when a question offers multiple bits of information, starting with the last piece can often be a way of dramatically simplifying the problem.

Take the following problem that a tutoring student of mine encountered on her GMATPrep test:

Mary’s income is 60 percent more than Tim’s income, and Tim’s income is 40% less than Juan’s income. What percent of Juan’s income is Mary’s income?

A) 124%

B) 120%

C) 96%

D) 80%

E) 64%

She approached the question like many test-takers would: she started with the first piece of information, and called Mary’s income \$100. And then she got stuck. She realized that Tim’s income isn’t \$40 here, as \$100 is more than double \$40, so clearly Mary’s income would not then be 60% greater than Tim’s (though Tim’s would have been 60% less than Mary’s.) So then, I suggested, why not start at the end?

The last person mentioned here is Juan, so let’s call Juan’s income \$100. She then knocked out the remaining calculations in about 30 seconds. If Juan’s income is \$100, and Tim’s income is 40% less than Juan’s, than Tim’s income would be \$60. And if Tim’s income is \$60, and Mary’s income is 60% more than Tim’s, Mary’s income would be 60 + 60% of 60 = 60 + 36 = 96. (Or 1.6 * 60 = 96.) If Mary’s income is \$96 and Juan’s is \$100, then clearly, Mary’s income is 96% of Juan’s, and the answer is C. Not bad.

Let’s try it again on another question:

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5000 have been vaccinated against both, how many have been vaccinated only against rubella?

A) 2500

B) 7500

C) 10000

D) 15000

E) 17500

First, note that this is a classic overlapping sets questions, so let’s set up a simple matrix:

But now, let’s start by inserting the last piece of information we’re given. 5000 have been vaccinated against both, so that goes in the Mumps/Rubella Vaccine cell. Now we’ve got:

Next, we’ll work backwards. We’re told that the number that have been vaccinated against both (5000) is twice the number that have been vaccinated against only mumps. So the number that have been vaccinated against only mumps must be 2500. Now our table looks like this:

Now we know that 7500 people have been vaccinated against Mumps. Last, we’re told that the number vaccinated against Rubella is twice the number that have been vaccinated against Mumps, which means that 15,000 people have been vaccinated against Rubella. If 15,000 total have been vaccinated against Rubella, and 5000 of those have been vaccinated against both, then, according to our table, 10,000 have been vaccinated against only Rubella. So C is our answer.

Takeaway: The GMAT question writer is going to provide information to you in a very strategic way. If the most useful piece of info comes at the end of a lengthier question, the question will be harder if you start at the beginning. So be like my zany grad school teacher and start at the end. It may ruin the suspense, but as a consolation, you’re more likely to get the question right, and I’m guessing that’s a trade-off most of us are more than happy to make.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

# The GMAT Quant Decimal Trend You NEED to Know

Whenever GMAC releases new material, I’m always on the lookout for conspicuous trends – esoteric or little known rules that end up being applicable in multiple questions. One type of question that has recently shown up with greater frequency involves terminating decimals. The concept isn’t, in the abstract, a terribly hard one. ½, for example, is .5, and so this is a terminating decimal. It ends. 1/3, on the other hand is .33333…, and continues indefinitely, so it’s not a terminating decimal. That’s not so hard. So, you say to yourself: all I have to do is perform a little division, and then I can see for myself if the decimal terminates or not, right?

But then you see a question like this:

Which of the following fractions has a decimal equivalent that is a terminating decimal?

A) 10/189

B) 15/196

C) 16/225

D) 25/144

E) 39/128

Once you spend a little time trying to divide 10 by 189, you realize that the question is going to be incredibly painful and time-consuming if you have to keep applying this approach until you find a fraction that results in a terminating decimal. So let’s be mindful of the fact that the purpose of the GMAT is not to test one’s facility for engaging in tedious arithmetic, but rather to assess our ability to recognize patterns under pressure.

Generally speaking, the best way to uncover a pattern is to use simple numbers first and then extrapolate our results to the more complex scenario we’re tasked with evaluating. We already established above that ½ is a terminating decimal and 1/3 is not. Let’s continue in that vein and see what we find (terminating decimals are in bold):

½ = .5

1/3 = .3333…

¼ = .25

1/5 = .2

1/6 = .166666…

1/7= .142857…

1/8 = .125

1/9 = .1111

1/10 = .1

Next, let’s examine our terminating decimal expressions and see if these numbers have any elements in common. Each of these fractions, it turns out, has a denominator whose prime factorization is composed solely of two prime bases, 2 or 5 or both. This turns out to be a general principle: if a fraction has been simplified, and the prime factorization of the denominator can be expressed in the form of 2^x * 5^y where x and y are non-negative integers, the fraction can be expressed as a terminating decimal.

Now back to our question. We can rephrase the question to be, “Which of the following denominators has a prime factorization that consists solely of 2’s or 5’s or both?”

Not bad. That certainly makes life a little easier. But before we dive in and begin taking prime factorizations with reckless abandon, let’s think like the test-maker. There is no way to do this question without working with the answer choices. Most test-takers will begin with A and work their way down. If you’re trying to create a difficult time-consuming question, where would you bury the correct answer? Probably towards D or E. So when we encounter this kind of scenario, we’re better off if we start at the bottom and work our way up.

E) 39/128. The denominator is 128, which has a prime factorization of 2^7. Because the denominator consists solely of 2’s, this fraction, when expressed as a decimal, must terminate. We’re done. E is the answer. (Intuitively, this makes sense, as all we’re really doing is cutting our numerator in half seven times.) Much easier than doing long division.

Before we commit this principle to memory, let’s make sure that it will be helpful in other contexts. After all, the rule that unlocks a single question won’t be terribly useful to us. So here is the same concept utilized in a Data Sufficiency question:

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100

(2) s = 4

Notice how much easier this question is if we rephrase it as “if r/s is in its most simplified form, does the prime factorization of the denominator consist entirely of 2’s or 5’s?”

Statement 1 can’t be sufficient on its own, as it tells us nothing about the denominator. 91/2 is a terminating decimal, for example, but 91/3 is not.

Statement 2 tells us that the denominator is 4, or 2^2. If we’ve internalized our terminating decimal rule, we see right away that this must be sufficient, as anything dividing by 4 will result in a terminating decimal. The answer is B, Statement 2 alone is sufficient to answer the question.

Takeaway: When studying for the GMAT, it can feel as though there are an infinite number of rules, axioms, and formulas to memorize. Our job, when preparing, is to find the rules that are applicable in multiple contexts and internalize those. If we encounter a problem that seems unusually time-consuming, and no rule springs to mind, we can derive the necessary pattern on the spot by working with simple numbers.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

# 6 Simple Steps to Attack Critical Reasoning Questions on the GMAT

The first step in attacking any Critical Reasoning question on the GMAT is to identify the premises and conclusions of the argument being presented. While Strengthen, Weaken, Assumption and Resolve the Paradox questions include a conclusion in the stimulus, Inference questions require you to select the conclusion (answer choice) that directly follows from the information presented in the stimulus.

This can be difficult because several of the answers can appear attractive. Keep in mind, however, that for Inference questions, the correct answer must be true. Answers that are “likely to be true” or “could be true” based on the information provided in the stimulus seem attractive at first, but if they are not true 100% of the time, in every situation, then they are not the correct answer.

Another difficulty in approaching Inference questions is that with the many of the other question types (Strengthen, Weaken, etc.), your job is to select the answer that includes new information that either undermines or supports the conclusion. For Inference questions, you do not want to bring in information that is not in the stimulus. All of the information required to answer the question will be included in the stimulus.

Here is a 6-step approach that can help you to efficiently attack GMAT Critical Reasoning Inference questions:

1) Read the question stem first.

This will allow you quickly categorize the type of Critical Reasoning question (Strengthen, Weaken, Inference, etc.) and let you focus on identifying the premises in the stimulus. Questions such as, “Which of the following can be correctly inferred from the statements above?” and, “If the statements above are true, which of the following must also be true?” signify that you are dealing with an Inference question.

2) Speculate what you think the correct conclusion is.

Sometimes this may be difficult to verbalize, but having an outline or framework of what the “must be true” answer should include will help to eliminate some answer choices.

4) Become a Defense Lawyer.

When comparing your list of possible answers, try to come up with plausible scenarios that would prove the answer being considered not true. Just because the stimulus says that “everyone sitting in the dentist’s office waiting room at 9:00 a.m. was a patient” does not necessarily mean that they were waiting for an appointment. Some could have already finished their appointment, and some could have been there dropping off another patient. Like a defense lawyer, you need to find every every scenario in which an answer choice might not be true in order to eliminate it from your options.

5) Be aware of exaggerated or extreme answers.

Because the correct answer must always be true, modifiers that exaggerate an element of the premise or make an extreme claim usually signify an incorrect answer. If the stimulus says, “Some of the widgets produced by Company X were defective,” an attractive, yet incorrect answer choice may exaggerate this statement with a modifier such as “most” by claiming, “Most of Company X’s widgets were found to be defective.” Furthermore, answers that include the terms “always”, “never”, “none” and the like are good indicators that the answer will not be true 100% of the time.

6) Be aware of answers that change the scope of the stimulus.

On more difficult Inference questions (as if they were not difficult enough), the test makers will tempt you to select an answer choice that slightly changes an element of the facts laid out in the stimulus. For example, the stimulus might discuss the decrease in the violent crime rate in City A over a certain time period.

The attractive answer that follows all of the elements of having to be true 100% of the time, but is still incorrect might discuss decrease in the murder rate of City A over that time period. While the answer would seem to fit the bill, the murder rate is not the same as the rate of violent crime – this changes the scope of the initial stimulus and we can therefore rule that answer out.

The correct inference or conclusion on Critical Reasoning Inference questions is very close to what is stated explicitly in the stimulus. Remember, the right answer choice on these question types must be true 100% of the time.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By Dennis Cashion, a Veritas Prep instructor based in Denver.

# How to Use the Answer Choices to Solve GMAT Quant Problems

In your approach to solving Quantitative problems on the GMAT, do not forget that the answers are part of the problem and often provide valuable information.

Take for example, the following question:

If 3x4y = 177,147 and x – y = 11, then x =?

A) Undefined

B) 0

C) 11

D) 177,136

E) 177,158

Where do we begin here? 177,147 is a large (not familiar) number and there are not one, but two exponents in the equation.  Looking at the answer choices, we can see that D and E cannot be the answer as they are too large, so at least now we have a starting point.  Additionally, we can see that our choices come down to some mixture of x and y, all y, or all x.

If x = 0, then we can say that 177, 147 is not divisible by 3 and is divisible by 4, so checking the divisibility rule is the ticket! Knowing that to be divisible by 4, the last two digits must be divisible by 4, we can see that 177,147 is not divisible by 4, so 4y becomes irrelevant and we realize y must equal 0.  The sum of the digits of 177, 147 is 27, which is divisible by 3, so we can see that the 3portion of the equation is relevant. We can now (correctly) conclude that the correct answer is answer choice C, x = 11.

Answer choices are little used resources by GMAT test takers.  In the heat of battle, we become so focused on solving the problems in front of us that we forget to utilize all of the information at our disposal.  Another way the answer choices can help you is by plugging them back into the problem to see if they work.

This “back-plugging” is useful when the problem to be solved is algebraic in nature and the answer choices are numbers (not variables). You may find it is easier on a certain problem to arithmetically calculate 2, 3 or even 5 answers by plugging in the answer choices, than in creating and manipulating a complex algebraic equation.  In these cases, plugging in answer choice C first will help you to eliminate up to 60% of the answers on the first calculation.

Many times, just understanding what the correct answer should “look like” by employing some reasoning on the front end will allow you to eliminate some, if not all of the incorrect answers.  Consider this problem:

((-1.9)(o.6) – (2.6)(1.2))/6.0 = ?

A) -0.71

B) 1.00

C) 1.07

D) 1.71

E) 2.71

This is not a difficult problem by any measure, and some test takers will not hesitate to jump in and begin multiplying and dividing decimals.  However, by spending a little bit of time looking at the big picture of this problem, an astute test taker would see that the answer must be negative.  The first term is negative and we are subtracting a larger number from it.  Therefore, the correct answer must be A.

So, instead of jumping in and crunching numbers on the GMAT, you can save yourself some time and brain power by using the answer choices to assist you in reasoning your way to the correct answer – or at least in eliminating several of the incorrect answers.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By Dennis Cashion, a Veritas Prep instructor based in Denver.

# Min/Max Questions on the GMAT are a Piece of Cake (or Pie)!

When I was a child, dessert was serious business. If my family were having pie, that pie had to be evenly distributed among family members, or violence would ensue. Portion size was something we understood at a primal, instinctive level. A larger piece for my brother meant a smaller piece for me. If I wanted to be generous, I could cut myself a smaller piece, thus providing one of my fortunate brothers with a larger dessert share. Every child knows this. But somehow what a child knows intuitively about pie, an adult can forget when dealing with a GMAT question.

I’m talking specifically about min/max questions. For these problems, there are only two things we need to do. First, we need to determine the size of the pie. Then, if we’re trying to maximize one slice, we need to minimize the size of all the other slices and see what’s left over. Similarly, if we’re trying to minimize one slice, we need to maximize all the other slices. Let’s see this principle in action with an official question:

Five pieces of wood have an average length (arithmetic mean) of 124 centimeters and a median length of 140 centimeters. What is the maximum length, in centimeters, of the shortest piece of wood?

A) 90

B) 100

C) 110

D) 130

E) 140

First, let’s determine the size of the pie. If the average is 124 centimeters, and there are five pieces of wood, we know that the total sum of all the pieces of wood would be 5*124 = 620. Let’s call the smallest piece, ’s.’ So far, we have the following:

s ___, 140, ___, ___

Next, we want to maximize the smallest piece. Think pie. If I want to maximize the size of one piece, in this case ‘s,’ I want to minimize the size of all the other slices. The minimum size for the second smallest slice is ‘s.’ (If it were any smaller, it would be the smallest slice.) The minimum size for our two larges slices is 140. (If those were any smaller, the median would change.)

Now, we’re left with the following set:

s, s, 140, 140, 140.

Well, we already know that the sum is 620, so now we have the following equation:

s + s + 140 + 140 + 140 = 620.

2s + 420 = 620

2s = 200

s = 100. The answer is B.

Let’s try a tougher one:

For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.

There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?

A) 0

B) 1

C) 2

D) 3

E) 4

We know it’s a min/max question, so first we need to determine the size of the pie. We’re told that a team will earn 6 – n points whenever one of its members finishes in nth place. The team that has the first place finisher (n = 1) will earn 6 – 1 = 5 points. The second place finisher (n =2) will earn 6 – 2 = 4 points. The trend quickly becomes clear:

First place: 5 points

Second place: 4 points

Third place: 3 points

Fourth place: 2 points

Fifth place: 1 point

One of the conditions of the problem is that ‘n’ cannot be any larger than 5, so at this point, there are no more points to earn. Summing all the available points, we get 1 + 2 + 3 + 4 + 5 = 15. So there are 15 points total for the three teams to divvy up.

Now we’re trying to minimize the number of points one team earned. What did we do in the Goldstein household when we were feeling particularly sadistic and wished to stick my youngest brother with the smallest possible piece of pie? We’d maximize the size of all the other pieces, leaving the youngest, most vulnerable Goldstein with a sad pile of unpalatable mush. Let’s do the same here.

We’re told that no team scored more than 6 points, so 6 is the max number of points a team could have earned. If two teams earned the max – 6 points – they’d have earned 12 points between them. If there are 15 points total, and two of the teams earn a total of 12 points, that leaves 3 points for the stragglers. D is the answer.

Takeaway: As soon as you see a min/max term such as “least,” “most,” “minimum,” “or “maximum,” you’ll be well-served to summon some traumatic memories of divvying up your favorite childhood dessert.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

# Strategies for the New GMAT Questions that You Need to Know!

About a month ago, GMAC released the latest version of the GMAT Official Guide, 25% of which consisted of new questions. Though the GMAT tends not to change too drastically over time – how else could a school compare a score received by one candidate in 2015 to a score received by another candidate in 2010? – there can be subtle shifts of emphasis, and paying attention to the composition mix of the questions in the latest version of the Official Guide is a good way to ascertain if any such shift is in the offing.

My concern as an instructor is whether the philosophy I’m advocating and the techniques I’m teaching are as relevant for the newer questions as they have been for the older ones.

This philosophy can be summarized as follows: the GMAT is not, fundamentally, a content-based test, but rather, uses certain elements of our academic background to test how we think under pressure. Because the test is evaluating how we think, and not what we know, the cultivation of simple strategies, such as using the answer choices or picking easy numbers, is just as important as the re-mastery of the content you may have initially learned in eighth grade, but have subsequently forgotten.

Having thoroughly dissected the new questions in the latest version of the Official Guide, I can confidently report that this philosophy is more relevant than ever. Of the over 200 new quantitative questions, I didn’t do extensive calculations for a single problem. If anything, the kind of fluid logic-based approach that we preach at Veritas is more critical than ever.

Take this new question, for example:

Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

A) (m+4)/[m(m-4)]
B) (2m-4)/[m(m-4)]
C) (4m-4)/[m(m-4)]
D) (4m-8)/[m(m-4)]
E) (4m-12)/[m(m-4)]

Of course, we could do this question algebraically. But if the GMAT is testing our ability to make good decisions under pressure, and if the algebra feels hard for you, then a better option is to make your life as easy as possible and select a simple number for m. If m is larger than 4, let’s say that m = 5. “m” represents the number of students, so now we have 5 students and, we’re told in the question stem, a total of 4 sandwiches. (The question of what kind of negligent, hard-hearted school knowingly packs only 4 sandwiches for all of its students to share will have to be addressed in another post. This question feels straight out of Oliver Twist.)

Okay. We’re told that 3 of the sandwiches are divided evenly among the 5 students. (3 sandwiches)/(5 students) means each student gets 3/5 of a sandwich.

Additionally, we’re told that 4 of the students don’t want any part of the remaining sandwich. Because we only have 5 students and 4 of them don’t want the remaining sandwich, the last student will get the entire fourth sandwich.

To summarize what we have so far: Each of the 5 students initially received 3/5 of a sandwich, and then one student received an entire additional sandwich, on top of that initial 3/5. The lucky fifth student received a total of 3/5 + 1 = 8/5 of a sandwich.

Last, we ‘re told that Carol ate a piece of each of the four sandwiches. But we established that only one student ate a piece of every sandwich, so Carol has to be that lucky student! Therefore, Carol ate 8/5 of a sandwich.

We’re asked what fraction of a sandwich Carol ate, so the answer is simply 8/5. Now all we have to do is plug ‘5’ in place of ‘m’ in each answer choice, and the one that gives us 8/5 will be our answer.

Most test-takers will simply start with A and work their way down until they find an option that works. The question-writer knows that this is how most test-takers proceed. Therefore, it’s a more challenging question if the correct answer is towards the bottom of our answer choices. So let’s use this logic to our advantage, start with E, and work our way up.

Substituting ‘5’ in place of ‘m,’ we get (4*5 – 12)/[5(5-4) = 8/5. That’s it! We’re done. The correct answer is E.

Takeaway: Keep reminding yourself that the GMAT (even with its new questions) is not designed to test what you know. While it is important to brush up on all of the fundamentals you acquired years before, the most successful test-takers will fluidly incorporate simple strategies when attacking complex questions, rather than simply grinding through longer calculations. Each new version of the Official Guide validates the wisdom of this approach.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

# How to Tackle Evenly Spaced Sets on the GMAT

There’s an amusing anecdote told about the great 18th century mathematician, Carl Friedrich Gauss. Apparently, when Gauss was young, he was something of a troublemaker in school, and as a punishment for one of his disruptive outbursts, his teacher ordered him to calculate the sum of all the numbers from 1 to 100 inclusive, thinking that such a calculation would be taxing and time-consuming. Gauss simply scratched his head, thought for a few seconds, and then astonished his teacher and classmates by spitting out the answer: 5,050. He was about seven years old when this happened.

So then, how is it possible for a child – a genius, perhaps, but still a child – to do such an extensive computation in his head? The answer involves exploiting certain properties of evenly spaced sets. An evenly spaced set, as the name implies, is one in which the gap between each successive element in the set is equal. So a set consisting of consecutive integers would be evenly spaced, as would a set consisting of consecutive multiples of 2 or consecutive multiples of 3, etc.

It is always true of evenly spaced sets that the median – the middle term of the set – is equal to the mean, or arithmetic average, of the set. Moreover, the mean can be calculated by adding the high and the low terms of the set, and then dividing by 2. We can use this property in conjunction with the equation: Average * Number of Terms = Sum to calculate the sum of any large evenly spaced set.

In the case of the set of the integers from 1 to 100 inclusive, it works like this:

Average = (High + Low)/2 = (100 + 1)/2 = 101/2 = 50.5.

The Number of Terms = 100. Technically, the equation for finding the number of terms in an evenly spaced set is [(High-Low)/increment] + 1, but clearly, there are 100 terms between 1 and 100. Just remember, when using this formula, we want to add one to make sure we’re not leaving off the last term.

Average * Number = 50.5 * 100 = 5050.

Not too bad, even for a seven-year-old. (Note to those curious about the history of mathematics, this isn’t exactly how Gauss did the calculation, but it’s close enough.)

Now let’s see this concept in action on the GMAT:

For any positive integer n, the sum of the first n positive integers equals (n(n+1))/2. What is the sum of all the even integers between 99 and 301?
A) 10,000
B) 20,200
C) 22,650
D) 40,200
E) 45,150

Notice that we don’t have to bother with the formula they give us. The set of all evens from 99 to 301 inclusive will really be from 100 to 300, as those are the lowest and highest even terms of the set, respectively.

Average = (High + Low)/2 = (300 + 100)/2 = 400/2 = 200.

Number of Terms = [(High-Low)/increment] + 1 = [(300-100)/2] + 1 = 101. (Note: we divide by ‘2’ here because we only want even numbers, or multiples of 2. Thus, there is an increment of 2 between each successive term in the set.)

Average * Number = 200 * 101 = 20,200. The answer is B. Not bad.

Great, you think. Now I can just go on autopilot and apply these formulas anytime I encounter a huge evenly spaced set. But the GMAT doesn’t work like that. Sometimes we use a formula, but just as often, we’ll use logic, or we’ll pick a number, or we’ll work with the answer choices.

This cannot be repeated enough: Quantitative Reasoning is not a math test. It’s a test that requires some mathematical knowledge in order to make good decisions under pressure. Sometimes the best decision is doing little or no math at all.

Consider the following question:

How many positive three-digit integers are divisible by both 3 and 4?
A) 75
B) 128
C) 150
D) 225
E) 300

First, note that any number that is divisible by both 3 and 4 will be divisible by 12, as 12 is the least common multiple of 3 and 4. Perhaps you also noted that we’re dealing with an evenly spaced set here, and that, if the set consists of multiples of 12, the increment is clearly 12. But this question is very different from the previous one because we’re not required to calculate a sum. We just need to know how many multiples of 12 exist between 100 and 999.

If my increment is 12, I know I’ll be dividing by 12 at some point. But I can see that my (High – Low) will be at most (999 – 100) = 899. (Technically, our highest multiple of 12 in this set is 996 and our low term is 108, but there’s actually no need to discern this.) Clearly 899/12 will be less than 100, so there have to be fewer than 100 terms in the set. Now look at the answer choices. Only A is less than 100, so I’m done. I don’t have to finish the calculation.

Takeaway: You will be learning many useful formulas for the GMAT, but make sure you don’t use them blindly. Expect to mix formal algebra with the well-worn strategies of picking numbers and working with the answer choices. On the GMAT, flexibility and mental agility will always take precedence over rote memorization.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

# Why is There “Math” in the GMAT Critical Reasoning Section?

The Critical Reasoning portion of the GMAT will sometimes test basic mathematical concepts. My more verbally-minded students sometimes complain that this tendency is unfair, as the test seems to have imported a question-type from the section of the test that they find less agreeable into the section they consider their strength. But the truth is that the “math” in Critical Reasoning is really about logic and intuition rather than higher-level abstraction.

Take percentages, for instance. We can understand percentage reasoning without doing much calculation. When I introduce this topic, I’ll offer a simple real-world example:

In the 2014 playoffs, Lebron James made roughly 56% of his field goal attempts. In the 2015 playoffs, he made roughly 42% of his attempts. Therefore, he made fewer field goals in 2015 than in 2014.

You don’t need to be an avid basketball fan to recognize the glaring logical flaw in this statement. To determine whether that percentage dip is meaningful, we have to know how many shot attempts he was taking. Because he took so many more shots in 2015 than in 2014, he ended up making more field goals in that year, when his field goal percentage was lower. The notion that a percentage isn’t terribly meaningful without knowing the percent of what is obvious to everyone.

What the GMAT will typically do, however, is to test the exact same concept using a scenario that we may not grasp quite as intuitively. Consider the following official argument:

In the United States, of the people who moved from one state to another when they retired, the percentage who retired to Florida has decreased by three percentage points over the last ten years.  Since many local businesses in Florida cater to retirees, these declines are likely to have a noticeably negative economic effect on these businesses and therefore on the economy of Florida.

Which of the following, if true, most seriously weakens the argument given?

1. People who moved from one state to another when they retired moved a greater distance, on average, last year than such people did ten years ago.
2. People were more likely to retire to North Carolina from another state last year than people were ten years ago.
3. The number of people who moved from one state to another when they retired has increased significantly over the past ten years.
4. The number of people who left Florida when they retired to live in another state was greater last year than it was 10 years ago.
5. Florida attracts more people who move form one state to another when they retired than does any other state.

The logic here may not be as obvious as the Lebron example, but it is, in fact, identical. The argument’s conclusion is that Florida’s economy will suffer negative consequences. The central premise is that of the people moving from one state to another, a smaller percentage are going to Florida now than were going to Florida ten years ago. The assumption is that a smaller percentage moving to Florida means fewer people moving to Florida.

This line of reasoning is no more valid than asserting that Lebron shooting a lower percentage in 2015 than in 2014 means he made fewer shots in 2015. Just as we needed to know if there was a change in the total number of shots Lebron was taking in order to evaluate whether the change in percentage was meaningful, we need to know if there was a change in the total number of people moving from one state to another in order to properly assess whether it’s meaningful that a smaller percentage are moving to Florida.

Let’s evaluate the answer choices one by one:

1. The distance people moved doesn’t matter. Out of Scope. A is out.
2. North Carolina isn’t relevant to what’s happening in Florida. Out of Scope. B is out.
3. This is the logical equivalent of pointing out that Lebron took many more shots in 2015 than in 2014. If far more people are moving from one state to another now than were moving from one state to another ten years ago, it’s possible that more total people are moving to Florida, even if a smaller percentage of movers are going to Florida. This looks good.
4. First, the number of people leaving Florida has no bearing on whether a smaller percentage of people moving to Florida will have an impact on Florida’s economy. Moreover, we’re trying to weaken the idea that Florida’s economy will suffer. If more people are leaving Florida, it would strengthen the notion that Florida’s economy will endure negative consequences. That’s the opposite of what we want. D is out.
5. Tempting perhaps, but ultimately, irrelevant. Just because Lebron led the league in field goals made in both 2015 and 2014 (he didn’t, but play along), doesn’t mean he didn’t make fewer field goals in 2015. E is out.

The answer is C.  If more people are moving from state to state, a lower percentage moving to Florida may not mean that fewer people are coming to Florida, just as Lebron’s dip in field goal percentage does not mean he was making fewer field goals if he was taking more shots.

Takeaway: The “math” concepts tested in Critical Reasoning are, in fact, logic concepts. By connecting the prompt to a more concrete real-world example, we make this logic far more intuitive and easily graspable when we encounter it on the test.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

# 99th Percentile GMAT Score or Bust! Lesson 7: Read Like You Drive

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms. He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation. In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

First, take a look at lessons 1, 2, 3, 4, 5, and 6!

Lesson Seven:

Read Like You Drive: very few GMAT examinees will make mistakes driving to the GMAT test center, but most test-takers will make several Reading Comprehension mistakes once they’re there. As Ravi will discuss in this video, however, the two activities are much more similar than you realize: your job is to follow the signs. Certain keywords in Reading Comprehension passages will tell you when to yield, stop, turn, and pass with care, and if you’re following those signs properly you can proceed much faster than your self-imposed “speed limit” (most people read the passages far too slowly – stay out of the left lane!) and save valuable time for the questions themselves.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

By Brian Galvin

# Master the GMAT by Applying Jedi-like Skills

Once you begin studying for the GMAT, you’ll realize quickly that there are different levels of mastery. There’s that initial level of competence in which you learn, or relearn, many of the foundational concepts that you learned in middle school and have since forgotten. There’s a more intermediate level of mastery in which you’re able to blend strategic thinking with foundational concepts.

Then there’s the highest level in which you achieve a kind of trance-like, fugue state that allows you to incorporate multiple strategies to break down a single complex problem and then seamlessly shift to a fresh set of strategies on the next problem, which, of course, will be testing slightly different concepts from the previous one.

It’s the GMAT equivalent of becoming a Jedi who can anticipate his opponent’s next light saber strike several moves in advance or becoming Neo in the Matrix, finally deciphering the structure of the streaming code that animates his synthetic world. Pick whatever sci-fi analogy you like – it’s this kind of expertise that we’re shooting for when we prepare for the test. The pertinent questions are then the following: how do we accomplish this level of expertise, and what does it look like once we’re finally there?

Fortunately for you, dear student, our books are organized with this philosophy in mind. Once you’ve worked through the skill-builders and the lessons, you’ll likely be at the intermediate level of competence. Then it will be through drilling with homework problems and taking practice tests that you’ll achieve the level of mastery we seek. But let’s take a look at a Sentence Correction question to get a sense of how our thought processes might unfold, once we’re functioning in full Jedi-mode.

Unlike most severance packages, which require workers to stay until the last day scheduled to collect, workers at the automobile company are eligible for its severance package even if they find a new job before they are terminated.

(A) the last day scheduled to collect, workers at the automobile company are eligible for its severance package

(B) the last day they are scheduled to collect, workers are eligible for the automobile company’s severance package

(C) their last scheduled day to collect, the automobile company offers its severance package to workers

(D) their last scheduled day in order to collect, the automobile company’s severance package is available to workers

(E) the last day that they are scheduled to collect, the automobile company’s severance package is available to workers

Having done hundreds of questions, you’ll notice one structural clue leap immediately: “unlike.” When you see words such as “like” or “unlike” you know that you’re dealing with a comparison, so your first task is to make sure you’re comparing appropriate items. You’ll also note that the clause beginning with “which require” modifies “severance packages,” so whatever is compared to these severance packages will come after the modifier.

In A, you’re comparing “severance packages” to “workers.” We’d rather compare severance packages to severance packages or workers to workers. No good.

In B, again, you’re comparing “severance packages” to “workers.”

In C, you’re comparing “severance packages” to “the automobile company.” Nope.

That leaves us with D and E, both of which compare “severance packages” to “automobile’s company severance package.” Here, you’re comparing one group of severance packages to another, so this is logical. But now you have to switch gears – the comparison issue allowed you to eliminate some incorrect answer choices, but you’ll have to use another issue to differentiate between your remaining options.

Once we’re down to two options, you can simply read the two sentences and look for differences. One difference is that E contains the word “that” in the phrase “the last day that they are scheduled to collect.” Perhaps it sounds okay to your ear, but you’ll recall that when “that” is used as a relative pronoun, it should touch the noun it modifies. In this case, it touches, “last day.” Read literally, the phrase, “the last day that they are scheduled to collect,” makes it sound as though “they” are collecting the “last day.” Surely this isn’t what the sentence intends to convey, so we’re then left with ‘D,’ which is the correct answer.

Takeaway:

Notice how many disparate concepts you had to juggle here: You had to recognize the structural clue indicating that “unlike” signifies a comparison; recognize that temporarily skipping over a longer modifying phrase is an effective way to get a sense of the core clause you’re evaluating; recall that once you’re down to two answer choices, you can simply zero in on differences between your options; remember the rule stipulating that relative pronouns must touch what they modify; and last, you had to recognize that Sentence Correction is not only about grammar but also about logic and meaning, and all in under a minute and a half. I’d say that’s pretty Jedi-like.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# 99th Percentile GMAT Score or Bust! Lesson 6: Practice Tests Aren’t Real Tests

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

First, take a look at Lessons 1, 2, 3, 4 and 5!

Lesson Six:

Practice Tests Aren’t Real Tests: read the popular GMAT forums and you’ll see lots of handwringing and bellyaching about practice tests scores…but not very much analysis beyond the scores themselves.  In this video, Ravi (along with his alter ego Allen Iverson) talks about practice, stressing the importance of using the tests to increase your score more than to merely try to predict it.  Pacing is paramount and diagnosis is divine; as Ravi will explain, practice tests are critical for learning how you would perform if that were the real thing, with the added bonus of having the opportunity to fix those things that you don’t like about that practice performance.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

By Brian Galvin

# Think Like Einstein to Answer GMAT Data Sufficiency Questions

I recently read Manjit Kumar’s, Quantum, which is about the philosophical disagreement between Niels Bohr and Albert Einstein with respect to the nature of reality.  In high school physics, we learned about Heisenberg’s Uncertainty Principle, which posits that we can never know both the position and the momentum of an electron with absolute certainty. The more precisely we measure an electron’s position, the less we know about its momentum, and vice versa.

There are two ways to interpret this phenomenon. Einstein thought that an electron had a defined position and momentum. We simply weren’t capable of documenting both at the same time due to the clumsiness of our measuring instruments. Bohr, on the other hand, believed that an electron didn’t have a position or momentum until we measured it. In other words, the electron doesn’t exist before it’s observed (which, of course, raises knotty metaphysical questions about how the observer exists, if the observer is herself made of sub-atomic particles, none of which exist before they’re observed. But this one is a little harder to connect to the GMAT, so the reader is invited to contemplate such a conundrum in his or her own time, once the test is in the rear view mirror).

Though physicists, by and large, are more likely to accept Bohr’s interpretation than Einstein’s, on the GMAT we’ll want to reason more like Einstein, particularly when it comes to Data Sufficiency. In almost every class I teach, a student will ask a question along the lines of, “Is it possible that, in a value question, Statement 1 will tell you definitively that x equals 8, and that Statement 2 will tell you definitively that x equals some other number?” The answer is a resounding “No” – x has a unique value, the question is whether we can definitively divine what that value is. If Statement 1 tells us decisively that x = 8, Statement 2 cannot tell us that x equals, say, 10.

Let’s see how this principle can be helpful in action:

If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?

1)     If the integer is divided by 45, the remainder is 30.

2)     The integer is divisible by 2

Statement 1 tells me that when I divide an integer by 45, I get a remainder of 30. So I could test 75, because that will give a remainder of 30 when divided by 45 (And, just as importantly, it gives a remainder of 3 when divided by 9 – I have to satisfy the conditions embedded in the question stem too!). The question asks me for the remainder when the integer is divided by 5. Well, 75/5 will give no remainder, so the remainder, in this case, is 0.

Let’s see if that will always be the case. Next, we’ll test 105, which gives a remainder of 30 when divided by 45, and gives a remainder of 3 when divided by 9 [note: I can generate fresh numbers to test by simply adding the divisor, 30, to the previous number I test (75 + 30 = 105)]. Clearly 105/5 will give a remainder of 0, as any number that ends in 5 will be divisible by 5. The same will be true of 145, or 175, or 205. The remainder, when the integer in question is divided by 5 will always be 0, so Statement 1 is sufficient.

Now let’s reason like Einstein. We know that the answer to the question has a definitive value of 0. That can’t change. The only way Statement 2 can be sufficient is if it gives us that same value. So let’s pick a number that is divisible by 2 but gives a remainder of 3 when divided by 9. 12 will work. The remainder, when 12 is divided by 5, is 2. All we need to see is that we did not get 0.

We don’t have to test another number. Statement 2 cannot, alone, be sufficient, because we already know – the Einsteins that we are – that the value in question is 0. Statement 2 cannot tell us that the value is definitively 2 (if we continued to test, we’d eventually find values that gave us a remainder of 0 when we divided by 5, but because there are other possibilities, Statement 2 doesn’t give us enough information to determine, without a doubt, that the value is 0). We’re done. Statement 2 is insufficient. The answer is A: Statement 1 alone is sufficient.

Note that this same logic will work on “YES/NO” questions as well. If Statement 1 tells us that the answer to the question is definitively “YES”, Statement 2 cannot tell us that the answer is definitively “NO”, and vice versa. Recognizing this can save us valuable time.

Takeaway: Although Niels Bohr might say that there is no answer to a Data Sufficiency question until we evaluate a statement, for these questions we want to think more like Einstein and recognize that, in the mind of the question-writer, there is an objective answer – the question is whether we have enough information to definitely deduce what that answer is. There may be no objective reality in the quantum world, but on the GMAT, there most certainly is.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# Catching Sneaky Remainder Questions on the GMAT

One of my favorite topics to teach is remainders. We learn about remainders in grade school and when I introduce the topic in class, the response is often amused incredulity. It isn’t hard to see that when 16 is divided by 7, the remainder is 2. How can it possibly be the case that something we learned in fifth grade is included on a test that helps determine where we go to graduate school?

But in mathematics, seemingly basic topics often have broader applications. So let’s consider both simple and complex applications of remainders on the GMAT. The most straightforward scenario is for the question to ask what the remainder is in a given context. We’ll start by looking at an official Data Sufficiency question of moderate difficulty:

What is the remainder when x is divided by 3?

1) The sum of the digits of x is 5

2) When x is divided by 9, the remainder is 2

Pretty straightforward question. In Statement 1, we could approach by simply picking numbers. If the sum of the digits of x is 5, x could be 14. When 14 is divided by 3, the remainder is 2. Similarly, x could be 32. When 32 is divided by 3, the remainder will again be 2. Or x could be 50, and still, the remainder when x is divided by 3 will be 2. So no matter what number we pick, the remainder will always be 2. Statement 1 alone is sufficient.

Note that if we know the rule for divisibility by 3 – if the digits of a number sum to a multiple of 3, the number itself is a multiple of 3 – we can reason this out without picking numbers. If the sum of the digits of x were exactly 3, the remainder would be 0. If the sum of the digits of x were 4, then logically, the remainder would be 1. Consequently, if the sum of the digits of x were 5, the remainder would have to be 2.

Again, in Statement 2, we can pick numbers. We’re told that when x is divided by 9, the remainder is 2. To quickly generate a list of numbers that we might test, we can start with multiples of 9: 9, 18, 27, 36, etc. Then, we can add two to each of those multiples of 9 to get the following list of numbers: 11, 20, 29, 38, etc.  All of these numbers will give us a remainder of 2 when divided by 9. Now we can test them. If x is 11, when x is divided by 3, the remainder will be 2. If x is 20, when x is divided by 3, the remainder will be 2. We’ll quickly see that the remainder will always be 2, so Statement 2 is also sufficient on its own. The answer to this question is D, either statement alone is sufficient. That’s not too bad.

But the GMAT won’t always be so conspicuous about what category of math it’s testing. Take this more challenging question, for example:

June 25, 1982 fell on a Friday. On which day of the week did June 25, 1987 fall. (Note: 1984 was a leap year.)

A)     Sunday

B)     Monday

C)     Tuesday

D)    Wednesday

E)     Thursday

If you’re anything like my students, it’s not blindingly obvious that this is a remainder question in disguise. But that is precisely what we’re dealing with. Consider a very simple case. Say that June 1 is a Monday, and I want to know what day of the week it will be 14 days later. Clearly, that would also be a Monday. And if I asked you what day of the week it would be 16 days later, you’d know that it would be a Wednesday – two days after Monday. Put another way – because we’re dealing with weeks, or increments of 7 – all we need to do is divide the number of days elapsed by 7 and then find the remainder in order to determine the day of the week. 16 divided by 7 gives a remainder of 2, so if June 1 is a Monday, 16 days later must be 2 days after Monday.

Suddenly the aforementioned question is considerably more approachable. From June 25, 1982 to June 25, 1983 a total of 365 days will pass. 365/7 gives a remainder of 1, so if June 25, 1982 was a Friday, June 25 1983 will be a Saturday. From June 25, 1983 to June 25, 1984, 366 days will pass because 1984 is a leap year. 366/7 gives a remainder of 2, so if June 25, 1983 was a Saturday, June 25, 1984 will be 2 days later, or Monday. We already know that in a typical 365 day year, the remainder will be 1, so June 25, 1985 will be Tuesday, June 25, 1986 will be Wednesday and June 25, 1987 will be Thursday, which is our answer.

Takeaway: the challenge of the GMAT isn’t necessarily that questions are asking you to do difficult math, but that it can be hard to figure out what the questions are asking you to do. When you encounter something that seems unfamiliar or strange, remind yourself that virtually every problem you encounter will involve the application of a concept considerably simpler than the nebulous wording the question might suggest.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# The Importance of Estimation on the GMAT

In the first session of every new class I teach, I try to emphasize the power and effectiveness of estimating when dealing with potentially complex calculations. No one ever disputes that this is a good approach, but an unspoken assumption is that while you may save a bit of time by estimating, it isn’t absolutely crucial to do so. After all, how long does it take to do a little arithmetic? The problem is that, under pressure, hard arithmetic can cause us to freeze. To illustrate this, I’ll ask, “quick, what’s 1.3 divided by 3.2?” This is usually greeted by blank stares or nervous laughter. But when I ask “okay, what’s 1 divided by 3?” they see the point: trying to solve 1.3/3.2 won’t just be time-consuming, but can easily lead to a careless mistake prompted by arithmetical paralysis.

I didn’t make up that 1.3/3.2 calculation. It comes directly from an official question, and it’s quite clearly designed to elicit the panicked response it usually gets when I ask it in class. Here is the full question:

The age of the Earth is approximately 1.3 * 10^17 seconds, and one year is approximately 3.2 * 10^7 seconds. Which of the following is closest to the age of the Earth in years?

1. 5 * 10^9
2. 1 * 10^9
3. 9 * 10^10
4. 5 * 10^11
5. 1 * 10^11

Most test-takers quickly see that in order to convert from seconds to years, we have to perform the following calculation: 1.3 * 10^17 seconds * 1 year/3.2 * 10^ 7 seconds or (1.3 * 10^17)/(3.2 * 10^ 7.)

It’s here when many test-takers freeze. So let’s estimate. We’ll round 1.3 down to 1, and we’ll round 3.2 down to 3. Now we’re calculating or (1* 10^17)/(3 * 10^ 7.) We can rewrite this expression as (1/3) * (10^17)/(10^7.) This becomes .333  * 10^10. If we borrow a 10 from 10^10, we’ll get 3.33 * 10^9. We know that this number is a little smaller than the correct answer, because we rounded the numerator down from 1.3 to 1, and this was a larger change than the adjustment we made to the denominator. If 3.33 * 10^9 is a little smaller than the correct answer, the answer must be B.  (Similarly, if we were to estimate 13/3, we’d see that the number is a little bigger than 4.)

This strategy will work just as well on tough Data Sufficiency questions:

If it took Carlos ½ hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (1 mile = 5280 feet.)

1. The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
2. The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.

The fact that we’re given the conversion from miles to feet is a dead-giveaway that we’ll need to do some unit conversions to solve this question. So we know that the time is ½ hour, or 30 minutes. We want to know if the distance is greater than 6 miles. We’ll call the rate ‘r.’ If we put this question into the form of Rate * Time  = Distance, we can rephrase the question as:

Is r * 30 minutes > 6 miles?

We can simplify further to get: Is r > 6 miles/30 minutes or Is r > 1 mile/5 minutes?

A quick glance at the statements reveals that, ultimately, I want to convert into feet per second. I know that 1 mile is 5280 feet and that 5 minutes is 5 *60, or 300 seconds.

Now Is r > 1 mile/5 minutes? becomes Is r > 5280 feet/ 300 seconds. Divide both by 10 to get Is r > 528 feet/30 seconds. Now, let’s estimate. 528 is pretty close to 510. I know that 510/30 is the same as 51/3, or 17. Of course, I rounded down by 18 from 528 to 510, and 18/30 is about .5, so I’ll call the original question:

Is r > 17.5 feet/second?

If we get to this rephrase, the statements become a lot easier to test. Statement 1 tells me that Carlos cycled at a speed greater than 16 feet/second. Well, that could mean he went 16.1 feet/second, which would give me a NO to the original question, or he could have gone 30 feet/second, so I can get a YES to the original question. Not Sufficient.

Statement 2 tells me that his average speed was less than 18 feet/second. That could mean he went 17.9 feet/second, which would give me a YES. Or he could have gone 2 feet/second, which would give me a NO.

Together, I know he went faster than 16 feet/second and slower than 18 feet/second. So he could have gone 16.1 feet/second, which would give a NO, and he could have gone 17.9, which would give a YES, so even together, the statements are not sufficient, and the answer is E.

The takeaway: estimation isn’t simply a luxury on the GMAT; on certain questions, it’s a necessity. If you find yourself grinding through a host of ungainly arithmetical calculations, stop, and remind yourself that there has to be a better, more time-efficient approach.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# A Secret Shortcut to Increase Your GMAT Score

The GMAT is an exam that aims to test how you think about things. Many people have heard this mantra when studying for the GMAT, but it’s not always clear what it means. While there are many formulae and concepts to know ahead of taking the exam, you will be constantly thinking throughout the exam about how to solve the question in front of you. The GMAT specializes in asking questions that require you to think about the solution, not just to plug in numbers mindlessly and return whatever your calculator tells you (including typos and misplaced decimals).

There are many ways the GMAT test makers ensure that you’re thinking logically about the solution of the question. One common example is that the question will give you a story that you have to translate into an equation. Anyone with a calculator can do 15 * 6 * 2 but it’s another skill entirely to translate that a car dealership that’s open every day but Sunday sells 3 SUVs, 5 trucks and 7 sedans per day for a sale that lasts a fortnight (sadly, the word fortnight is somewhat rare on the GMAT). Which skill is more important in business, crunching arbitrary numbers or deciphering which numbers to crunch? (Trick question: they’re both important!) The difference is a computer will calculate numbers much faster than a human ever will, but being able to determine what equation to set up is the more important skill.

This distinction is rather ironic, because the GMAT often provides questions that are simply equations to be solved. If the thought process is so important, why provide questions that are so straight forward? Precisely because you don’t have a calculator to solve them and you still need to use reasoning to get to the correct answer. An arbitrarily difficult question like 987 x 123 is trivial with a calculator and provides no educational benefit, simply an opportunity to exercise your fingers (and they want to look good for summer!) But without a calculator, you can start looking at interesting concepts like unit digits and order of magnitude in order to determine the correct answer. For business students, this is worth much more than a rote calculation or a mindless computation.

Let’s look at an example that’s just an equation but requires some analysis to solve quickly:

(36^3 + 36) / 36 =

A) 216
B) 1216
C) 1297
D) 1333
E) 1512

This question has no hidden meaning and no interpretation issues. It is as straight forward as 2+2, but much harder because the numbers given are unwieldy. This is, of course, not an accident. A significant number of people will not answer this question correctly, and even more will get it but only after a lengthy process. Let’s see how we can strategically approach a question like this on test day.

Firstly, there’s nothing more to be done here than multiplying a couple of 2-digit numbers, then performing an addition, then performing a division. In theory, each of these operations is completely feasible, so some people will start by trying to solve 36^3 and go from there. However, this is a lengthy process, and at the end, you get an unwieldy number (46,656 to be precise). From there, you need to add 36, and then divide by 36. This will be a very difficult calculation, but if you think of the process we’re doing, you might notice that you just multiplied by 36, and now you’ll have to divide by 36. You can’t exactly shortcut this problem because of the stingy addition, but perhaps we can account for it in some manner.

Multiplying 36 by itself twice will be tedious, but since you’re dividing by 36 afterwards, perhaps you can omit the final multiplication as it will essentially cancel out with the division. The only caveat is that we have to add 36 in between multiplying and dividing, but logically we’re adding 36 and then dividing the sum by 36, which means that this is tantamount to just adding 1. As such, this problem kind of breaks down to just 36 * 36, and then you add 1. If you were willing to multiply 36^3, then 36^2 becomes a much simpler calculation. This operation will yield the correct answer (we’ll see shortly that we don’t even need to execute it), and you can get there entirely by reasoning and logic.

Moreover, you can solve this question using (our friendly neighbour) algebra.  When you’re facing a problem with addition of exponents, you always want to turn that problem into multiplication if at all possible. This is because there are no good rules for addition and subtraction with exponents, but the rules for multiplication and division are clear and precise. Taking just the numerator, if you have 36^3 + 36, you can factor out the 36 from both terms. This will leave you with 36 *(36^2 + 1). Considering the denominator again, we end up with (36 *(36^2 + 1)) / 36. This means we can eliminate both the 36 in the numerator and the 36 in the denominator and end up with just (36^2 + 1), which is the same thing we found above.

Now, 36*36 is certainly solvable given a piece of paper and a minute or so, but you can tell a lot from the answer by the answer choices that are given to you. If you square a number with a units digit of 6, the result will always end with 6 as well (this rule applies to all numbers ending in 0, 1, 5 and 6). The result will therefore be some number that ends in 6, to which you must add 1. The final result must thus end with a 7. Perusing the answer choices, only answer choice C satisfies that criterion. The answer must necessarily be C, 1297, even if we don’t spend time confirming that 36^2 is indeed 1,296.

In the quantitative section of the GMAT, you have an average of 2 minutes per question to get the answer. However, this is simply an average over the entire section; you don’t have to spend 2 minutes if you can shortcut the answer in 30 seconds. Similarly, some questions might take you 3 minutes to solve, and as long as you’re making up time on other questions, there’s no problem taking a little longer. However, if you can solve a question in 30 seconds that your peers spend 2 or 3 minutes solving, you just used the secret shortcut that the exam hopes you will use.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# How to Evaluate the Entire Sentence on Sentence Correction GMAT Questions

As the Donald Trump sideshow continues to dominate American news, politics is again being pushed to the forefront as the country gears up for an election in 15 months. The nominees are not yet confirmed, but many candidates are jockeying for position, trying to get their names to resonate with the American population. This election will necessarily have a new candidate for both parties, as Barack Obama will have completed the maximum of two elected terms allowed by the Constitution (via the 22nd amendment).

This means that we can soon begin to discuss Barack Obama’s legacy. As with any legacy, it’s important to look at the terms globally, and not necessarily get bogged down by one or two memorable moments. A legacy is a summary of the major points and the minor points of one’s tenure. As such, it’s difficult to sum up a presidency that spanned nearly a decade and filter it down to simply “Obamacare” or “Killing Bin Laden” or “Relations with Cuba”. Not everyone will agree on what the exact highlights were, but we must be able to consider all the elements holistically.

On the GMAT, Sentence Correction is often the exact same way. If only a few words are highlighted, then your task is to make sure those few words make sense and flow properly with the non-underlined portion. If, however, the entire sentence is underlined, you have “carte blanche” (or Cate Blanchett) to make changes to any part of the sentence. The overarching theme is that the whole sentence has to make sense. This means that you can’t get bogged down in one portion of the text, you have to evaluate the entire thing. If some portion of the phrasing is good but another contains an error, then you must eliminate that choice and find and answer that works from start to finish.

Let’s look at a topical Sentence Correction problem and look for how to approach entire sentences:

Selling two hundred thousand copies in its first month, the publication of The Audacity of Hope in 2006 was an instant hit, helping to establish Barack Obama as a viable candidate for president.

A) Selling two hundred thousand copies in its first month, the publication of The Audacity of Hope in 2006 was an instant hit, helping to establish Barack Obama as a viable candidate for president.
B) The publication in 2006 of the Audacity of Hope was an instant hit: in two months it sold two hundred thousand copies and helped establish Barack Obama as a viable candidate for president.
C) Helping to establish Barack Obama as a viable candidate for president was the publication of The Audacity of Hope in 2006, which was an instant hit: it sold two hundred thousand copies in its first month.
D) The Audacity of Hope was an instant hit: it helped establish Barack Obama as a viable candidate for president, selling two hundred thousand copies in its first month and published in 2006.
E) The Audacity of Hope, published in 2006, was an instant hit: in two months, it sold two hundred thousand copies and helped establish its author, Barack Obama, as a viable candidate for president.

An excellent strategy in Sentence Correction is to look for decision points, significant differences between one answer choice and another, and then make decisions based on which statements contain concrete errors. However, when the whole sentence is underlined, this becomes much harder to do because there might be five decision points between statements, and each one is phrased a little differently. You can still use decision points, but it might be simpler to look through the choices for obvious errors and then see if the next answer choice repeats that same gaffe (not a giraffe).

Looking at the original sentence (answer choice A), we see a clear modifier error at the beginning. Once the sentence begins with “Selling two hundred thousand copies in its first month,…” the very next word after the comma must be the noun that has sold 200,000 copies. Anything else is a modifier error, whether it be “Barack Obama wrote a book that sold” or “the publication of the book” or any other variation thereof. We don’t even need to read any further to know that it can’t be answer choice A. We’ll also pay special attention to modifier errors because if it happened once it can easily happen again in this sentence.

Answer choice B, unsurprisingly, contains a very similar modifier error. The sentence begins with: “The publication in 2006 of the Audacity of Hope was an instant hit:…”. This means that the publication was a hit, whereas logically the book was the hit. This is an incorrect answer choice again, and so far we haven’t even had to venture beyond the first sentence, so don’t let the length of the answer choices daunt you.

Answer choice C, “helping to establish Barack Obama as a viable candidate for president was the publication of The Audacity of Hope in 2006, which was an instant hit: it sold two hundred thousand copies in its first month” contains another fairly glaring error. On the GMAT, the relative pronoun “which” must refer to the word right before the comma. In this case, that would be the year 2006, instead of the actual book. Similarly to the first two choices, this answer also contains a pronoun error because the “it” after the colon would logically refer back to the publication instead of the book as well. One error is enough, and we’ve already got two, so answer choice C is definitely not the correct selection.

Answer choice D, “The Audacity of Hope was an instant hit: it helped establish Barack Obama as a viable candidate for president, selling two hundred thousand copies in its first month and published in 2006” sounds pretty good until you get to the very end. The “published in 2006” is a textbook dangling modifier, and would have been fine had it been placed at the beginning of the sentence. Unfortunately, as it is written, this is not a viable answer choice (you are the weakest link).

By process of elimination, it must be answer choice E. Nonetheless, if we read through it, we’ll find that it doesn’t contain any glaring errors: “The Audacity of Hope, published in 2006, was an instant hit: in two months, it sold two hundred thousand copies and helped establish its author, Barack Obama, as a viable candidate for president.” The title of the book is mentioned initially, a modifier is correctly placed and everything after the colon describes why it was regarded as a hit. Holistically, there’s nothing wrong with this answer choice, and that’s why E must be the correct answer.

Overall, it’s easy to get caught up in one moment or another, but it’s important to look at things globally. A 30-word passage entirely underlined can cause anxiety in many students because there are suddenly many things to consider at the same time. There’s no reason to panic. Just review each statement holistically, looking for any error that doesn’t make sense. If everything looks good, even if it wasn’t always ideal, then the answer choice is fine. It’s important to think of your legacy, and on the GMAT, that means getting a score that lets you achieve your goals.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 1 Strategy That Will Lead You to Better Pacing on the GMAT

Let’s look at a vastly important testing issue that is largely misunderstood and its seriousness under-appreciated.  Throughout multiple years of tutoring, this has been one of the most common and detrimental problems that I have had to work to correct in my students.  It pertains to the entire GMAT exam, but is typically more relevant to the quant section as students often struggle more with pacing during quant.

No single question matters unless you let it.

Reflect on that for a second, because it’s super important, weird, true, and again…important.  The GMAT exam is not testing your ability to get as many questions right as you can.  You can get the exact same percentage of questions right on two different exams and end up getting very different scores as a result of the complicated scoring algorithm.  Mistakes that will crush your score are a large string of consecutive incorrect answers, unanswered questions remaining at the end of the section (these hurt your score even more than answering them incorrectly would), and a very low hit rate for the last 5 or 10 questions.  These are all problems that are likely to arise if you spend way too much time on one/several questions.

Each individual question is actually pretty insignificant.  The GMAT has 37 quantitative questions to gauge your ability level (currently ignoring the issue of experimental questions), so whether you get a certain question right or wrong doesn’t matter much.  Let’s look at a hypothetical example and pick on question #17 for a second (just because it looked at me wrong!).  If you start question 17, realize that it is not going your way, and ultimately make an educated guess after about 2 minutes and get it wrong…that doesn’t hurt you a lot.  You missed the question, but you didn’t let it burn a bunch of your time and you live to fight another day (or in this case question).

Now let’s look at question 17 again, but from the perspective of being stubborn.  If you start the question and are struggling with it but refuse to quit, thinking something like “this is geometry, I am so good at geometry, I have to get this right!”, then it will become very significant.  In a bad way.  In this example you spend 6 minutes on the question and you get it right.  Congratulations!  Except…you are now statistically not even going to get to attempt to answer two other questions because of the time that you just committed to it (with an average of 2 minutes per question on the quant section, you just allocated 3 questions’ worth of time to one question).

So your victory over infamous question 17 just got you 2 questions wrong!  That’s a net negative.  Loop in the concept of experimental questions, the fact that approximately one-fourth of quant questions don’t count, and therefore it is entirely possible that #17 isn’t even a real question, and the situation is pretty depressing.

Pacing is critical, and your pacing on quant questions should very rarely ever go above 3 minutes.  Spending an excess amount of time on a question but getting it right is not a success; it is a bad strategic move.  I challenge you to look at any practice tests that you have taken and decide whether you let this happen.  Were there a few questions that you spent way over 2 minutes on and got right, but then later in the test a bunch of questions that you had to rush on and ended up missing, even though they may not have been that difficult?  If that’s the case, then your timing is doing some serious damage.  Work to correct this fatal error ASAP!

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Brandon Pierpont is a GMAT instructor for Veritas Prep. He studied finance at Notre Dame and went on to work in private equity and investment banking. When he’s not teaching the GMAT, he enjoys long-distance running, wakeboarding, and attending comedy shows.

# Find Time-Saving Strategies for GMAT Test Day

I’ve often heard from people studying for the GMAT that they would score much higher on the test if there were no time limit to each section. The material covered on the exam is not inherently complicated, but the combination of subtle wordplay and constant stress about time management creates an environment where test takers often rush through prompts and misinterpret questions. Unfortunately, time management and stress management are two of the major skills being tested on the GMAT, so the time limit isn’t going away any time soon (despite my frequent letters to the GMAC). Instead, it’s worth mastering simple techniques to save time and extrapolate patterns based on smaller samples.

As an example, consider a simple question that asks you how many even numbers there are between 1 and 100. Of course, you could write out all 100 terms and identify which ones are even, say by circling them, and then sum up all the circled terms. This strategy would work, but it is completely inefficient and anyone who’s successfully passed the fourth grade would be able to see that you can get the answer faster than this. If every second number is even, then you just have to take the number of terms and divide by 2. The only difficulty you could face would be the endpoints (say 0 to 100 instead), but you can adjust for these easily. The next question might be count from 1 to 1,000, and you definitely don’t want to be doing that manually.

Other questions might not be as straight forward, but can be solved using similar mathematical properties. It’s important to note that you don’t have a calculator on the GMAT, but you will have one handy for the rest of your life (even in a no-WiFi zone!). This means that the goal of the test is not to waste your time executing calculations you would execute on your calculator in real life, but rather to evaluate how you think and whether you can find a logical shortcut that will yield the correct answer quickly.

Let’s look at an example that can waste a lot of time if you’re not careful:

Brian plays a game in which he rolls two die. For each die, an even number means he wins that amount of money and an odd number means he loses that amount of money. What is the probability that he loses money if he plays the game once?

A) 11/12
B) 7/12
C) 1/2
D) 5/12
E) 1/3

First, it’s important to interpret the question properly. Brian will roll two die, independently of one another. For each even number rolled, he will win that amount of money, so any given die is 50/50. If both end up even, he’s definitely winning some money, but if one ends up even and the other odd, he may win or lose money depending on the values. The probability should thus be close to being 50/50, but a 5 with a 4 will result in a net loss of 1\$, whereas a 5 with a 6 will result in a net gain of 1\$. Clearly, we need to consider the actual values of each die in some of our calculations.

Let’s start with the brute force approach (similar to writing out 1-100 above). There are 6 sides to a die, and we’re rolling 2 dice, so there are 6^2 or 36 possibilities. We could write them all out, sum up the dollar amounts won or lost, and circle each one that loses money. However, it is essentially impossible to do this in less than 2 minutes (or even 3-4 minutes), so we shouldn’t use this as our base approach. We may have to write out a few possibilities, but ideally not all 36.

If both numbers are even, say 2 and 2, then Brian will definitely win some money. The only variable is how much money, but that is irrelevant in this problem. Similarly, if he rolls two odd numbers, say 3 and 3, then he’s definitely losing money. We don’t need to calculate each value; we simply need to know they will result in net gains or net losses. For two even numbers, in which we definitely win money, this will happen if the first die is a 2, a 4 or a 6, and the second die is a 2, a 4 or a 6. That would leave us with 9 possibilities out of the 36 total outcomes. You can also calculate this by doing the probability of even and even, which is 3/6 * 3/6 or 9/36. Similarly, odd and odd will also yield 9/36 as the possibilities are 1, 3, and 5 with 1, 3, and 5. Beyond this, we don’t need to consider even/even or odd/odd outcomes at all.

The interesting part is when we come to odds and evens together. One die will make Brian win money and the other will make him lose money. The issue is in the amplitude. Since we’ve eliminated 18 possibilities that are all entirely odd or even, we only need to consider the 18 remaining mixed possibilities. There is a logical way to solve this issue, but let’s cover the brute force approach since it’s reasonable at this point. The 18 possibilities are:

Odd then even:                                                                                                                Even then odd:

1, 2                         3, 2                         5, 2                                                         2, 1                         4, 1                         6, 1

1, 4                         3, 4                         5, 4                                                         2, 3                         4, 3                         6, 3

1, 6                         3, 6                         5,6                                                          2, 5                         4, 5                         6, 5

Looking at these numbers, it becomes apparent that each combination is there twice ((2,1) or (1,2)). The order may matter when considering 36 possibilities, but it doesn’t matter when considering the sums of the die rolls. (2,1) and (1,2) both yield the same result (net gain of 1), so the order doesn’t change anything to the result. We can simplify our 18 cases into 9 outcomes and recall that each one weighs 1/18 of the total:

(1,2) or (2,1): Net gain of 1\$

(1,4) or (4,1): Net gain of 3\$

(1,6) or (6,1): Net gain of 5\$

Indeed, no matter what even number we roll with a 1, we definitely make money. This is because 1 is the smallest possible number. Next up:

(3,2) or (2,3): Net loss of 1\$

(3,4) or (4,3): Net gain of 1\$

(3,6) or (6,3): Net gain of 3\$

For 3, one of the outcomes is a loss whereas the other two are gains. Since 3 is bigger than 2, it will lead to a loss.  Finally:

(5,2) or (2,5): Net loss of 3\$

(5,4) or (4,5): Net loss of 1\$

(5,6) or (6,5): Net gain of 1\$

For 5, we tend to lose money, because 2/3 of the possibilities are smaller than 5. Only a 6 paired with the 5 would result in a net gain. Indeed, all numbers paired with 6 will result in a net gain, which is the same principle as always losing with a 1.

Summing up our 9 possibilities, 3 led to losses while 6 led to gains. The probability is thus not evenly distributed as we might have guessed up front. Indeed, the fact that any 6 rolled with an odd number always leads to a gain whereas any 1 rolled with an even number always leads to a loss helps explain this discrepancy.

To find the total probability of losing money, we need to find the probability of reaching one of these three odd-even outcomes. The chance of the dice being odd and even (in any order) is ½, and within that the chances of losing money are 3/9: (3, 2), (5, 2), and (5, 4). Thus we have 3/9 * ½ = 3/18 or 1/6 chance of losing money if it’s odd/even. Similarly, if it ends up odd/odd, then we always lose money, and that’s 3/9 * 3/9 = 9/36 or ¼. We have to add the two possibilities since any of them is possible, and we get ¼ + 1/6, if we put them on 12 we get 3/12 + 2/12 which equals 5/12. This is answer choice D.

It’s convenient to shortcut this problem somewhat by identifying that it cannot end up at 50/50 (answer choice C) because of the added weight of even numbers. Since 6 will win over anything, you start getting the feeling that your probability of losing will be lower than ½. From there, your choices are D or E, 15/36 or 12/36. Short of taking a guess, you could start writing out a few possibilities without having to consider all 36 outcomes, and determine that all odd/odd combinations will work. After that, you look at the few possibilities that could work ((5,4), (4,5), etc) and determine that there are more than 12 total possibilities, locking you in to answer choice D.

Many students struggle with problems such as these because they appear to be simple if you just write out all the possibilities. Especially when your brain is already feeling fatigued, you may be tempted to try and save mental energy by using brute force to solve problems. Beware, the exam wants you to do this (It’s a trap!) and waste precious time. If you need to write out some possibilities, that’s perfectly fine, but try and avoid writing them all out by using logic and deduction. On test day, if you use logic to save time on possible outcomes, you won’t lose.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# When You’ll Need to Bring Outside Knowledge to the GMAT

It is often said that outside knowledge is not required on the GMAT. The idea is that everyone should be on relatively equal footing when starting to prepare for this exam, minimizing the advantage that someone with a B.Comm might have over someone with an engineering or philosophy degree. Of course, it’s difficult to determine at what point does outside knowledge begin and end. Knowing that there are 26 letters in the (English) alphabet or that blue and red are different colors is never explicitly mentioned in the GMAT preparation, but the concepts certainly can come up in GMAT questions.

This statement “No outside knowledge is required on the GMAT” is true in spirit, but a fundamental understanding of certain basic concepts is sometimes required. The exam won’t expect you to know the distance between New York and Los Angeles (19,600 furlongs or so), but you should know that both cities exist. The exam will always give you conversions when it comes to distances (miles to feet, for example), temperatures (Fahrenheit to Celsius) or anything else that can be measured in different systems, but the basic concepts that any human should know are fair game on the exam.

If you think about the underlying logic, it makes sense that a business person needs to be able to reason things out, but the reasoning must also be based on tenets that people can agree on. You won’t need to know something like all the variables involved in a carbon tax or on the electoral process of Angola, but you should know that Saturday comes after Friday (and Sunday comes afterwards).

Let’s look at a relatively simple question that highlights the need to think critically about outside knowledge that may be important:

Tom was born on October 28th. On what day of the week was he born?

1) In the year of Tom’s birth, January 20th was a Sunday.
2) In the year of Tom’s birth, July 17th was a Wednesday.

A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D) Each statement alone is sufficient to answer the question.

Since this is a data sufficiency question, it’s important to note that we must only determine whether or not the information is sufficient, we do not actually need to figure out which day of the week it is. Once we know that the information is knowable, we don’t need to proceed any further.

In this case, we are trying to determine Tom’s birthday with 100% certainty. There are only 7 days in a week, but we need a reference point somewhere to determine which year it is or what day of the year another day of that same year falls (ideally October 27th!).

Statement 1 gives us a date for that same year. This should be enough to solve the problem, except for one small detail: the day given is in January. Since the Earth’s revolution around the sun is not an exact multiple of its rotation around itself, some years contain one extra day on February 29th, and are identified as leap years. The day of January 20th gives us a fixed point in that year, but since it is before February 28th, we don’t know if March 1st will be 40 days or 41 days away from January 20th.   Since this is the case, October 28th could be one of two different days of the week, depending on whether we are in a leap year, and so this statement is insufficient.

Statement 2, on the other hand, gives us a date in July. Since July is after the possible leap day, this means that the statement must be sufficient. Specifically, if July 17th was a Wednesday, then October 28th would have to be a Monday. You could do the calculations if you wanted to: there are 14 more days in July, 31 in August, 30 in September and 28 in October, for a total of 103 days, or 14 weeks and 5 days. The 14 weeks don’t change anything to the day of the week, so we must advance 5 days from Wednesday, taking us to the following Monday. Statement 2 must be sufficient, even if we don’t need to execute the calculations to be sure.

Interestingly, if you consider January 20th to be a Sunday, then you could get a year like 2013 in which the 28th of October is a Monday. 2013 is not a leap year, so July 17th is also a Wednesday and either statement would lead to the same answer. However, if you consider January 20th to be a Sunday, you could also get a year like 2008, which was a leap year, and then October 28th was a Tuesday. July 17th would no longer be a Wednesday, which is why the second statement is consistently correct whereas the first statement could lead to one of two possibilities. Some students erroneously select answer choice D, that both statements together solve this issue. While the combination of statements does guarantee one specific answer, you’re overpaying for information because statement 2 does it alone. The answer you should pick is B.

On the GMAT, it’s important that outside knowledge not be tested explicitly because it’s a test of how you think, not of what you know. However, some basic concepts may come up that require you to use logic based on things you know to be true.  You will never be undone on a GMAT question because “I didn’t know that,” but rather because “Oh, I forgot to take that into account.” The GMAT is primarily a test of thinking, and it’s important to keep in mind little pieces of knowledge that could have big implications on a question. As they say, knowing is half the battle (G.I. Joe!).

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Interpreting the Language of the GMAT

Everyone who writes the GMAT must speak English to some degree. Since English is the default language of business, the GMAT is administered exclusively in that language. Some people feel that this is unfair. If you take an exam in your mother tongue, you tend to do better than if you took the exam in your second, third or even fourth language (I consider Klingon as my fourth language). However, even if you’re a native English speaker, the GMAT offers many linguistic challenges that make many people feel that they don’t actually speak the language. (¿Habla GMAT?)

There are different ways of asking the same thing on the GMAT. Sometimes, the question is simply: Find the value of x. Other times, you get a convoluted story that summarizes to: Find the value of x. While these two questions are essentially the same, and both have the same answer, the first scenario is easier for most students to understand than the second scenario. This is because the second question is exactly the first question but with an extra step at the beginning (watch your step!), and if you don’t solve the first step, you never even get to the crux of the question.

Consider the following two problems. The first one simply asks you to divide 96 by 6. Even without a calculator, this question should take no more than 30 seconds to solve. Now consider a similar prompt: “Sally goes to the store to buy 7 dozen eggs. When she leaves the store, she accidentally drops one carton containing 12 eggs. Unable to salvage any, she goes back into the store and buys two more cartons of 12 eggs each. Once home, she separates the eggs into bags of 6, in order to save space in the fridge. How many bags of eggs does Sally make?”

The second prompt is exactly the same as the first question, but takes much longer to read through, execute rudimentary math of (7 x 12 – 12 + 24) / 6, and yield a final answer of 16. Anyone who can solve the first question should be able to solve the second question, but fewer students answer the second question correctly. Between the two is the fine art of translating GMATese (patent pending) to a simple mathematical formula. Even for native English speakers, this can be difficult, and is often the difference between getting the correct answer and getting the right answer to a different question.

Let’s look at such a question that looks like it needs to be deciphered by a team of translators:

“X and Y are both integers. If X / Y = 59.32, then what is the sum of all the possible two digit remainders of X / Y?”

A) 560
B) 616
C) 672
D) 900
E) 1024

While this question may appear to be giving you a simple formula, it’s not that easy to interpret what is being asked. One integer is being divided by another, and the result is a quotient and a remainder. The remainder is then only one of multiple possible remainders, and all these possible remainders must be summed up to give a single value. The GMAT isn’t giving us a story on this question, but there’s a lot to chew on.

First off, the quotient doesn’t actually matter in this equation. X / Y = 59.32, but it could have been 29.32 or 7.32 or any other integer quotient, the only thing we care about is the remainder. This means that essentially X/Y is 0.32, and we must find possible values for that. Clearly, X could be 32 and Y could be 100, thus leaving a remainder of 32 and the equivalent of the fractional component of 0.32 in the quotient. This could work, and is two digits, which means that it’s one possible remainder on the list that we must sum up.

What could we do next? Well if 32/100 works, then all other fractional values that can be simplified from that proportion should work as well. This means that 16/50, which is half of the original fraction, should work as well. If we divide by 2 again, we get 8/25. This value satisfies the fraction of the quotient, but not the requirement that it must be two digits. We cannot count 8 as a possible remainder, but this does help open up the pattern of the remainders.

The fraction 8/25 is the key to solving all the other fractions, because it cannot be reduced any further. From 8/25, every time we increase the numerator by 8, we can increase the denominator by 25, and we will maintain the same fractional value. As such, we can have 16/50, 24/75, 32/100, 40/125, etc, without changing the value of the fraction. How far do we need to go? Well the question is asking for 2-digit remainders, so we only need to increase the numerator by 8 until it is no longer 2-digits. The denominator can be truncated, because when it comes to 40/125, all the question wants is 40.

Once we understand what this question is really asking for, it just wants the sum of all the 2-digit multiples of 8. There aren’t that many, so you can write them all down if you want to: 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 and 96. Outside this range, the numbers are no longer 2-digits. This whole question could have been rewritten as: “Sum up the 2-digit multiples of 8” and we would have saved a lot of time (more than last month’s leap second brouhaha).

Solving for our summation is simple when we have a calculator, but there is a handy shortcut for these kinds of calculations. Since the numbers are consecutive multiples of 8, all we need to do is find the average and multiply by the number of terms. The average is the (biggest + smallest) / 2, which becomes (96 + 16) / 2 = 56. From there, we wrote out 11 terms, so it’s just 56 x 11 = 616, answer choice B.

It’s worth mentioning that there’s a formula for the number of terms as well: Take the biggest number, subtract the smallest number, divide by the frequency, and then add back 1 to account for the endpoints. This becomes ((96 – 16) /8) + 1, or (80 / 8) + 1 or 10 + 1, which is just 11.  If you only have about a dozen terms to sum up, it’s not hard to consider writing each one down, but if you had to sum up the 3-digit multiples of 8, you wouldn’t spend hours writing out all the different values (hint: there are 112). It’s always better to know the formula, just in case.

On the GMAT, you’re often faced with questions that end up throwing curveballs at you. Interpreting what the question is looking for is half the difficulty, and solving the equations in a relatively short amount of time is the other half. If all the questions were written in straight forward mathematical terms, the exam would be significantly easier. As it is, you want to make sure that you don’t give away easy points on questions that you know how to solve. On test day, the exam will ask you: “¿Habla GMAT?” and your answer should be a resounding “¡si!”

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Attack Data Sufficiency GMAT Questions from the Weakest Point

It is a common axiom that the best strategy in any competition is to attack your opponent at his weakest point. If you’ve been studying for the GMAT for any length of time, you’ve probably noticed that not all Data Sufficiency statements are created equal. At times the statements are mind-bendingly complex. Other times we can evaluate a statement almost instantaneously, without needing to simplify or calculate.

Anytime you’re confronted with a question that offers one complex statement and one simple statement, you’ll want to attack the question at its weakest point and start with the simpler of the two. Evaluating the easier statement will not only allow you to eliminate some wrong answer choices, but will offer insights into what might be happening in the more complex statement. (And generally speaking, whenever you’re confronted with this dynamic, it is more often than not the case that the complex statement is sufficient on its own.)

Let’s apply this strategic thinking to a complex-looking official problem*:

You can see immediately that the first statement is a tough one. So let’s start with statement 2. In natural language, it’s telling us that ‘x’ is less than 5 units away from 0 on the number line. So x could be 4, in which case, the answer to the question “Is x >1?” would be YES. But x could also be 0, in which case the answer to the question would be NO, x is not greater than 1. So statement 2 is not sufficient, and we barely had to think. Now we can know that the answer cannot be that 2 Alone is sufficient and it cannot be Either Alone is sufficient.

Now take a moment and think about this from the perspective of the question writer. It’s obvious that statement 2 is not sufficient. Why bother going to the trouble of producing such a complex statement 1 if this too is not sufficient? This isn’t to say that we know for a fact that statement 1 will be sufficient alone, but I’m certainly suspicious that this will be the case.

When evaluating statement 1, we’ll use some easy numbers. Say x = 100. That will clearly satisfy the statement as (100+1)(|100| – 1) is greater than 0. Because 100 is greater than 1, we have a YES to the question, “Is x >1?” Now the question is: is it possible to pick a number that isn’t greater than one, but that will satisfy our statement?  What if x = 1? Plugging into the statement, we’ll get (1+1)(|1| – 1) or (2)*(0), which is 0. Well, that doesn’t satisfy the statement, so we cannot use x = 1. (Note that we must satisfy the statement before we test the original question!) What if x = -1? Now we’ll have: (-1+1)(|-1| – 1) = 0. Again, we haven’t satisfied the statement. Maybe you’d test ½. Maybe you’d test -3. But you’ll find that no number that is not greater than 1 will satisfy the statement. Therefore x has to be greater than 1, and statement 1 alone is sufficient. The answer is A.

Alternatively, we can think of statement 1 like this: anytime we multiply two expressions together to get a positive number, it must be the case that both expressions are positive or both expressions are negative. In this statement, it’s easy to make (x+1) and (|x| – 1) both positive. Just pick any number greater than 1. However, as mentioned in the previous paragraph, we can immediately see that x=1 will make the second term 0, and x = -1 will make the first term 0. Multiplying 0 by anything will give us 0, so we can rule those options out. Moreover, we can quickly see that any number between -1 and 1 (not inclusive) will make (|x| – 1) negative and make (x+1) positive, so that range won’t work. And any term less than -1 will made (x+1) negative and (|x| – 1) positive, so that range won’t work either. The only values for x that will satisfy the condition must be greater than 1. Therefore the answer to the question is always YES, and statement 1 alone is sufficient to answer the question.

The takeaway: this question became a lot easier once we tested statement 2, saw that it obviously would not work on its own, and became suspicious that the complex-looking statement 1 would be sufficient alone. Once we’ve established this mindset, we can rely on our conventional strategies of picking numbers or using number properties to prove our intuition. Anytime the GMAT does you the favor of giving you a simple-looking statement, take advantage of that favor and adjust your strategic thinking accordingly.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# How to Interpret GMAT Critical Reasoning Questions

Interpreting what is being asked on a question is arguably the most important skill required in order to perform well on the GMAT. After all, since the topics are taken from high school level material, and the test is designed to be difficult for college graduates, the difficulty must often come from more than just the material. In fact, it is very common on the GMAT to find that you got “the right answer to the wrong question.” This phrase is so well-known that it merits quotation marks (and eventually perhaps its own reality show).

What does this expression really mean? (Rhetorical question) It means that you followed the logic and executed the calculations properly, but you inputted the wrong parameters. As an example, a problem could ask you to solve a problem about the price of a dozen eggs, but along the way, you have to calculate the price of a single egg. If you’re going too fast and you notice that there’s an answer choice that matches your result, you might be tempted to pick it without executing the final calculation of multiplying the unit price by twelve. While this expression is often used for math problems, the same concept can also be applied to the verbal section of the exam.

The question category that most often exploits erroneous interpretations of a question is Critical Reasoning. In particular, the method of reasoning subcategory appropriately named “Mimic the Reasoning”. These types of questions are reminiscent of SAT questions (or LSAT questions for some) and hinge on properly interpreting what is actually stated in the problem.

Let’s look at an example to highlight this issue:

Nick: The best way to write a good detective story is to work backward from the crime. The writer should first decide what the crime is and who the perpetrator is, and then come up with the circumstances and clues based on those decisions.

Which one of the following illustrates a principle most similar to that illustrated by the passage?

A) When planning a trip, some people first decide where they want to go and then plan accordingly, but, for most of us, much financial planning must be done before we can choose where we are going.
B) In planting a vegetable garden, you should prepare the soil first, and then decide what kind of vegetables to plant.
C) Good architects do not extemporaneously construct their plans in the course of an afternoon; an architectural design cannot be divorced from the method of constructing the building.
D) In solving mathematical problems, the best method is to try out as many strategies as possible in the time allotted. This is particularly effective if the number of possible strategies is fairly small.
E) To make a great tennis shot, you should visualize where you want the shot to go. Then you can determine the position you need to be in to execute the shot properly.

This type of question is asking us to mimic, or copy, the line of reasoning even though the topic may be totally different. The issue is thus to interpret the passage, paraphrase the main ideas in our own words, and then determine which answer choice is analogous to our summary. Theoretically, there could be thousands of correct answers to a question like this, but the GMAT will provide us with four examples to knock out and one correct interpretation (though sometimes it feels like a needle in a haystack).

Let’s look at the original sentence again and try to interpret Nick’s point. The first sentence is: The best way to write a good detective story is to work backward from the crime. This means that, wherever we want to go, we should recognize that we should start at the end and work our way backwards. This is a similar principle as solving a maze (or reading “Of Mice and Men”). The second sentence is: The writer should first decide what the crime is and who the perpetrator is, and then come up with the circumstances and clues based on those decisions. This means that, once we know the ending, we can layer the text with hints so that the ending makes sense to the audience. Astute readers may even guess the ending based on the clues (R+L = J), and will feel rewarded for their keen observations.

Summarizing this idea, the author wants us to start at the end and work our way backwards so that we end up exactly where we want. The next step is to apply this logic to each answer choice in turn:

For answer choice A, when planning a trip, some people first decide where they want to go and then plan accordingly, but, for most of us, much financial planning must be done before we can choose where we are going, the first part about choosing a destination is perfect. However, the second part goes off the rails by introducing a previously unheralded concept: limitations. The author was not initially worried about limitations, financial or otherwise, so answer choice A is half right, which is not enough on this test. We can eliminate A.

Answer choice B, in planting a vegetable garden, you should prepare the soil first, and then decide what kind of vegetables to plant. While this is good general advice, it has nothing to do with our premise. Starting with the soil is the very definition of starting at the beginning. A more correct (plant-based) answer choice would state that we want to start with which plants we want in the garden and then work backwards to find the right soil. This is incorrect, so answer choice B is out.

Answer choice C, good architects do not extemporaneously construct their plans in the course of an afternoon; an architectural design cannot be divorced from the method of constructing the building, changes the timeline (much like Terminator Genysis). We must consider both issues simultaneously, which is not what the original passage postulated. We can eliminate answer choice C.

Answer choice D is: in solving mathematical problems, the best method is to try out as many strategies as possible in the time allotted. This is particularly effective if the number of possible strategies is fairly small. This is not only incorrect, but particularly bad advice for aspiring GMAT students. In fact, the author is describing backsolving, because we are starting at the answer and working our way backwards. We are not proposing “throw everything at the wall and see what sticks”. Answer D is out.

This leaves answer choice E, to make a great tennis shot, you should visualize where you want the shot to go. Then you can determine the position you need to be in to execute the shot properly. Not only must it be the correct answer given that we’ve eliminated the other four selections, but also it perfectly recreates the logic of planning backwards from the end. Answer choice E is the correct selection.

For method of reasoning questions, and on the GMAT in general, it’s very important to be able to interpret wording. If you cannot paraphrase the statements presented, then you won’t be able to easily eliminate incorrect answer choices. Part of acing the GMAT is not giving away easy points on questions that you actually know how to solve. If you read carefully and paraphrase concepts as they come up, you’ll be interpreting a high score on test day.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 99th Percentile GMAT Score or Bust! Lesson 5: Procrastinate to Calculate

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

First, take a look at Lesson 1, Lesson 2, Lesson 3, and Lesson 4!

Lesson Five:

Procrastinate to Calculate: in much of your academic and professional life, it’s a terrible idea to procrastinate.  But on the GMAT?  Procrastination is often the most efficient way to do math.  In this video, Ravi will demonstrate why waiting until it’s absolutely necessary to do math is a time-saving and accuracy-boosting strategy. So whatever it is you would be doing right now, put that off for later and immediately watch this video. The sooner you learn that procrastination is your friend on the GMAT, the more time you’ll save.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

By Brian Galvin

# The Importance of Recognizing Patterns on the GMAT

In life, we often see certain patterns repeat over and over again. After all, if everything in life were unpredictable, we’d have a hard time forecasting tomorrow’s weather or how long it will take to go to work next week. Luckily, many patterns repeat in recurring, predictable patterns. A simple example is a calendar. If tomorrow is Friday, then the following day will be Saturday, and Sunday comes afterwards (credit: Rebecca Black). Moreover, if today is Friday, then 7 days from now will also be Friday, and 70 days from now will also be Friday, and onwards ad infinitum (even with leap years). These patterns are what allow us to predict things with 100% certainty.

Some patterns are inexact, or can change dramatically based on external factors. If you think of the stock market or the weather, people often have a general sense of prediction but it is hardly an exact science. Some patterns are more rigid, but can still fluctuate a little. Your work schedule or the weekly TV guide tend to remain the same for long stretches of time, but are not always exactly the same year over year. Finally, there are patterns that never change, like the Earth’s rotation or the number of days in a year (accounting for the dreaded leap year). These patterns are rigid, and can be forecasted decades ahead of time.

On the GMAT, this same concept of rigid prediction is utilized to solve mathematical questions that would otherwise require a calculator. A common example would be to ask for the unit digit of a huge number, as something like 15^16 is far too large to calculate quickly on exam day, but the unit digit pattern can help provide the correct answer. Given any number that ends with a 5, if we multiply it by another number that ends with a 5, the unit digit will always remain a 5. This pattern will never break and will continue uninterrupted until you tire of calculating the same numbers over and over. A similar pattern exists for all numbers that end in 0, 1, 5 or 6, as they all maintain the same unit digit as they are squared over and over again.

For the other six digits, they all oscillate in predetermined patters that can be easily observed. Taking 2 as an example, 2^2 is 4, and 2^3 is 8. Afterwards, 2^4 is 16, and then 2^5 is 32. This last step brings us back to the original unit digit of 2. Multiplying it again by 2 will yield a unit digit of 4, which is 64 in this case. Multiplying by 2 again will give you something ending in 8, 128 in this case. This means that the units digit pattern follows a rigid structure of 2, 4, 8, 6, and then repeats again. So while it may not be trivial to calculate a huge multiple of 2, say 2^150, its unit digit can easily be calculated using this pattern.

Let’s look at a problem that highlights this pattern recognition nicely:

What is the units digit of (13)^4 * (17)^2 * (29)^3?

(A) 9
(B) 7
(C) 4
(D) 3
(E) 1

Looking at this question may make many of you wish you had access to a calculator, but the very fact that you don’t have a calculator on exam day is what allows the GMAT to ask you a question like this. There is no reasoning, no shrewdness, required to solve this with a calculator. You punch in the numbers, hope you don’t make a typo and blindly return whatever the calculator displays without much thought (like watching San Andreas). However, if you’re forced to think about it, you start extrapolating the patterns of the unit digit and the general number properties you can use to your advantage.

For starters, you are multiplying 3 odd numbers together, which means that the product must be odd. Given this, the answer cannot possibly be answer choice C, as this is an even number. We’ve managed to eliminate one answer choice without any calculations whatsoever, but we may have to dig a little deeper to eliminate the other three.

Firstly, recognize that the unit digit is interesting because it truncates all digits other than the last one. This means this is the same answer as a question that asks: (3^4) * (7^2) * (9^3). While we could conceivably calculate these values, we only really need to keep in mind the unit digit. This will help avoid some tedious calculations and reveal the correct answer much more quickly.

Dissecting these terms one by one, we get:

3^4, which is 3*3*3*3, or 9*9, or 81.

7^2, which is just 49.

9^3, which is 9*9*9, or 81 * 9, or 729.

The fact that we truncated the first digit of the original numbers changes nothing to the result, but does serve to make the calculations slightly faster. Furthermore, we can truncate the tens and hundreds digits from this final calculation and easily abbreviate:

81 * 49 * 729 as

1 * 9 * 9.

This result again gives 81, which has a units digit of 1. This means that the correct answer ends up being answer choice E. It’s hard to see this without doing some calculations, but the amount of work required to solve this question correctly is significantly less than what you might expect at first blush. An unprepared student may approach it by calculating 13^4 longhand, and waste a lot of time getting to an answer of 28,561. (What? You don’t know 13^4 by heart?) Especially considering that the question only really cares about the final digit of the response, this approach is clearly more dreary and tedious than necessary.

The units digit is a favorite question type on the GMAT because it can easily be solved by sound reasoning and shrewdness. In a world where the biggest movie involves Jurassic Park dinosaurs and a there is a Terminator movie premiering in a week, it’s important to note that trends recur and form patterns. Sometimes, those patterns are regular enough to extrapolate into infinity (and beyond!).

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# The GMAT Shortcut That Can Help You Solve a Variety of Quantitative Questions

One thing I’m constantly encouraging my students to do is to seek horizontal connections between seemingly disparate problems. Often times, two quantitative questions that would seem to fall into separate categories can be solved using the same approach. When we have to sift through dozens of techniques and strategies under pressure, we’re likely to become paralyzed by indecision. If, however, we have a small number of go-to approaches, we can quickly consider all available options and arrive at one that will work in any given context.

One of my favorite shortcuts that we teach at Veritas Prep, and that will work on a variety of questions, is to use a number line to find the ratio of two elements in a weighted average. Say, for example, that we have a classroom of students from two countries, which we’ll call “A” and “B.” They all take the same exam. The average score of the students from country A is 92 and the average score of the students from country B is 86. If the overall average is 90, what is the ratio of the number of students from A to the number of students in B? We could solve this algebraically. If we call the number of students from county A, “a” and the number of students from country B “b,” we’ll have a total of a + b students, and we can set up the following chart.

 Average Number of Terms Sum Country A 92 a 92a Country B 86 b 86b Total 90 a + b 90a + 90b

The sum of the scores of the students from A when added to the sum of the scores of the students from B will equal the sum of all the students together. So we’ll get the following equation: 92a + 86b = 90a + 90b.

Subtract 90a from both sides: 2a + 86b = 90b

Subtract 86b from both sides: 2a = 4b

Divide both sides by b: 2a/b = 4

Divide both sides by 2: a/b =4/2 =2/1. So we have our ratio. There are twice as many students from A as there are from B.

Not terrible. But watch how much faster we can tackle this question if we use the number line approach, and use the difference between each group’s average and the overall average to get the ratio:

b              Tot       a

86——–90—-92

Gap:  4           2

Ratio a/b = 4/2 = 2/1. Much faster. (We know that the ratio is 2:1 and not 1:2 because the overall average is much closer to A than to B, so there must be more students from A than from B. Put another way, because the average is closer to A, A is exerting a stronger pull. Generally speaking, each group corresponds to the gap that’s farther away.)

The thing to see is that this approach can be used on a broad array of questions. First, take this mixture question from the Official Guide*:

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%
B. 33 1/3%
C. 40%
D. 50%
E. 66 2/3%

In a mixture question like this, we can focus exclusively on what the mixtures have in common. In this case, they both have ryegrass. Mixture X has 40% ryegrass, Mixture Y has 25% ryegrass, and the combined mixture has 30% ryegrass.

Using a number line, we’ll get the following:

Y          Tot             X

25—–30———40

Gap: 5             10

So our ratio of X/Y = 5/10 = ½. (Because X is farther away from the overall average, there must be less X than Y in the mixture.) Be careful here. We’re asked what percent of the overall mixture is represented by X. If we have 1 part X for every 2 parts of Y, and we had a mixture of 3 parts, then only 1 of those parts would be X. So the answer is 1/3 = 33.33% or B.

So now we see that this approach works for the weighted average example we saw earlier, and it also works for this mixture question, which, as we’ve seen, is simply another variation of a weighted average question.

Let’s try another one*:

During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

a) 180
b) 170
c) 156
d) 150
e) 105

First, we’ll plot the win percentages on a number line.

Remaining             Total           First 100

50—————70———-80

Gap           20                     10

Remaining Games/First 100 = 10/20  = ½.

Put another way, the number of the remaining games is ½ the number of the first 100. That means there must be (½) * 100 = 50 games remaining. This gives us a total of 100 + 50 = 150 games played. The answer is D.

Note the pattern of all three questions. We’re taking two groups and then mixing them together to get a composite. We could have worded the last question, “mixture X is 80% ryegrass and weighs 100 grams, and mixture Y is 50% ryegrass. If a mixture of 100 grams of X and some amount of Y were 70% ryegrass, how much would the combined mixture weigh?” This is what I mean by making horizontal connections. One problem is about test scores, one is about ryegrass, and one is about baseball, but they’re all testing the same underlying principle, and so the same technique can be applied to any of them.

Takeaway: always try to pay attention to what various questions have in common. If you find that one technique can solve a variety of questions, this is a technique that you’ll want to make an effort to consciously consider throughout the exam. Any time we’re stuck, we can simply toggle through our most useful approaches. Can I pick numbers? Can I back-solve? Can I make a chart? Can I use the number line? The chances are, one of those approaches will not only work but will save you a fair amount of time in the process.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# The Easiest Type of Reading Comprehension Question on the GMAT

Reading comprehension questions on the GMAT are primarily an exercise in time management. If you gave yourself 30 minutes to complete a single Reading Comprehension passage along with four questions, you would find the endeavour very easy. Most questions on the GMAT feature some kind of trap, trick or wording nuance that could easily lead you astray and select the wrong answer. Reading Comprehension questions, while occasionally tricky, are typically the most straightforward questions on the entire exam.

So why doesn’t everyone get a perfect score on these questions? Often, it’s simply because they are pressed for time. Reading a 300+ word passage and then answering a question about the subject matter may take a few minutes, especially if English isn’t your first language or you’re not a habitual reader (you’ve only read Game of Thrones once?). Add to that the possibility of two or three answer choices seeming plausible, and you frequently waste time re-reading the same paragraphs over and over again in the passage.

Luckily, there is one type of question in Reading Comprehension that rarely requires you to revisit the passage and search for a specific sentence. Universal questions ask about the passage as a whole, not about specific actions, passages or characters. I often define universal questions as the “Wikipedia synopsis” (or Cliff’s notes for the older generation) of the passage. The question is concerned with the overarching theme of the passage, not about a single element. As such, it should be easy to answer these questions after reading the passage only once as long as you understood what you were reading.

Let’s delve into this further using a Reading Comprehension passage (note: this is the same passage I used previously for function, specific and inference questions).

Nearly all the workers of the Lowell textile mills of Massachusetts were unmarried daughters from farm families. Some of the workers were as young as ten. Since many people in the 1820s were disturbed by the idea of working females, the company provided well-kept dormitories and boarding-houses. The meals were decent and church attendance was mandatory. Compared to other factories of the time, the Lowell mills were clean and safe, and there was even a journal, The Lowell Offering, which contained poems and other material written by the workers, and which became known beyond New England. Ironically, it was at the Lowell Mills that dissatisfaction with working conditions brought about the first organization of working women.

The mills were highly mechanized, and were in fact considered a model of efficiency by others in the textile industry. The work was difficult, however, and the high level of standardization made it tedious. When wages were cut, the workers organized the Factory Girls Association. 15,000 women decided to “turn out”, or walk off the job. The Offering, meant as a pleasant creative outlet, gave the women a voice that could be heard by sympathetic people elsewhere in the country, and even in Europe. However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families. The same limitation hampered the effectiveness of the Lowell Female Labor Reform Association (LFLRA), organized in 1844.

No specific reform can be directly attributed to the Lowell workers, but their legacy is unquestionable. The LFLRA’s founder, Sarah Bagley, became a national figure, testifying before the Massachusetts House of Representatives. When the New England Labor Reform League was formed, three of the eight board members were women. Other mill workers took note of the Lowell strikes, and were successful in getting better pay, shorter hours, and safer working conditions. Even some existing child labor laws can be traced back to efforts first set in motion by the Lowell Mill Women.

The primary purpose of the passage is to do which of the following?

(A) Describe the labor reforms that can be attributed to the workers at the Lowell mills
(B) Criticize the proprietors of the Lowell mills for their labor practices
(C) Suggest that the Lowell mills played a large role in the labor reform movement
(D) Describe the conditions under which the Lowell mills employees worked
(E) Analyze the business practices of early American factories

The most frequent universal question you’ll see is something along the lines of “what is the primary purpose of this passage”. In essence, it’s asking you to summarize the 300+ word passage into one sentence, and that is difficult to do if you don’t remember anything about the passage. Ideally, you retained the key elements during your initial read. If need be, you can reread the passage, noting the main point of each paragraph in about five words. The synopsis of each paragraph, especially the last one, should give you a good idea about the overall goal of the passage.

In this passage, each paragraph is talking about the labour strife at the Lowell textile mills of Massachusetts in the 1820s. The first paragraph describes the conditions at the mill and sets the stage, the second paragraph describes the worker strike and subsequent resolution, and the third paragraph discusses the legacy of these workers. The overall theme has to capture the spirit of the entire passage, which is often summarized in the final paragraph (often the author’s conclusion). Pay special attention to that paragraph in order to determine why the author wrote this text and what he or she wanted you to learn from it.

Let’s look at the answer choices in order. Answer choice A, describe the labor reforms that can be attributed to the workers at the Lowell mills, is a popular incorrect answer. The goal of the passage is to shed light on these events, and describing the labor reforms attributed to these workers seems like a good conclusion, but it is specifically refuted by the first line of the third paragraph: “No specific reform can be directly attributed to the Lowell workers…” This means that answer choice A, while tempting, is hijacking the actual conclusion of the passage, as we cannot describe things that do not exist, and is therefore incorrect.

Answer choice B, criticize the proprietors of the Lowell mills for their labor practices, seems like something the reader could agree with, but is completely out of the scope of the passage. The mill is not being scrutinized for their labor practices; rather, the efforts of certain people are being underlined. If anything, the text suggests that the conditions at this mill were better than most at the time (and still today in certain countries). Answer choice B is somewhat righteous, but ultimately wrong in this passage.

Answer choice C, suggest that the Lowell mills played a large role in the labor reform movement, is supported by what is being said in the final paragraph. The legacy of the Lowell mills is being discussed, and since other workers were inspired by the events that transpired at these mills, the Lowell mills played a significant part in the larger labor reform movement. While this answer focuses somewhat on the third paragraph, don’t forget that the final paragraph has the most sway in the majority of passages, just as the last section of a movie is usually the most important section (the denouement, in proper English). Answer choice C is correct here, as the passage is primarily discussing the legacy of these events.

Let’s continue on for completion’s sake. Answer choice D, describe the conditions under which the Lowell mills employees worked, focuses on one small portion of the first paragraph, and even then the conditions are not covered in great detail. It’s a big stretch to try and claim that this is the primary focus of the entire passage, and thus can be eliminated fairly quickly.

Answer choice E, analyze the business practices of early American factories, is an answer choice that seems to bring some larger context to the passage, but is even more out of scope than answer choice B because it’s much broader. Only one mill is being examined in the passage, and its business practices were not even the main focus of the passage, so broadening the scope to all American factories is certainly incorrect. Answer choice E can also be eliminated, leaving only answer choice C as the correct selection.

Generally, universal questions do not require a rereading of the passage as the questions are primarily concerned with the broad strokes of the passage. If you didn’t grasp the major facets of the passage when reading through it, you probably didn’t understand the passage at all. If you understand the major elements of the passage as you read through it the first time, noting the primary purpose of each paragraph as you go along, you’ll be ready for any question in the universe.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# The Importance of Sorting Answer Choices on the GMAT

On the GMAT, as in life, you have multiple choices you can make at every juncture you face. On the standardized test, your choices are limited to only five, which is more manageable than the plethora of choices you encounter every day. However, even five answer choices can cause a lot of frustration for people who have difficulty differentiating among them.

The good news is, the exam is mandated to have five different answer choices on every question, but some of these answer choices are redundant. While you won’t actually see the same answer choice twice on the test (unless you’re seeing double), many answer choices don’t differ from another answer choice in a meaningful way.

As an example, if you’re looking for the product of two even integers, such as 4 and 6, you know the product can never be odd. So while one answer choice may be 25 and another may be 33, they can both be eliminated for the same reason, greatly streamlining your task if you’re eliminating possible answer choices based on sound reasoning. Sometimes, a question may have two or three answer choices you can eliminate without having to do any math, as long as you can sort multiple answers into the same bucket (think Gryffindor).

Let’s look at such a question and how we can consider eliminating answer choices without actually calculating them longhand:

If x^4 > x^5 > x^3, which one could be the value of x?

A) -3

B) -2

C) -2/3

D) 2/3

E) 3

This question seems complicated because it is very abstract. We’re dealing with some unknown variable x raised to various uncomfortable powers. A great strategy here would be to try and make it easier to understand by using actual numbers. This will allow us to better visualize what is actually happening in the problem.

Let’s begin with the base case. Say we set x to be a simple positive integer, such as 2. If we square 2, we get 4. If we multiply by 2 again, we get 8. This is 2^3. We can continue by multiplying by 2 again and getting 16 for 2^4, and one final time to get 32 for 2^5. It should come as no surprise that the variable gets bigger as the powers increase.

However, this situation does not satisfy our original premise of x^4 > x^5 > x^3 because x^5 is the biggest value. Beyond eliminating the number 2 from contention, we can eliminate 3, 4, and every other positive integer bigger than 1. This is because all positive integers greater than one will increase in amplitude as the powers increase. Knowing this, we can eliminate answer choice E, which follows the same mould.

The remaining answer choices seem to either be negative, fractional or both. We might also recognize that numbers smaller than 1 will follow a different pattern, because successive increases in power will make the number smaller and smaller. Furthermore, negative numbers can break the pattern as well, as they will oscillate between positive results for even powers and negative results for odd powers. In fact, these two axes will be the only determining factors in identifying the correct result. The answer will be only one of the following structures: positive and less than 1, negative and less than 1, positive and more than 1, or negative and more than 1. Our job is to sort these out (like the sorting hat at Hogwarts).

We have already observed that positive and greater than 1 doesn’t satisfy the given inequality, so let’s look at positive and less than 1. We can take ½ as an example and extrapolate that to any result 0 > x > 1. If we square ½, we get ¼. If we continue to multiply by ½, we get 1/8, 1/16 and 1/32 respectively. Unsurprisingly, these are the reciprocals of the values found for x = 2. This batch doesn’t satisfy the inequality either, as x^3 is actually the biggest number here. This eliminates answer choice D. If it’s not obvious, the relative sizes of the exponents are easier to see if we use the number line:

___________________________________________________________________

0     1/32           1/16                      1/8                                                                                                             1

x^5            x^4                      x^3

Now that we’ve eliminated two possibilities (Hufflepuff and Ravenclaw), let’s look at the remaining choices: -3, -2 and -2/3. At this point, it should make sense that all negative numbers with absolute value greater than 1 will behave the exact same way in this inequality. This means that the answer cannot be either -3 or -2, as they are indistinguishable inputs on this question (also both Slytherin). Thus, if -2 worked, so would -3, and vice versa. Since only one answer choice can be correct, neither of these will be correct, and the answer must be -2/3. Let’s go through the calculation to confirm, but we already know it must be correct.

When we square a negative number, we are multiplying a negative by a negative and yielding a positive. When we multiply that number by a negative again, we revert to negative numbers. Thus, every odd numbered power will be negative and every even numbered power will be positive. Knowing this, we can easily calculate that x = -2/3, then x^2 = 2^2/3^2. Multiplying by -2/3 again, we get -2^3/3^3 for x^3. The next values will be 2^4/3^4 for x^4 and -2^5/3^5 for x^5. If it’s easier to see, you can calculate each of these values and get:

x^2 = 4/9

x^3 = -8/27

x^4 = 16/81

x^5 = -32/243

Using the number line again as a visual aid (roughly to scale):

________________________________________________________________________

-1                                           -8/27                    -32/243        0                   16/81                                                      1

x^3                       x^5                                      x^4

This confirms that x^4 is the biggest (most to the right) value while x^3 is the smallest and x^5 is the middle value. This also highlights the issue that -2 and -3 would have, as the amplitude increases, x^5 would be much smaller than x^3. Of the choices given, the only value that works is answer choice C: -2/3.

On the GMAT, one of the five answer choices must always be correct, but the other four can give you insight into what you should consider to solve the question. Oftentimes, you can figure out what the key issues are by perusing the choices provided. And more often than not, you can eliminate swaths of answer choices based on a logical understanding of the question. On test day, you don’t want to waste time considering answer choices that are obviously incorrect. If you can sort through the various answer choices quickly, you’ll end up in the house of your choice (I’d opt for Gryffindor).

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 99th Percentile GMAT Score or Bust! Lesson 4: Think Like a Lawyer on Critical Reasoning

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

Lesson Four:

Think Like a Lawyer.  Your natural inclination is to just click “I agree” to the iTunes Terms & Conditions, but to lawyers each word in that agreement is carefully chosen to build a case.  Thankfully, on the GMAT the Critical Reasoning problems you see will be 99% shorter than those Terms & Conditions, but you’ll need to train yourself to think like a lawyer and notice how carefully chosen those words in the prompt are.  In this video, Ravi will demonstrate how his law degree has helped him become a master of GMAT Critical Reasoning, and how you can summon your inner Elle Woods (or Johnnie Cochran) to conquer CR, too.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Want to learn more from Ravi? He’s taking his show on the road for one-week Immersion Courses in San Francisco and New York this summer, and teaches frequently in our new Live Online classroom.

By Brian Galvin

# Avoid the Tempting Trap Answer on GMAT Questions

When looking through answer choices on Critical Reasoning questions, there is always one correct answer to the question. After all, it wouldn’t be fair if two different answers were both legitimate responses to the query being posed. However, just because the other four answers are incorrect, it doesn’t mean that they aren’t tempting. In fact, there is usually one choice the exam is pointing you towards selecting, even though it isn’t the correct option. This is often referred to as the sucker choice.

The sucker choice is an answer that seems to answer the question on the surface, but in actuality it is only a red herring. Answers like this will frequently provide redundant information, or play into your preconceived notions. As an example, if a couple has two children, and you’re told that child A is taller than child B, you’d naturally think that child A is older than child B. However, this doesn’t have to be the case, as the children could be adults (ironic, no?). A taller child does not necessarily imply an older child, but it’s certainly an assumption a lot of people would make.

Other examples of the sucker choice involve providing known information on a strengthen/weaken question, or giving an answer choice that seems reasonable but not 100% assured on an inference question. The choices will always seem reasonable, and in many cases, they will be the most popular answer choices selected. In many ways, the sucker answer choice is like smoking. It seemed like a good idea at the time, it feels good, and it can be bad for your (GMAT) health long term.

Let’s look at a question that deals with this very topic:

A system-wide county school anti-smoking education program was instituted last year. The program was clearly a success. Last year, the incidence of students smoking on school premises decreased by over 70 percent.

Which of the following, if true, would most seriously weaken the argument in the passage?

(A) The author of this statement is a school system official hoping to generate good publicity for the anti-smoking program.
(B) Most students who smoke stopped smoking on school premises last year continued to smoke when away from school.
(C) Last year, another policy change made it much easier for students to leave and return to school grounds during the school day.
(D) The school system spent more on anti-smoking education programs last year than it did in all previous years.
(E) The amount of time students spent in anti-smoking education programs last year resulted in a reduction of in-class hours devoted to academic subjects

On this Critical Reasoning weaken question, it’s important to note the conclusion and the supporting evidence. The conclusion is the middle sentence (The program was clearly a success) as that is unmistakably the author’s main point in this passage. The evidence is everything else, but especially the last sentence, because a decrease of 70% of student smoking on the premises would seem to support the author’s conclusion. We’re tasked with weakening this conclusion, so we must find evidence that refutes this evidence or otherwise makes the conclusion less likely to occur.

There is one trap answer on this question that a lot of students gravitate towards. I’ll let you reread the choices to see which one you singled out (cue jeopardy music).

The answer choice that most people like is B: students who smoke stopped smoking on school premises last year continued to smoke when away from school. After all, the logic seems sound. If students stopped smoking at school, and we’re trying to weaken the conclusion, then it would follow that students smoking everywhere else (at home, in the street, at the Peach Pit…) would weaken the conclusion. Furthermore, this is new evidence that seems to perfectly solve every element we care about. Many students select B here and move on with nary a thought that they just fell into a GMAT trap. (It’s a trap!)

Let’s re-examine the conclusion. The conclusion stated that the program was a success, and the program was defined as a county school anti-smoking education program. This means that the students were being educated in an effort to reduce smoking at school. If incidents of smoking at school decreased by 70%, then the program was a success, regardless of whether the students were smoking elsewhere. Indeed, the goal of the program was to reduce smoking in school, and answer choice B does not weaken that conclusion. It weakens the goal of curbing out smoking altogether, but that is a slightly different conclusion that is beyond the scope of this particular argument.

As such, answer choice B seems like a logical answer, but fails to meet the necessary criteria to be the right response. This means that we need to peruse the other four answer choices to identify the correct choice.

Answer choice A, “the author of this statement is a school system official hoping to generate good publicity for the anti-smoking program”, implies that the author may have a hidden agenda. While this may be true, it doesn’t account for the 70% decrease of on-campus smoking, so it doesn’t do a good job of weakening the argument given the evidence presented. We can eliminate this choice.

Answer choice C, “Last year, another policy change made it much easier for students to leave and return to school grounds during the school day” does indeed weaken this argument. If your only evidence is the decrease in smoking on campus, then any alternative explanation as to why that happened weakens your argument. The students may not be smoking on the grounds anymore, but they are still smoking at school, just a little further away than before. Indeed, the smoking policy may have had absolutely no effect on students’ habits whatsoever, greatly weakening the conclusion.

Answer choice D, “The school system spent more on anti-smoking education programs last year than it did in all previous years” actually somewhat strengthens the argument. If the school system put a lot of money into the program, then it would be more likely to succeed. Even if the school overspent, the success of the program is determined by the students’ smoking habits, not the program’s budget.

Answer choice E, “the amount of time students spent in anti-smoking education programs last year resulted in a reduction of in-class hours devoted to academic subjects” is also somewhat tempting, because it introduces the concept of side-effects. In the real world, we might do something that has unintended consequences, and look back on the decision as a mistake. Side effects don’t affect the success rate of the program, so this answer choice can be eliminated.

As we saw, answer choice C is the correct selection. However, it may not be the most common selection on this exam, as another answer choice was more enticing for a lot of students. The GMAT is designed to provide tempting answer choices that almost solve the issue at hand, but fall short in one crucial measure. On test day, be wary of these tempting sucker choices, or your exam score will go up in smoke.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 2 Ways to Improve Your Pattern Recognition on GMAT Questions

In 1946, a fascinating study about chess masters revealed that, for the most part, they had unexceptional working memories. This finding flew in the face of conventional wisdom, which held that chess masters must have had photographic memories to absorb thousands and thousands of scenarios they’d encountered throughout their years of training. Instead of relying on superior recall, it turns out that they were simply better than most at recognizing patterns.

Similarly, for all the dizzying content the GMAT requires you to internalize, the exam, more than anything else, is about pattern recognition. There are two ways we can improve at pattern recognition. The first, and most obvious, is that by doing many practice questions, our brains, like those of the aforementioned chess masters, will subconsciously absorb recurring patterns.

The second is to learn to recognize certain signposts and triggers that indicate what’s being tested. In Sentence Correction, for example, there are certain classic trigger words for parallel construction, such as “both,” “either/or,” and “not only/but also.” As soon as we see one of these constructions, we can immediately zero in on this part of the sentence and evaluate whether the items that follow the signpost are parallel to one another. If a phrase begins with “both in x,” for example, I know I want to see the parallel construction, “and in y,” in that same sentence. All of the other grammatical, stylistic, and logical considerations can temporarily be put aside. Once I’ve resolved this issue, if I’m left with more than one answer choice, I’ll look for other differences, but I’ll likely have narrowed my possibilities so much that the problem will be much less taxing than it would have been otherwise.

Take this Official Guide* problem, for example:

Many of the earliest known images of Hindu deities in India date from the time of the Kushan empire, fashioned either from the spotted sandstone of Mathura or Gandharan grey schist.

A) Empire, fashioned either from the spotted sandstone of Mathura or
B) Empire, fashioned from either the spotted sandstone of Mathura or from
C) Empire, either fashioned from the spotted sandstone of Mathura or
D) Empire and either fashioned from the spotted sandstone of Mathura or from
E) Empire and were fashioned either from the spotted sandstone of Mathura or from

The moment I see that “either” I’m focusing on this part of the sentence. Now watch how quickly I can eliminate incorrect options:

A) “either from spotted sandstone of Mathura or grey schist.” I want “either from x” or “from” I don’t have a second “from” here. A is out.

B) “either the spotted sandstone of Mathura or from grey schist.” See what they did here. Parallel construction begins when we see the parallel marker “either.” Now there is no “from” before the first item, but we do have it before the second one. “either x or from y” is not parallel. B is out.

C) “either fashioned from the spotted sandstone of Mathura or gray schist” Now we’re back to the original error of having “from x or y” rather than the desired “from x or from y.” C is out.

D) “either fashioned from the spotted sandstone of Mathura or from grey” A little better. We’d prefer “either fashioned from x or fashioned from y,” but at least we have the preposition “from” in front of both items. But now read that full first clause, “Many of the earliest known images of Hindu deities in India date from the time of the Kushan Empire and either fashioned from the spotted sandstone…” Well, that doesn’t make any sense. We’d want to say that the images date from the time of the Kushan Empire and were fashioned from the spotted sandstone. Without the verb “were,” the sentence is incoherent. Eliminiate D.

E) “either from the spotted sandstone of Mathura or from grey schist.” Now we see it. “either from x or from y.” We have our parallel construction. E is correct.

Let’s try another example*:

Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.

A) Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted
B) Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both
C) Jazz pianist and composer Thelonious Monk, who produced a body of work rooted
D) Jazz pianist and composer Thelonious Monk produced a body of work that was rooted
E) Jazz pianist and composer Thelonious Monk produced a body of work rooted both

Again, we see one of the parallel trigger words. In this case, “both.” So the first thing I’ll do is examine the items that follow the parallel marker, “both rooted in the stride piano tradition.” If I begin a phrase with “rooted in x” I’ll want to follow that with “in y.” Notice that not only does the original sentence fail to do this, but the portion of the sentence we wish to change isn’t even underlined! Because we cannot produce a parallel construction here, we’ll need to eliminate the parallel marker “both” altogether. That means A, B, and E are all out. Now let’s evaluate C and D.

C) the clause, “who produced a body of work…” is set off by commas and functions as a modifier of Thelonious Monk. This means that the clause is incidental to the meaning of the sentence. But if we read the sentence without the modifier, we get, “Jazz pianist and composer Thelonious Monk, yet in many ways he stood apart from the mainstream jazz repertory.” Well, that doesn’t make any sense. “Yet” should connect two full clauses, but in this case, it connects the noun phrase, “Jazz pianist and composer Thelonious Monk” to the full clause, “in many ways he stood apart from the mainstream jazz repertory.” This is incoherent. Eliminate C.

That leaves us with D, which is our answer. Recognizing the pattern and focusing on parallel construction allowed us to ignore the rest of what was a fairly complex sentence.

Takeaways: The GMAT is less a test of memorization than it is an exercise in pattern recognition. There’s no getting around having to see many examples of questions to prime our brains to recognize these patterns on test day, but there are certain structural clues that provide insight into what a particular question is testing. If we internalize those structural clues, suddenly the patterns we’re tasked with recognizing become far more conspicuous.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# Don’t Let Your Prior Knowledge Get in the Way on GMAT Questions

As a true Canadian, I’m always on the lookout for questions that are specifically about Canada. Sometimes a question is about trains travelling from Toronto to Montreal, and other times a Reading Comprehension passage deals with a certain Canadian prime minister. Sometimes, the question is just very polite!

Whatever the Canadian content, I’m always happy to see a question concerning something I already know, because I feel like I start with a leg up on the question. Indeed, I’m motivated whenever I see a question about a familiar topic, but I’m particularly excited when it’s aboot Canada (see what I did there?).

In actuality, questions that arouse your own interests can be dangerous. This is because they can sometimes cloud your judgment or make you feel like you know something that isn’t explicitly stated in the text (I know a 6 cylinder car accelerates faster than 4 cylinder car…). While this may be true in the real world, don’t forget that you can’t bring any outside knowledge with you to the GMAT.

The reason behind this is simple: anybody should be able to solve the question with the information provided in the question. Yes, you might already know something pertinent to the situation, but you cannot use it to solve the question unless it’s explicitly stated in the question. Especially on Critical Reasoning questions, these red herrings can come influence your decision without you even noticing it.

This doesn’t mean that you can’t get excited when a question mentions your favorite team; it just means that you have to maintain your objectivity regardless. I may be one of very few people who get excited when he sees a GMAT question about hockey, but as a Canadian I have to a duty to share as much hockey as possible with the world (and sing the national anthem before every home game).

There are 16 teams in a hockey league and each team plays each of the others once. Given that each game is played by two teams, how many total games will be played?

A) 120
B) 169
C) 196
D) 230
E) 256

Now, ignoring that most leagues don’t play perfect round-robin tournaments because they are time consuming, but this question could be adopted to any sport of choice (perhaps even WWE wrestling) and would be solved the same way. I enjoy the casual mention of hockey in this problem, but you’re free to imagine your favorite sport instead if it makes seeing the pattern easier for you.

Let’s approach this in a brute strength manner first and refine our strategy as we go along. Each team will have to play each other team in the league. This means that the first team, which we’ll call team 1 for simplicity, has to play against team 2, team 3, team 4, etc up until team 16. This would comprise of 15 matches for team 1. Next, we consider team 2. Team 2 already faced team 1, so that game is off the books, and their schedule would start against team 3, then team 4, etc, up until team 16. This would lead to 14 separate matches.

We seem to have something of a pattern here, but let’s do a third team just to compare our hypothesis (H0: It will be 13 matches. HA: We’ll have to find another way). Team 3 has already faced teams 1 and 2, meaning that their schedule begins at team 4, and then goes on to team 5, etc up until team 16. This does indeed add up to 13 more games being played. The pattern seems to hold up logically, every team plays one fewer game than the last because they’ve already faced any opponent with a team number lower than theirs.

Now, this approach gives the correct answer, but yields a difficult sequence to be summed: 15+14+13+12+11+10+9+8+7+6+5+4+3+2+1. We can shortcut this calculation because the sequence is comprised of consecutive integers, which means the total will be the average multiplied by the number of terms. Since the terms run from 1 to 15 (easier to see this forwards than backwards), the average is (1+15)/2 or 8, and there are 15 terms. 15 x 8 is 120, answer choice A, and this is the correct answer.

The brute force approach is rarely the best strategy, but it’s worth noting that it does get you to the correct answer. You can also shortcut this calculation by ignoring the fact that some teams have already played against one another in your initial count. That is to say: Team 1 has to face 15 opponents, and Team 2 has to face 15 opponents as well. Team 3 will end up facing 15 opponents too, and eventually all 16 teams will face 15 opponents, meaning the total number of games should be 15*16. This math isn’t trivial, but you can get to 240 relatively quickly. The problem with 240 is that you have double counted all the games (i.e. 1 vs. 2 and 2 vs. 1). Simply taking this product and dividing it by two will eliminate the double counting and yield the correct answer of 120.

The final strategy I want to point out here is that we’re essentially making all the unordered pairs of a group. This means we can use combinations to get the correct number.  If we have n = 16 teams, and we’re trying to make all the combinations of 2 teams (k = 2), then we have a combination of the form:

n! / (k! * (n-k)!)

This formula gives us 16! / (2! * (16-2)!).

Solving for the subtraction gives us:

16! / (2! * 14!)

Simplifying by eliminating the redundant 14! from both numerator and denominator gives:

16 * 15 / 2.

This of course simplifies to 8 * 15 or the aforementioned 120. No matter the approach, you should get the same result, which is still choice A.

The GMAT will ask you all kinds of questions about topics you’ve never heard of, but sometimes it will contain a topic that’s near and dear to your heart. It’s okay to be a little elated; you need some positive moments during the 4 hour GMAT marathon. Just keep in mind that the question will be like any other problem, you solve it using the information contained in the question and your hours of GMAT prep. If you do that properly, you’ll be able to put the puck in the net on test day.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Fishing for the Right Answer to Critical Reasoning GMAT Questions

While preparing for the GMAT, there will be certain question types that will appear over and over again. If you’re studying math, you know that you’ll see at least a couple of exponent problems that you’ll need to solve through algebra. If you’re studying sentence correction, you know that you’ll see at least a couple of misplaced modifiers that need to be modified in the correct answer choice. Some question types are so obvious that you know you have to prepare for them, even if you somehow manage to not see a single one on test day (kind of like fishing).

However, there are other question types that you rarely see on the GMAT. Questions about the volume of spheres (or the winds of winter), or conjugating verbs in the subjunctive mood just don’t come up that often on the GMAT. This means that some people feel like they can skip these lessons and concentrate on the “big fish”, as it were (more fishing analogies).

The problem is that, when you inevitably stumble upon a question you haven’t bothered to prepare for, you start panicking. Sometimes, the panic is not noticeable, but subconsciously you begin to lose confidence and wonder how you’re going to answer this question. The sad truth is that there’s a good chance you’ll have to take an educated guess and move on. This isn’t so bad, as long as the negative effects are limited only to the question being asked. Unfortunately, these qualms tend to linger with most test takers for at least a few questions afterwards.

The best strategy for someone who wants to do really well on the GMAT is to know every type of question that can be asked of you. Understandably, you should spend more time on the broad topics that are sure to be covered more frequently, but there should not be any “oh gosh” moments on the GMAT (unless you took the exam in the ‘50s) to zap your confidence.

Let’s look at an example and what to do if we’re really not sure what to do on a question.

Economic analysts predict that by 2030 populations of urban areas will have increased by 60%. This will have tremendous impact on the demand for water in these areas. The increased demand will exhaust the local supplies of water and potable water sources will be drawn to urban areas from longer distances, resulting in a dramatic rise in the price of water.

Which of the following roles do the two boldfaced portions play?

A) The first is the conclusion of the argument; the second is a prediction that serves as the basis for the argument.

B) The first is a prediction that serves as the basis for the argument; the second is the conclusion of the argument.

C) The first is a conclusion that serves as the basis of the argument; the second is a prediction that follows from the conclusion and is used to support the argument.

D) The first is a prediction that serves as the basis for the argument; the second is a prediction that follows from the conclusion.

E) The first is a prediction that serves as the basis for the argument; the second is a consequence that follows from the prediction and is used to support the argument.

Questions that ask about the roles of boldface sections fall under the Method of Reasoning subsection of Critical Reasoning.  These questions are somewhat rare on the GMAT, and as a result students don’t tend to have much experience with them. Trying to decipher them without much experience is eminently doable, but a little practice ahead of time will help ensure that your grade doesn’t sink on test day (I’ve definitely jumped the shark with these water metaphors).

The beauty of roles of boldface questions is that they’re asking you to evaluate two phrases, and the answer choices contain two elements. This means that you can look at them one at a time, independently of the other half of the answer choice, and eliminate the choices that don’t match up to your expectations.

Let’s look at the first section “Economic analysts predict that by 2030 populations of urban areas will have increased by 60%.The five answer choices all have a selection that ends with a semi-colon to describe this phrase. Looking at the choices above, A and C state “the first is a conclusion of the argument”, while B, D and E state “the first is a prediction that serves as the basis for the argument”. This section certainly seems like a prediction (the third word is even “predict”), but let’s dive into the passage more to identify the conclusion. This should be easy; as you’re tasked with finding the conclusion for any strengthen or weaken Critical Reasoning questions.

Using the “why?” test, it becomes apparent that the conclusion is the last line: “resulting in a dramatic rise in the price of water.” Why? Because of the increase in demand. Why? Because the increased demand will mean water will come from further away. Why? Because people are moving more and more to urban areas. Why? (I feel like Steve Austin here) We don’t know that, it’s just stated as a premise. Now that we’ve identified what the conclusion of this passage is, we can more convincingly knock off incorrect answer choices.

The first section is clearly a prediction, and the conclusion of the passage is the following sentence, so we can eliminate answer choices A and C because they do not correctly identify the role of this phrase. We then move on to the second bolded section of the passage: potable water sources will be drawn to urban areas from longer distances. Looking at the second half of the three remaining choices, we have:

B) “The second is the conclusion of the argument”

D) “The second is a prediction that follows from the conclusion”

E) “The second is a consequence that follows from the prediction and is used to support the argument”

Since we’ve already identified the conclusion of the passage, we can quickly eliminate answer choice B. The conclusion is that the price of water will increase given the increased demand, so answer choice D inverses the relationship between the bolded section and the conclusion. Logically, the fact that water will need to be drawn from further away will contribute to the increase in the price of water, not the other way around. Since this is used to support the argument, answer choice E will be the correct choice.

Logically, you should spend most of your time on question types you know are going to show up on the exam. That means that there may be some instances of seeing question types for the first time on test day. If that happens, remember that the GMAT is primarily a test of how you think, so use the same logical tenets you would use on any other question. Here, we identified the conclusion of a passage, eliminated answer choices inconsistent with our analysis, and ultimately found the only correct answer choice. If you do the same on test day, you’ll end up with a whale of a score.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Expecting the Unexpected on GMAT Quant Questions

After studying for the GMAT for a few months (or years, in my case), you start to form expectations of exam questions. If you’re doing sentence correction, and you see a pronoun, there’s a good chance that the various answer choices will have different pronouns to ensure that you pick the correct one. If you’re doing math with three or four digit numbers, there’s a good chance that you have to deal with unit digits in order to shortcut the calculations. And if you’re doing geometry, there’s a good chance that the Pythagorean Theorem will show up, directly or indirectly. (My money is on directly.)

However, it does sometimes happen that a question shatters your expectations. You see the question, you peruse the answer choices, and you immediately look for the properties that you expect to show up. Then, after reading the question, you still don’t have what you expect, and you’re a little lost as to how you should proceed. After all, if you’ve seen the same type of question ten times in a row, a deviation on the 11th time can be somewhat discombobulating.

And yet, this is a strategy that the GMAT frequently employs. At the mid level questions (think 25th-75th percentile), the exam tests the same concepts repeatedly, driving home some crucial ideas through repetition. At the higher level questions (above 75th percentile), the questions tend to get trickier by using your own crutches against you. This throws you out of your comfort zone, and forces you to have to look at a problem through a different vantage point.

Let’s look at such a problem:

In right triangle ABC, BC is the hypotenuse. If BC = 13 and AB + AC = 15, what is the area of the triangle?

A) 2 √7
B) 2 √14
C) 14
D) 28
E) 56

Reading through this problem, we note that it’s a right angle triangle with a hypotenuse of 13. Immediately, my brain jumps to the fairly common 5-12-13 triangle that the GMAT likes to use. Apart from the ubiquitous 3-4-5 right angle triangle, the 5-12-13 triangle is the next smallest right triangle with all integer sides. Perusing the rest of the question, I fully expect AB + AC to be 5 + 12 or 17. However, the question states that AB + AC is not equal to 17, which takes me completely by surprise (and almost makes me question my very existence).

Now, knowing that this isn’t a 5-12-13 triangle isn’t that big of a deal, but it does shatter my expectations of this problem. Clearly, there’s still a solution because the question is being asked, but it deviates from what I thought I had to do. It’s like going to work and your usual route is blocked off. You won’t head back home and sulk, you just have to find an alternate route. Similarly, I now have to take a different approach to solve this geometry question.

Let’s review what we know: it’s a right angle triangle, which means it’s almost guaranteed that we’ll need to use the Pythagorean Theorem. The area is being asked, which is ½ Base * Height, as long as Base and Height are orthogonal to one another. The fact that it’s a right angle triangle and BC is the hypotenuse assures us that AB and AC will be the 90 degree angle we need. All we need to do is multiply AB by AC and divide the product by 2 to get our area.

The problem is that we only have one equation given: AB + AC = 15. To solve for two unknowns, we need two (independent) equations. The second equation will have to come from Pythagoras (possibly by text message). We know that the square of the two right angle sides will equal the square of the hypotenuse, meaning here we know AB^2 + AC^2 = BC^2. Since we know BC is 13, we really have

AB^2 + AC ^2 = 13^2 or

AB^2 + AC ^2 = 169

Combine this with our earlier equation of

AB + AC = 15

And we have two equations and two unknowns. This should be solvable, but the fact that one equation is linear and the other is quadratic can be somewhat disconcerting. We can square the second equation and use the elimination method to isolate variables and get to the right answer.

AB + AC = 15. We now want to square both sides.

(AB + AC)^2 = (15)^2. Remember to square each side, not the individual elements.

AB^2 + 2 AB*AC + AC^2 = 225. This is a perfect square on the left hand side.

Bringing back in the Pythagorean equation:

AB^2 + AC^2 = 169. Using the elimination method to subtract one statement from the other, we can eliminate two variables in one fell swoop, leaving us with:

AB^2 + 2 AB*AC + AC^2 = 225

AB^2 + AC^2 = 169

AB^2 + 2 AB*AC + AC^2 = 225

AB^2 + AC^2 = 169

2 AB*AC = 56.

Meaning that AB*AC = 28.

Finally, AB * AC is really just the Base * the Height. Since that is what we’re looking for, we don’t need to manipulate the algebra any further. However, there is one final step. The equation we’re looking for is ½ Base * Height, so we need to divide the result by 2 again, yielding just 14. Answer choice C is thus correct.

There are several clues that this solution is on the right track. Firstly, the answer we found is among the answer choices. Moreover, two other answer choices are steps we had to pass through in order to find the final answer, making for perfect trap answer choices for overzealous students. Finally, the area of the triangle is very small, which makes sense because the hypotenuse is 13 and the sum of the other two sides is 15. Even the 5-12-13 triangle, which is a relatively thin triangle with an area of 30 (Pythagoras FTW) is twice as big as this thin triangle. The sides of this triangle won’t be integers, but given their relative sizes, it’s something like 2.5-12.5-13, which is quite thin.

If you know the Pythagorean Theorem and can apply the elimination method to two equations, this problem isn’t that difficult once you start solving for variables. The difficulty lies primarily in getting started and not getting caught in trying to backsolve or pick numbers for this problem. When going through it, your mind might automatically think of 5-12-13, or whatever typical information is provided for similar questions. Sometimes you have to think of the problem from a different vantage point in order to solve it. Indeed, on the GMAT, you should expect the unexpected.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# GMAT Tip of the Week: Serenity and Sentence Correction

If you’re reading this, you’re probably hoping for a 700+ score on the GMAT.  You’re probably wishing for a 700+ score on the GMAT.  And you may well be praying for a 700+ score on the GMAT.

And if you’re praying, one prayer in particular is your best hope to maximize your GMAT Verbal performance, regardless of whether you can benefit from divine intervention.  No matter your faith or belief system, the Serenity Prayer is critical to your Sentence Correction success:

God, grant me the serenity to accept the things I cannot change,
The courage to change the things I can,
And the wisdom to know the difference.​

You can view this as a prayer or simply a personal mantra.  But you’d better keep it close to heart.  On GMAT Sentence Correction problems you MUST maintain the serenity to accept that there will be sentence structures and word choices that you cannot change, and you MUST instead focus on changing those things that you can. Now let’s supply the wisdom to know the difference.

YOU CANNOT CHANGE:

The non-underlined portion.  Particularly when studying, many GMAT students love to protest problems on the basis that the non-underlined portion “doesn’t sound right” or “is awkward and clumsy” or “I think it has an error…this question is flawed!”.  In truth, the GMAT (and reputable creators of replica study problems) intentionally uses strange structures in large part to test your ability to maintain that serenity.  You can only change what they give you the option to change, and those who can’t handle the stress of having limited control are at a distinct disadvantage.

The five answer choices.  For many GMAT problems we all would prefer to just rewrite our own sentence.  How many times have you started to write a sentence in an email or essay then realized “I’m not sure if this is grammatically correct” and then deleted and written a brand-new sentence to avoid that uncertainty?  We all do that, regularly, and so on the GMAT you have that primal desire to want to write your own sentence. But you don’t have that option.  You have to accept that you can’t write your own answer choice and that “the game” is largely about your ability to play it by the test’s rules.

YOU CAN CHANGE:

The underlined portion of the sentence.  They give you five ways to phrase that section and the only real choice you have in the matter is which of those five provides a logical meaning and is free from error.  That’s your job, so harness your “courage to change the things you can” toward making that choice effectively.

The way that you approach SC problems.  Most of us read from left to right and from top to bottom, but on Sentence Correction problems you can and should change that approach to suit your strengths. Attack major grammatical errors first, emphasizing those that you know you’re best at (for most of us those include subject-verb agreement, pronoun agreement, and verb tenses).  Defer choices that you’re not 100% certain on while you search for better ones; no one said you have to make a decision on A first, then B, then C…  You can hunt for the errors you feel most comfortable spotting, then work your way toward major differences between the remaining answer choices.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

# Watch Movies with a Critical Eye as You Study for the GMAT This Summer

With the summer blockbuster season around the corner, it’s easy for your studying motivation to wane. After all, the GMAT doesn’t have the same allure as the big budget Hollywood movies people line up to see every summer. However, while seeing a movie can be a welcome distraction, there is a lot we can learn from movies when studying for the GMAT.

As an example, when Tony Stark verbally jousts with Ultron in the latest Avengers movie, he is demonstrating critical reasoning and trying very hard to weaken his opponents’ argument. In Jurassic World, a hybrid dinosaur is created using data from various sources, as a conclusion would be created from various sources on a Reading Comprehension question. And in Terminator Genisys, a fractured timeline is created that resembles many tense errors in Sentence Correction (to say nothing of misspelling the title).

Arguably, every movie you see this summer will incorporate some elements of what’s covered on the GMAT (I’m still working on Magic Mike XXL).  The exam is designed to test your knowledge of logic using elements you have already covered previously in an academic environment. Moreover, the topics on the GMAT often arouse your own interests and pertain to things you care about. Indeed, sometimes the questions asked will even make you think of the movie you saw the week before to take your mind off the GMAT!

Let’s look at such an example, combining movies and GMAT in one sleek Sentence Correction question:

At major Hollywood studios, a much greater proportion of the population is employed than is employed by independent movie production companies.

A) At major Hollywood studios, a much greater proportion of the population is employed than is employed by independent movie production companies.

B) At major Hollywood studios they employ a much greater proportion of the population than independent movie production companies do.

C) A much greater proportion of the major Hollywood studios’ population is employed than independent movie production companies employ.

D) Major Hollywood studios employ a much greater proportion of the population than the employment of independent movie production companies.

E) Major Hollywood studios employ a much greater proportion of the population than independent movie production companies do.

This question begins with an absolute phrase “At major Hollywood studios…” that modifies the rest of the sentence. The second half of the sentence is a comparison between big budget studios and independent companies, highlighted by the trigger word “than”. With comparisons, we must always ensure that we are comparing similar elements and that these elements are in a parallel form.

Looking specifically at answer choice A, the absolute phrase “At major Hollywood studios” would need to apply to the rest of the sentence. (This is similar to the classic trailer opening “In a world…”). This structure would only be correct if the rest of the sentence were limited in scope to the major Hollywood studios. Anything outside of this scope would create an illogical discord between the modifying phrase and the rest of the sentence. Since the sentence deals with the entire population, it does not make sense to limit it only to the Hollywood studios, and this answer choice can be eliminated for this error in logical meaning.

Answer choice B, “At major Hollywood studios they employ a much greater proportion of the population than independent movie production companies do”, there is a pronoun error in the first five words. The antecedent for “they” is nebulous, because it conceivably refers to the studios, or the executives at the studios, or perhaps the HR department at the studios, or something else. The rest of the sentence isn’t great either, but one glaring pronoun error is enough to definitively eliminate this choice from contention.

Answer choice C, “A much greater proportion of the major Hollywood studios’ population is employed than independent movie production companies employ” changes the meaning into something that is not exactly English. The population has now been restricted to only the Hollywood studios’ population, and the comparison being made is illogical as well, as it is now comparing a population proportion to a movie production. Answer choice C is perhaps the worst phrase of the bunch and hopefully can be eliminated rather quickly.

Answer choice D, “Major Hollywood studios employ a much greater proportion of the population than the employment of independent movie production companies” starts off well, but makes the same comparison error that we saw in answer C. If the sentence begins by comparing major studios to something else, then that something else has to be a studio (or something analogous, my cousin’s garage for example). By comparing studios to employment, the answer choice makes an illogical apples-to-oranges comparison that precludes it from consideration.

Answer choice E, “Major Hollywood studios employ a much greater proportion of the population than independent movie production companies do” correctly compares studios to production companies, and makes no other type of error along the way. By process of elimination, this had to be the correct choice, but it’s always nice when the last remaining choice doesn’t contain any obvious errors or omissions. This answer choice is correct, and we can confidently select E as our answer before moving on to the sequel (or next question, as the case may be.)

When it comes to summer blockbusters, there’s always something to learn. Sometimes we learn something helpful in grammar, and sometimes we learn that physics don’t always apply (thank you Furious 7!). This summer, if you’re studying for the GMAT, don’t forget to take the occasional break to go and enjoy a good movie to give your mind a break from the rigors of Sentence Correction problems. Just don’t get butter on your GMAT books.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 99th Percentile GMAT Score or Bust! Lesson 3: The Long Way is the Wrong Way

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

Lesson Three:

The Long Way is the Wrong Way.  For much of your math education you’ve been urged to go step-by-step and show all your work.  On a timed test like the GMAT, however, you don’t have that luxury of taking your time.  As Ravi demonstrates in this video, however, “the long way is the wrong way” on many GMAT problems, which instead are designed to reward you for making quality estimates, using answer choices as clues, and employing other shortcuts to definitively answer correctly without doing all the work.

Want to learn more from Ravi? He’s taking his show on the road for one-week Immersion Courses in San Francisco and New York this summer, and teaches frequently in our new Live Online classroom.

We also have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin