The post How to Simplify Sequences on the GMAT appeared first on Veritas Prep Blog.

]]>If you are one of the many people who fear and dislike sequences, your main consolation should come from the fact that the main weapon in the question writer’s arsenal is the very fear these questions might elicit. And if you have been a reader of this blog for any length of time, you know that the best way to combat this anxiety is to dive in and convert abstractions into something concrete, either by listing out some portion of the sequence, or by using the answer choices and working backwards.

Take this question for example:

*For a certain set of numbers, if x is in the set, then x – 3 is also in the set. If the number 1 is in the set, which of the following must also be in the set?** *

*I. **4*

*II. **-1*

*III. **-5*

*A) **I only*

*B) **II only*

*C) **III only*

*D) **I and II*

*E) **II and III *

Okay, so let’s list out the elements in this set. We know that 1 is in the set. If x= 1, then x – 3 = -2. So -2 is in the set. If x = -2 is in the set, then x – 3 = -5. So -5 is in the set.

By this point, the pattern should be clear: each term is three less than the previous term, giving us a sequence that looks like this: 1, -2, -5, -8, -11….

So we look at our options, and see we that only III is true. And we’re done. That’s it. The answer is C.

*Sure, Dave*, you may say. *That is much easier than any question I’m going to see on the GMAT. * First, this is an official question, so I’m not sure where you’re getting the idea that you’d never see a question like this. Second, you’d be surprised by how many test-takers get this wrong.

There is the temptation to assume that if 1 is in the set, then 4 must also be in the set. And note that this is, in fact, a possibility. If x = 4, then x – 3 = 1. But the question asks us what “must be” in the set. So it’s possible that 4 is in our set. But it’s also possible our set begins with 1, in which case 4 would not be included. This little wrinkle is enough to generate a substantial number of incorrect responses.

*Still, surely the questions get harder than this.* Well, yes. They do. *So what are you waiting for? *I’m not sure where this testy impatience is coming from, but if you insist:

*The sequence a _{1}, a_{2}, a_{3}, . . , a_{n} of n integers is such that a_{k} = k if k is odd and a_{k} = -a_{k-1} if k is even. Is the sum of the terms in the sequence positive?*

*1) **n is odd*

*2) **a _{n} is positive*

*Yikes!* Hey, you asked for a harder one. This question looks far more complicated than the previous one, but we can attack it the same way. Let’s establish our sequence:

*a _{1} *is the first term in the sequence. We’re told that

*a _{2} *is the second term in the sequence. We’re told that

So, here’s our sequence so far: 1, -1…

Let’s keep going.

a* _{3}* is the third term in the sequence. Remember that

*a _{4} *is the fourth term in the sequence. Remember that

Now our sequence looks like this: 1, -1, 3, -3…

By this point we should see the pattern. Every odd term is a positive number that is dictated by its place in the sequence (the first term = 1, the third term = 3, etc.) and every even term is simply the previous term multiplied by -1.

We’re asked about the sum:

After one term, we have 1.

After two terms, we have 1 + (-1) = 0.

After three terms, we have 1 + (-1) + 3 = 3.

After four terms, we have 1 + (-1) + 3 + (-3) = 0.

Notice the trend: after every odd term, the sum is positive. After every even term, the sum is 0.

So the initial question, “*Is the sum of the terms in the sequence positive?” c*an be rephrased as,* “Are there an ODD number of terms in the sequence?”*

Now to the statements. Statement 1 tells us that there are an odd number of terms in the sequence. That clearly answers our rephrased question, because if there are an odd number of terms, the sum will be positive. This is sufficient.

Statement 2 tells us that *a _{n} is positive. a_{n} is *the last term in the sequence. If that term is positive, then, according to the pattern we’ve established, that term must be odd, meaning that the sum of the sequence is positive. This is also sufficient. And the answer is D, either statement alone is sufficient to answer the question.

Takeaway: sequence questions are nothing to fear. Like everything else on the GMAT, the main obstacle we need to overcome is the self-fulfilling prophesy that we don’t know how to proceed, when, in fact, all we need to do is simplify things a bit.

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

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

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]]>The post You’re Fooling Yourself: The GMAT is NOT the SAT! appeared first on Veritas Prep Blog.

]]>There are pros and cons to applying to business school entry straight out of undergraduate – your application lacks the core work experience that many of the higher-tier programs prefer, but unlike the competition, you have not only taken a standardized test in the past 6 years, but you are also (likely) still in the studying mindset and know (versus trying to remember) exactly what it takes to prepare for a difficult exam.

However, you may also fall into a common trap that many younger test takers find themselves in – you decide to tackle the GMAT like your old and recent friend, the SAT.

Now, are there similarities between the GMAT and SAT? Of course.

For starters, the SAT and GMAT are both multiple-choice standardized exams. The math section of the SAT covers arithmetic, geometry, and algebra, just like the quantitative section of the GMAT, with some overlap in statistics and probability. Both exams test a core, basic understanding of English grammar, and ask you to answer questions based on your comprehension of dry, somewhat complex reading passages. The SAT and GMAT also both require you write essays (although the essay on the SAT is now optional), and timing and pacing are issues on both exams, though perhaps more so on the GMAT.

But this is largely where the overlap ends. So, does that mean everything you know and prepped for the SAT should be thrown out the window?

Not necessarily, but it does require a fundamental shift in thinking. While applying your understanding of the Pythagorean Theorem, factorization, permutations, and arithmetic sequences from the SAT will certainly help you begin to tackle GMAT quantitative questions, there are key differences in what the GMAT is looking to assess versus the College Board, and with that, the strategy in tackling these questions should also be quite different.

Simply put, the GMAT is testing how you think, not what you know. This makes sense, when you think about what types of skills are required in business school and, eventually, in the management of business and people. GMAC doesn’t hide what the GMAT is looking to assess – in fact, goals of the GMAT’s assessment are clearly stated on its website:

*The GMAT exam is designed to test skills that are highly important to business and management programs. It assesses analytical writing and problem-solving abilities, along with the data sufficiency, logic, and critical reasoning skills that are vital to real-world business and management success. In June 2012, the GMAT exam introduced Integrated Reasoning, a new section designed to measure a test taker’s ability to evaluate information presented in new formats and from multiple sources─skills necessary for management students to succeed in a technologically advanced and data-rich world.*

To successfully show that you are a candidate worth considering, in your preparation for the exam, make sure you consider what the right strategy and approach will be. Strategy, strategy, strategy. You need to understand which rabbit holes the GMAT can take you down, what tricks not to fall for (especially via misdirection), and how identification of question types can best inform the next steps you take.

An additional, and really, really important point is to keep in mind is that the GMAT is a computer-adaptive exam, not a pen-and-paper test.

Computer-adaptive means that your answer selection dictates the difficulty level of the next question – stacking itself up to a very accurate assessment of how easily you are able to answer easy, medium, and hard questions. Computer-adaptive also means you are not able to skip around, or go back to questions… including the reading comprehension ones. Just like on any game show, you must select your final answer before moving on.

As a computer-adaptive test, the GMAT not only punishes pacing issues, but can be even more detrimental to those who rush and make careless mistakes in the beginning. To wage war against the CAT format, test takers must be careful and methodical in assessing and answering test questions correctly.

Bottom line: don’t treat the GMAT like the SAT, or assume that because you did well on the SAT, you will also do so on the GMAT (or, vice versa). Make sure you are aware of the components of the GMAT that are different and where the similarities between the two tests end.

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

*By Ashley Triscuit, a Veritas Prep GMAT instructor based in Boston.*

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]]>The post GMAT Tip of the Week: Ernie Els, The Masters, and the First Ten GMAT Questions appeared first on Veritas Prep Blog.

]]>With 18 holes each day for 4 days (Quick mental math! 18×4 is the same as 9×8 – halve the first number and double the second to make it a calculation you know well – so that’s 72 holes), any one hole shouldn’t matter. So why was Els’ first hole such a catastrophe?

*It forces him to be nearly perfect the rest of the tournament, because he’s playing at such a disadvantage.*

Meanwhile, Day 1 leader Jordan Spieth shot par (“average”) his first few holes and Rory McElroy, in second place at the end of the day, bogeyed (one stroke worse than average) a total of four holes on day one. The leaders were far from perfect themselves – another important lesson for the GMAT – but by avoiding a disastrous start, they allowed themselves plenty of opportunities to make up for mistakes.

And that brings us to the GMAT. Everyone makes mistakes on the GMAT, and that often happens regardless of difficulty level. So if you’re shooting for a top score and you miss half of the first ten questions, you have a few problems to contend with.

For starters, you have to “get hot” here soon and go on a run of correct answers. Secondly, you now have a lot fewer problems available to go on that hot streak (there are only 27 more Quant or 31 more Verbal questions after the first ten). And finally, the scoring/delivery algorithm doesn’t see you as “elite” yet so the questions are going to be a little easier and less “valuable,” meaning that you’ll need to “get hot” both to prove to the computer that you belong at the top level and then to demonstrate that you can stay there.

That’s the Ernie Els problem – regardless of how good you are, you’re probably going to make mistakes, so when you force yourself to be nearly perfect on the “easier” problems you end up with a tricky standard to live up to. Even if you really should be scoring at the 700-level, you don’t have a 100% probability of answering every 500-level problem correctly. That may well be in the 90%+ range, and maybe your likelihood at the 600 level is 75 or 80%. Getting 7, 8, 9 problems right in a row is a tall order as you dig your way out of that hole.

So the first 10 problems ARE important, but not because they have that much more power over the rest of the test – it’s because the more of them you miss, the more unrealistically perfect you have to be. The key is to “not blow it” on the first 10, rather than to “do everything you can to get them all right,” which is the mindset that holds back plenty of test-takers.

Again take the Masters: the leaderboard on Thursday night is never that close to the leaderboard on Sunday evening. Very often it’s someone who starts well, but is a few strokes off the lead the first few days, who wins. The GMAT is similar: a lot can happen from questions 11 through 37 (or 41), so by no means can you celebrate victory a quarter of the way through. Your goal shouldn’t be to be perfect, but rather to get off to a good start. Getting 7 questions right and having sufficient time to complete the rest of the section is much, much better than getting 9 right but forcing yourself to rush later on.

Essentially, as Ernie Els and thousands of GMAT test-takers have learned the hard way, you won’t win it in the first quarter, but you can certainly lose it there. As you budget your time for the first 10 questions of each section, take a few extra seconds to double-check your work and make sure you’re not making egregious mistakes, but don’t over-invest at the expense of the critical problems to come.

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

*By Brian Galvin.*

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]]>The post Use This Tip to Avoid Critical Reasoning Traps on the GMAT appeared first on Veritas Prep Blog.

]]>Here is a problem I knew I’d be asked about often the moment I saw it:

*W, X, Y, and Z represent distinct digits such that **WX * YZ = 1995. **What is the value of W?*

*X is a prime number**Z is not a prime number*

The first instinct for most students I work with is, “I’m told nothing about W in either statement*.* There have to be many possibilities, so each statement alone is not sufficient.” When this thought occurs to you during the test, it’s important to resist it. By this, I don’t mean that you should simply assume that you’re wrong – there likely will be times when your first instincts are correct. Instead, what I mean is that you should take a bit more time to prove your assumptions to yourself. If there really are many workable scenarios, it won’t take much time to find them.

First, whenever there is an unusually large number and we’re dealing with multiplication, we want to take the prime factorization of that large number so that we can work with that figure’s basic building blocks and make it more manageable. In this case, the prime factorization of 1995 is 3 * 5 * 7 * 19. (First we see that five is a factor of 1995 because 1995 = 5*399. Next, we see that 3 is a factor of 399, because the digits of 399 sum to a multiple of 3. Now we have 5 * 3 * 133. Last, we know that 133 = 7 * 19, because if there are twenty 7’s in 140, there must be nineteen 7’s in 133.)

Now we can use these building blocks to form two-digit numbers that multiply to 1995. Here is a list of two-digit numbers we can assemble from those prime factors:

3 * 5 = 15

3 * 7 = 21

3 * 19 = 57

5 * 7 = 35

5 * 19 = 95

These are our candidates for WX and YZ. There aren’t many possibilities for multiplying two of these two-digit numbers and still getting a product of 1995. In fact, there are only two: 95*21 = 1995 and 35*57 = 1995. But we’re told that each digit must be unique, so 35*57 can’t work, as two of our variables would equal 5. This means that we know, before we even look at the statements, that our two two-digit numbers are 95 and 21 – we just need to know which is which.

It’s possible that WX = 95 and YZ = 21, or WX = 21 and YZ = 95. That’s it. What at first appeared to be a very open-ended question actually has very few workable solutions. Now that we’ve established our sample space of possibilities, let’s examine the statements:

Statement 1: If we know X is prime, we know that WX cannot be 21, as X would be 1 in this scenario and 1 is not a prime number. This means that WX has to be 95, and thus we know for a fact that W = 9. This statement alone is sufficient to answer the question.

Statement 2: If we know that Z is not prime, we know that YZ cannot be 95, as Z would be 5 in this scenario and 5 is, of course, prime. Thus, YZ is 21 and WX is 95, and again, we know for a fact that W is 9, so this statement alone is also sufficient.

The answer is D, either statement alone is sufficient to answer the question, a result very much at odds with most test-taker’s initial instincts.

Takeaway: the GMAT is engineered to wrong-foot test-takers, using our instincts against us. Rather than simply assuming our instincts are wrong – they won’t always be – we want to be methodical about proving our intuitions one way or another by confirming them in some instances, refuting them in others. By being thorough and methodical, we reduce the odds that we’ll step into one of the traps the question-writer has set for us and increase the odds that we’ll answer the question correctly.

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

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

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]]>The post GMAT Tip of the Week: Don’t Be the April Fool with Trap Answers! appeared first on Veritas Prep Blog.

]]>But in case your goal is to leave that job for the greener pastures of business school, anyway, keep that April Fool’s Day spirit with you throughout your GMAT preparation. Read skeptically and beware of the way too tempting, way too easy answer.

First let’s talk about how the GMAT “fools” you. At Veritas Prep we’ve spent years teaching people to “Think Like the Testmaker,” and the only pushback we’ve ever gotten while talking with the testmakers themselves has been, “Hey! We’re not *deliberately* trying to fool people.”

So what are they trying to do? They’re trying to reward critical thinkers, and by doing so, there need to be traps there for those not thinking as critically. And that’s an important way to look at trap answers – the trap isn’t set in a “gotcha” fashion to be cruel, but rather to reward the test-taker who sees the too-good-to-be-true answer as an invitation to dig a little deeper and think a little more critically. One man’s trash is another man’s treasure, and one examinee’s trap answer is another examinee’s opportunity to showcase the reasoning skills that business schools crave.

With that in mind, consider an example, and try not to get April fooled:

*What is the greatest prime factor of 12!11! + 11!10! ?*

*(A) 2*

* (B) 7*

* (C) 11*

* (D) 19*

* (E) 23*

If you’re like many – more than half of respondents in the Veritas Prep Question Bank – you went straight for the April Fool’s answer. And what’s even more worrisome is that most of those test-takers who choose trap answer C don’t spend very long on this problem. They see that 11 appears in both additive terms, see it in the answer choice, and pick it quickly. But that’s exactly how the GMAT fools you – the trap answers are there for those who don’t dig deeper and think critically. If 11 were such an obvious answer, why are 19 and 23 (numbers greater than any value listed in the expanded versions of those factorials 12*11*10*9…) even choices? Who are they fooling with those?

If you get an answer quickly it doesn’t necessarily mean that you’re wrong, but it should at least raise the question, “Am I going for the fool’s answer here?”. And that should encourage you to put some work in. Here, the operative verb even appears in the question stem – you have to factor the addition into multiplication, since factors are all about multiplication/division and not addition/subtraction. When you factor out the common 11!:

11!(12! + 10!)

Then factor out the common 10! (12! is 12*11*10*9*8… so it can be expressed as 12*11*10!):

11!10!(12*11 + 1)

You end up with 11!*10!(133). And that’s where you can check 19 and 23 and see if they’re factors of that giant multiplication problem. And since 133 = 19*7, 19 is the largest prime factor and D is, in fact, the correct answer.

So what’s the lesson? When an answer comes a little too quickly to you or seems a little too obvious, take some time to make sure you’re not going for the trap answer.

Consider this – there are only four real reasons that you’ll see an easy problem in the middle of the GMAT:

1) It’s easy. The test is adaptive and you’re not doing very well so they’re lobbing you softballs. But don’t fear! This is only one of four reasons so it’s probably not this!

2) Statistically it’s fairly difficult, but it’s just easy to you because it’s something you studied well for, or for which you had a great junior high teacher. You’re just that good.

3) It’s not easy – you’re just falling for the trap answer.

4) It’s easy but it’s experimental. The GMAT has several problems in each section called “pretest items” that do not count towards your final score. These appear for research purposes (they’re checking to ensure that it’s a valid, bias-free problem and to gauge its difficulty), and they appear at random, so even a 780 scorer will likely see a handful of below-average difficulty problems.

Look back at that list and consider which are the most important. If it’s #1, you’re in trouble and probably cancelling your score or retaking the test anyway. And for #4 it doesn’t matter – that item doesn’t count. So really, the distinction that ultimately matters for your business school future is whether a problem like the example above fits #2 or #3.

If you find an answer a lot more quickly than you think you should, use some of that extra time to make sure you haven’t fallen for the trap. Engage those critical thinking skills that the GMAT is, after all, testing, and make sure that you’re not being duped while your competition is being rewarded. Avoid being the April Fool, and in a not-too-distant September you’ll be starting classes at a great school.

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: OJ Simpson’s Defense Team And Critical Reasoning Strategy appeared first on Veritas Prep Blog.

]]>Robert Shaprio, Johnnie Cochran, F. Lee Bailey, Alan Dershowitz, and (yes, even) Robert Kardashian can provide you with the ultimate blueprint for GMAT Critical Reasoning success.

This past week’s third episode focused on the preparations of the prosecutors and of the defense, and showcased some crucial differences between success and failure on GMAT CR:

The prosecution made some classic GMAT CR mistakes, most notably that they went in to the case assuming the truth of their position (that OJ was guilty). On the other hand, the defense took nothing for granted – when they didn’t like the evidence (the bloody glove, for example) they looked for ways that it must be faulty evidence (Mark Fuhrman and the LAPD were racist).

This is how you must approach GMAT Critical Reasoning! The single greatest mistake that examinees make during the GMAT is in accepting that the argument they’re given is valid – like Marcia Clark, you’re a nice, good-natured person and you’ll give the argument the benefit of the doubt. But in law and on the GMAT, bullies like Travolta’s Robert Shapiro win the day. The name of the game is “Critical Reasoning” – make sure that you’re being *critical*.

What does that look like on the test? It means:

**Be Skeptical of Arguments**

From the first word of a Strengthen, Weaken, or Assumption question, you’re reading skeptically, and almost angrily so. You’re not buying this argument and you’re searching for holes immediately. Often times these arguments will actually seem pretty valid (sort of like, you know, “OJ did it, based on the glove, the blood in the Brondo, his footprint at the scene, etc.”), but your job is to attack them so you’d better start attacking immediately.

**Look for Details That Don’t Match**

If an argument says, for example, that “the murder rate is down, so the police department must be doing a better job preventing violent crime…” notice that murder is not the same thing as violent crime, and that even if violent crime is down, you don’t have a direct link to the police department being the catalysts for preventing it. This is part of not buying the argument – when the general flow of ideas suggests “yes,” make sure that the details do, too.

**Look for Alternative Explanations**

Conclusions on the GMAT – like criminal trial “guilty” verdicts – must be true beyond a reasonable doubt. So even though the premises might make it seem quite likely that a conclusion is true, if there is an alternate explanation that’s consistent with the facts but allows for a different conclusion, that conclusion cannot be logically drawn. This is where the Simpson legal team was so successful: the evidence was overwhelming in its suggestion that Simpson was guilty (as the soon-after civil trial proves), but the defense was able to create just enough suspicion that he could have been framed that the jury was able to acquit.

So whether you’re appalled or enthralled as you watch *The People v. OJ Simpson* and the defense team shrewdness it portrays, know that the show has valuable insight for you as you attempt to become a Critical Reasoning master. If you want to keep your GMAT verbal score out of jail, you might want to keep up with one particular Kardashian.

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Cam Newton’s GMAT Success Strategy appeared first on Veritas Prep Blog.

]]>**Why is Cam dancing and smiling so much?**

The answer? Because smiling may very well be the secret to success, both in the Super Bowl and on the GMAT.

Note: this won’t be the most mathematically tactical GMAT tip post you read, and it’s not something you’ll really be able to practice on Sunday afternoon while you hit the *Official Guide for GMAT Review* before your Super Bowl party starts. But it may very well be the tip that most impacts your score on test day, because managing stress and optimizing performance are major keys for GMAT examinees. And smiling is a great way to do that.

First, there’s science: the act of smiling itself is *known to release endorphins*, relaxing your mind and giving you a more positive outlook. And this happens regardless of whether you’re actually happy or optimistic – you can literally “fake it till you make it” by smiling through a stressful or unpleasant experience.

(Plus there’s the fact that smiling puts OTHER people in a better mood, too, which won’t really help you on the GMAT since it’s you against a computer, but for your b-school and job interviews, a smile can go a long way toward an upbeat experience for both you and the interviewer.)

There are plenty of ways to force yourself to smile. One is the obvious: just do it. Write it down on the top of your noteboard in all caps: **SMILE!** And force yourself to do it, even when it doesn’t feel natural.

But you can also laugh/smile at yourself more naturally: when Question 1 is a permutations problem and you were dreading the idea of a permutations problem, you can laugh at your bad luck but also at the fact that at least you’re getting it over with while you still have plenty of time to recover. When you blank on a rule and have to test small numbers to prove it, you can laugh at the fact that had you not been so fascinated with the video games on your calculator in middle school you’d know that cold. You can smile when you see a friend’s name in a word problem or a Sentence Correction reference to a place you want to visit someday.

And the tactical rationale there: when you can smile in relation to the subject matter on the test, you can remind yourself that, at least on some level, you enjoy learning and problem-solving and striving for achievement. The biggest difference between “good test takers” and “good students, but bad test takers” is in the way that each approaches problems: the latter group says, “I don’t know,” and feels doubt, while the former says, “I don’t know…yet,” and starts from a position of confidence and strength. Then when you apply that confidence and figure out a problem that for a second had you totally stumped, you’ve earned that next smile and the positive energy snowballs.

As you watch Cam Newton on Sunday (For you brand management hopefuls, he’ll be playing football between those commercials you’re so excited to see!), pay attention to that megawatt smile that’s been the topic of so much talk radio controversy the last few weeks. Cam smiles because he’s having fun out there, and then that smile leads to big plays, which is even more fun, and then he’s smiling again. Apply that Cam Newton “smile your way to success” philosophy on test day and maybe you’ll be the next one getting paid hundreds of thousands of dollars to go to school for two years… (We kid, Cam – we kid!)

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

*By Brian Galvin.*

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]]>The post Why Logic is More Important Than Algebra on the GMAT appeared first on Veritas Prep Blog.

]]>If you’ve followed this blog for any length of time, you know that one of the themes we stress is that Quantitative Reasoning is not, primarily, a math test. Though math is certainly involved – How could it not be? – logic and reasoning are far more important factors than conventional mathematical facility. I stress this in every class I teach. So why the misconception that we need to hone our algebra chops?

I suspect that the culprit here is the explanations that often accompany official GMAC questions. On the whole, they tend to be biased in favor of purely algebraic solutions. They’re always* technically* correct, but often suboptimal for the test-taker who needs to arrive at a solution within two minutes. Consequently, many students, after reviewing these solutions and arriving at the conclusion that they would not have been capable of the hairy algebra proffered in the official solution, think they need to work on this aspect of their prep. And for the most part it isn’t true.

Here’s a good example:

*If x, y, and k are positive numbers such that [x/(x+y)]*10 + [y/(x+y)]*20 = k and if x < y, which of the following could be the value of k? *

A) 10

B) 12

C) 15

D) 18

E) 30

A large percentage of test-takers see this question, rub their hands together, and dive into the algebra. The solution offered in the Official Guide does the same – it is about fifteen steps, few of them intuitive. If you were fortunate enough to possess the algebraic virtuosity to solve the question in this manner, you’d likely chew up 5 or 6 minutes, a disastrous scenario on a test that requires you to average 2 minutes per problem.

The upshot is that it’s important for test-takers, when they peruse the official solution, not to arrive at the conclusion that they need to solve this question the same way the solution-writer did. Instead, we can use the same simple strategies we’re always preaching on this blog: pick some simple numbers.

We’re told that x<y, but for my first set of numbers, I like to make x and y the same value – this way, I can see what effect the restriction has on the problem. So let’s say x = 1 and y = 1. Plugging those values into the equation, we get:

(1/2) * 10 + (1/2) * 20 = k

5 + 10 = k

15 = k

Well, we know this isn’t the answer, because x should be less than y. So scratch off C. And now let’s see what the effect is when x is, in fact, less than y. Say x = 1 and y = 2. Now we get:

(1/3) * 10 + (2/3) * 20 = k

10/3 + 40/3 = k

50/3 = k

50/3 is about 17. So when we honor the restriction, k becomes larger than 15. The answer therefore must be D or E. Now we could pick another set of numbers and pay attention to the trend, or we can employ a bit of logic and common sense. The first term in the equation x/(x+y)*10 is some fraction multiplied by 10. So this term, logically, is some value that’s less than 10.

The second term in the equation is y/(x+y)*20, is some fraction multiplied by 20, this term must be less than 20. If we add a number that’s less than 10 to a number that’s less than 20, we’re pretty clearly not going to get a sum of 30. That leaves us with an answer of 18, or D.

(Note that if you’re really savvy, you’ll recognize that the equation is a weighted average. The coefficients in the weighted average are 10 and 20. If x and y were equal, we’d end up at the midway point, 15. Because 20 is multiplied by y, and y is greater than x, we’ll be pulled towards the high end of the range, leading to a k that must fall between 15 and 20 – only 18 is in that range.)

Takeaway: Never take a formal solution to a problem at face value. All you’re seeing is one way to solve a given question. If that approach doesn’t resonate for you, or seems so challenging that your conclusion is that you must purchase a host of textbooks in order to improve your formal math skills, then you haven’t absorbed what the GMAT is really about. Often, the relevant question isn’t, “Can you do the math?” It’s, “Can you reason your way to the answer without actually doing the math?”

*Official Guide question courtesy of the Graduate Management Admissions Council.

**GMAT prep courses** starting all the time. And be sure to follow us on **Facebook**, **YouTube**, **Google+ **and **Twitter**!

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

The post Why Logic is More Important Than Algebra on the GMAT appeared first on Veritas Prep Blog.

]]>The post How to Choose the Right Number for a GMAT Variable Problem appeared first on Veritas Prep Blog.

]]>Now, you may be thinking, “How hard can it possibly be to pick numbers? I see an “x” and I decide x = 5. Not so complicated.” The art is in learning how to pick workable numbers for each question type. Different questions will require different types of numbers to create a scenario that truly is simpler than the algebra. The harder the problem, the more finesse that will be required when selecting numbers. Let’s start with a problem that doesn’t require much strategy:

*If n=4p, where p is prime number greater than 2, how many different positive even divisors does n have, including n? *

*(A) 2 *

*(B) 3 *

*(C) 4 *

*(D) 6 *

*(E) 8 *

Okay in this problem, “p” is a prime number greater than 2. So let’s say p = 3. If n = 4p, and 4p = 4*3 = 12. Let’s list out the factors of 12: 1, 2, 3, 4, 6, 12. The even factors here are 2, 4, 6, 12. There are 4 of them. So the answer is C. Not so bad, right? Just pick the first simple number that pops into your head and you’re off to the races. Bring on the test!

If only it were that simple for all questions. So let’s try a much harder question to illustrate the pitfalls of adhering to an approach that’s overly mechanistic:

*The volume of water in a certain tank is x percent greater than it was one week ago. If r percent of the current volume of water in the tank is removed, the resulting volume will be 90 percent of the volume it was one week ago. What is the value of r in terms of x?*

*(A) **x + 10*

*(B) **10x + 1*

*(C) **100(x + 10)*

*(D) **100 * (x+10)/(x+100)*

*(E) **100 * (10x + 1)/(10x+10)*

You’ll notice quickly that if you simply declare that x = 10 and r =20, you may run into trouble. Say, for example, that the starting value from one week ago was 100 liters. If x = 10, a 10% increase will lead to a volume of 110 liters. If we remove 20% of that 110, we’ll be removing .20*110 = 22 liters, giving us 110-22 = 88 liters. But we’re also told that the resulting volume is 90% of the original volume! 88 is not 90% of 100, therefore our numbers aren’t valid. In instances like this, we need to pick some simple starting numbers and then calculate the numbers that will be required to fit the parameters of the question.

So again, say the volume one week ago was 100 liters. Let’s say that x = 20%, so the volume, after water is added, will be 100 + 20 = 120 liters.

We know that once water is removed, the resulting volume will be 90% of the original. If the original was 100, the volume, once water is removed, will be 100*.90 = 90 liters.

Now, rather than arbitrarily picking an “r”, we’ll calculate it based on the numbers we have. To summarize:

Start: 100 liters

After adding water: 120 liters

After removing water: 90 liters

We now need to calculate what percent of those 120 liters need to be removed to get down to 90. Using our trusty percent change formula [(Change/Original) * 100] we’ll get (30/120) * 100 = 25%.

Thus, when x = 20, r =25. Now all we have to do is substitute “x” with “20” in the answer choices until we hit our target of 25.

Remember that in these types of problems, we want to start at the bottom of the answer choice options and work our way up:

*(E) 100 * (10x + 1)/(10x+10)*

100 * (10*20 + 1)/(10*20+10) = 201/210. No need to simplify. There’s no way this equals 25.

*(D) 100 * (x+10)/(x+100)*

100 * (20+10)/(20+100) = 100 * (30/120) = 25. That’s it! We’re done. The correct answer is D.

Takeaways: Internalizing strategies is the first step in your process of preparing for the GMAT. Once you’ve learned these strategies, you need to practice them in a variety of contexts until you’ve fully absorbed how each strategy needs to be tweaked to fit the contours of the question. In some cases, you can pick a single random number. Other times, there will be multiple variables, so you’ll have to pick one or two numbers to start and then solve for the remaining numbers so that you don’t violate the conditions of the problem. Accept that you may have to make adjustments mid-stream. Your first selection may produce hairy arithmetic. There are no style point on the GMAT, so stay flexible, cultivate back-up plans, and remember that mental agility trumps rote memorization every time.

**GMAT prep courses** starting all the time. And be sure to follow us on **Facebook**, **YouTube**, **Google+ **and **Twitter**!

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

The post How to Choose the Right Number for a GMAT Variable Problem appeared first on Veritas Prep Blog.

]]>The post Quarter Wit, Quarter Wisdom: Cyclicity in GMAT Remainder Questions appeared first on Veritas Prep Blog.

]]>First let’s look at a pattern:

**20/10** gives us a remainder of** 0** (as 20 is exactly divisible by 10)

**21/10** gives a remainder of **1**

**22/10** gives a remainder of **2**

**23/10** gives a remainder of **3**

**24/10** gives a remainder of **4**

**25/10** gives a remainder of **5**

and so on…

In the case of this pattern, 20 is the closest multiple of 10 that goes completely into all these numbers and you are left with the units digit as the remainder. Whenever you divide a number by 10, the units digit will be the remainder. Of course, if the units digit of a number is 0, the remainder will be 0 and that number will be divisible by 10 — but we already know that. So remainder when 467,639 is divided by 10 is 9. The remainder when 100,238 is divided by 10 is 8 and so on…

Along the same lines, we also know that every number that ends in 0 or 5 is a multiple of 5 and every multiple of 5 must end in either 0 or 5. So if the units digit of a number is 1, it gives a remainder of 1 when divided by 5. If the units digit of a number is 2, it gives a remainder of 2 when divided by 5. If the units digit of a number is 6, it gives a remainder of 1 when divided by 5 (as it is 1 more than the previous multiple of 5).

With this in mind:

**20/5** gives a remainder of** 0** (as 20 is exactly divisible by 5)

**21/5** gives a remainder of **1**

**22/5** gives a remainder of **2**

**23/5** gives a remainder of **3**

**24/5** gives a remainder of **4**

**25/5** gives a remainder of **0** (as 25 is exactly divisible by 5)

**26/5** gives a remainder of **1**

**27/5** gives a remainder of **2**

**28/5** gives a remainder of **3**

**29/5** gives a remainder of **4**

**30/5** gives a remainder of** 0** (as 30 is exactly divisible by 5)

and so on…

So the units digit is all that matters when trying to get the remainder of a division by 5 or by 10.

Let’s take a few questions now:

*What is the remainder when 86^(183) is divided by 10?*

Here, we need to find the last digit of 86^(183) to get the remainder. Whenever the units digit is 6, it remains 6 no matter what the positive integer exponent is (**previously discussed in this post**).

So the units digit of 86^(183) will be 6. So when we divide this by 10, the remainder will also be 6.

Next question:

*What is the remainder when 487^(191) is divided by 5?*

Again, when considering division by 5, the units digit can help us.

The units digit of 487 is 7.

7 has a cyclicity of 7, 9, 3, 1.

Divide 191 by 4 to get a quotient of 47 and a remainder of 3. This means that we will have 47 full cycles of “7, 9, 3, 1” and then a new cycle will start and continue until the third term.

7, 9, 3, 1

7, 9, 3, 1

7, 9, 3, 1

7, 9, 3, 1

…

7, 9, 3

So the units digit of 487^(191) is 3, and the number would look something like ……………..3

As discussed, the number ……………..0 would be divisible by 5 and ……………..3 would be 3 more, so it will also give a remainder of 3 when divided by 5.

Therefore, the remainder of 487^(191) divided by 5 is 3.

Last question:

*If x is a positive integer, what is the remainder when 488^(6x) is divided by 2?*

Take a minute to review the question first. If you start by analyzing the expression 488^(6x), you will waste a lot of time. This is a trick question! The divisor is 2, and we know that every even number is divisible by 2, and every odd number gives a remainder 1 when divided by 2. Therefore, we just need to determine whether 488^(6x) is odd or even.

488^(6x) will be even no matter what x is (as long as it is a positive integer), because 488 is even and we know even*even*even……(any number of terms) = even.

So 488^(6x) is even and will give remainder 0 when it is divided by 2.

That is all for today. We will look at some GMAT remainders-cyclicity questions next week!

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

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

The post Quarter Wit, Quarter Wisdom: Cyclicity in GMAT Remainder Questions appeared first on Veritas Prep Blog.

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