GMAT Tip of the Week: Ernie Els, The Masters, and the First Ten GMAT Questions

GMAT Tip of the WeekAt this weekend’s The Masters golf tournament, the most notable piece of news isn’t the leaderboard, but rather the guy least likely to get near it. Ernie Els set a record with a nine-stroke, quintuple bogey on his first hole of the tournament, effectively ending his tournament minutes after he began it. And in doing so, he also provided you with some insight into the “First Ten Questions” myth that concerns so many GMAT test-takers.

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, YouTubeGoogle+ and Twitter!

By Brian Galvin.

Use This Tip to Avoid Critical Reasoning Traps on the GMAT

GMAT TrapsWhen you’ve been teaching test prep for a while you begin to be able to anticipate the types of questions that will give your students fits. The reason isn’t necessarily because these questions are unusually hard in a conventional sense, but because embedded within these problems is a form of misdirection that is nearly impossible to resist. It’s often worthwhile to dissect these problems in greater detail to reveal some deeper truths about how the test works.

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?

  1. X is a prime number
  2. 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 FacebookYouTubeGoogle+ and Twitter!

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

GMAT Tip of the Week: Don’t Be the April Fool with Trap Answers!

GMAT Tip of the WeekToday, people across the world are viewing news stories and emails with a skeptical eye, on guard to ensure that they don’t get April fooled. Your company just released a press release about a new initiative that would dramatically change your workload? Don’t react just yet…it could be an April Fool’s joke.

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, YouTubeGoogle+ and Twitter!

By Brian Galvin.

GMAT Tip of the Week: OJ Simpson’s Defense Team And Critical Reasoning Strategy

GMAT Tip of the WeekIf you’re like many people this month, you’re thoroughly enjoying the guilty pleasure that is FX’s series The People v. OJ Simpson. And whether you’re in it to reminisce about the 1990s or for the wealth of Kardashian family history, one thing remains certain (even though, according to the state of California – spoiler alert! – that thing is not OJ’s guilt):

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, YouTubeGoogle+ and Twitter!

By Brian Galvin.

GMAT Tip of the Week: Cam Newton’s GMAT Success Strategy

GMAT Tip of the WeekAs we head into Super Bowl weekend, the most popular conversation topic in the world is the Carolina Panthers’ quarterback, Cam Newton. Many questions surround him: is he the QB to whom the Brady/Manning “Greatest of All Time” torch will be passed? Is this the beginning of a new dynasty? Why do people like/dislike him so much? What the heck is the Dab, anyway? And most commonly:

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, YouTubeGoogle+ and Twitter!

By Brian Galvin.

Why Logic is More Important Than Algebra on the GMAT

QuestioningOne common complaint I get from students is that their algebra skills aren’t where they need to be to excel on the GMAT. This complaint, invariably, is followed by a request for additional algebra drills.

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.

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

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

How to Choose the Right Number for a GMAT Variable Problem

Pi to the 36th digitWhen you begin studying for the GMAT, you will quickly discover that most of the strategies are, on the surface, fairly simple. It will not come as a terribly big surprise that selecting numbers and doing arithmetic is often an easier way of attacking a problem than attempting to perform complex algebra. There is, however, a big difference between understanding a strategy in the abstract and having honed that strategy to the point that it can be implemented effectively under pressure.

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.

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

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

Quarter Wit, Quarter Wisdom: Cyclicity in GMAT Remainder Questions

Quarter Wit, Quarter WisdomUsually, cyclicity cannot help us when dealing with remainders, but in some cases it can. Today we will look at the cases in which it can, and we will see why it helps us in these cases.

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 FacebookYouTube, 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!

Quarter Wit, Quarter Wisdom: Cyclicity of Units Digits on the GMAT (Part 2)

Quarter Wit, Quarter WisdomAs discussed last week, all units digits have a cyclicity of 1 or 2 or 4. Digits 2, 3, 7 and 8 have a cyclicity of 4, i.e. the units digit repeats itself every 4 digit:

Cyclicity of 2: 2, 4, 8, 6

Cyclicity of 3: 3, 9, 7, 1

Cyclicity of 7: 7, 9, 3, 1

Cyclicity of 8: 8, 4, 2, 6

Digits 4 and 9 have a cyclicity of 2, i.e. the units digit repeats itself every 2 digits:

Cyclicity of 4: 4, 6

Cyclicity of 9: 9, 1

Digits 0, 1, 5 and 6 have a cyclicity of 1, i.e. the units digit is 0, 1, 5, or 6 respectively.

Now let’s take a look at how to apply these fundamentals:

What is the units digit of 813^(27)?

To get the desired units digit here, all we need to worry about is the units digit of the base, which is 3.

Remember, our cyclicity of 3 is 3, 9, 7, 1 (four numbers total).

We need the units digit of 3^(27). How many full cycles of 4 will be there in 27? There will be 6 full cycles because 27 divided by 4 gives 6 as quotient and 3 will be the remainder. So after 6 full cycles of 4 are complete, a new cycle will start:

3, 9, 7, 1

3, 9, 7, 1

… (6 full cycles)

3, 9, 7 (new cycle for remainder of 3)

7 will be the units digit of 3^(27), so 7 will be the units digit of 813^(27).

Let’s try another question:

What is the units digit of 24^(1098)?

To get the desired units digit here, all we need to worry about is the units digit of the base, which is 4.

Remember, our cyclicity of 4 is 4 and 6 (this time, only 2 numbers).

We need the units digit of 24^(1098) – every odd power of 24 will end in 4 and every even power of 24 will end in 6.

Since 1098 is even, the units digit of 24^(1098) is 6.

Not too bad; let’s try something a little harder:

What is the units digit of 75^(25)^5

Note here that you have 75 raised to power 25 which is further raised to the power of 5.

25^5 is not the same as 25*5 – it is 25*25*25*25*25 which is far more complicated. However, the simplifying element of this question is that the last digit of the base 75 is 5, so it doesn’t matter what the positive integer exponent is, the last digit of the expression will always be 5.

Now let’s take a look at a Data Sufficiency question:

Given that x and y are positive integers, what is the units digit of (5*x*y)^(289)?

Statement 1: x is odd.

Statement 2: y is even.

Here there is a new complication – we don’t know what the base is exactly because the base depends on the value of x and y. As such, the real question should be can we figure out the units digit of the base? That is all we need to find the units digit of this expression.

When 5 is multiplied by an even integer, the product ends in 0.

When 5 is multiplied by an odd integer, the product ends in 5.

These are the only two possible cases: The units digit must be either 0 or 5.

With Statement 1, we do not know whether y is odd or even, we only know that x is odd. If y is odd, x*y will be odd. If y is even, x*y will be even. Since we don’t know whether x*y is odd or even, we don’t know whether 5*x*y will end in 5 or 0, so this statement alone is not sufficient.

With Statement 2, if y is even, x*y will certainly be even because an even * any integer will equal an even integer. Therefore, it doesn’t matter whether x is odd or even – regardless, 5*x*y will be even, hence, it will certainly end in 0.

As we know from our patterns of cyclicity, 0 has a cyclicity of 1, i.e. no matter what the positive integer exponent, the units digit will be 0. Therefore, this statement alone is sufficient and the answer is B (Statement 2 alone is sufficient but Statement 1 alone is not sufficient).

Finally, let’s take a question from our own book:

If n and a are positive integers, what is the units digit of n^(4a+2) – n^(8a)?

Statement 1: n = 3

Statement 2: a is odd.

We know that the cyclicity of every digit is either 1, 2 or 4. So to know the units digit of n^{4a+2} – n^{8a}, we need to know the units digit of n. This will tell us what the cyclicity of n is and what the units digit of each expression will be individually.

Statement 1: n = 3

As we know from our patterns of cyclicity, the cyclicity of 3 is 3, 9, 7, 1

Plugging 3 into “n”, n^{4a+2} = 3^{4a+2}

In the exponent, 4a accounts for “a” full cycles of 4, and then a new cycle begins to account for 2.

3, 9, 7, 1

3, 9, 7, 1

3, 9

The units digit here will be 9.

Again, plugging 3 into “n”, n^{8a} = 3^{8a}

8a is a multiple of 4, so there will be full cycles of 4 only. This means the units digit of 3^{8a} will be 1.

3, 9, 7, 1

3, 9, 7, 1

3, 9, 7, 1

3, 9, 7, 1

Plugging these answers back into our equation: n^{4a+2} – n^{8a} = 9 – 1

The units digit of the combined expression will be 9 – 1 = 8.

Therefore, this statement alone is sufficient.

In Statement 2, we are given what the exponents are but not what the value of n, the base, is. Therefore, this statement alone is not sufficient, and our answer is A (Statement 1 alone is sufficient but Statement 2 alone is not sufficient).

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTube, 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!

Quarter Wit Quarter Wisdom: Cyclicity of Units Digits on the GMAT

Quarter Wit, Quarter WisdomIn our algebra book, we have discussed finding and extrapolating patterns. In this post today, we will look at the patterns we get with various units digits.

The first thing you need to understand is that when we multiply two integers together, the last digit of the result depends only on the last digits of the two integers.

For example:

24 * 12 = 288

Note here: …4 * …2 = …8

So when we are looking at the units digit of the result of an integer raised to a certain exponent, all we need to worry about is the units digit of the integer.

Let’s look at the pattern when the units digit of a number is 2.

Units digit 2:

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^7 = 128

2^8 = 256

2^9 = 512

2^10 = 1024

Note the units digits. Do you see a pattern? 2, 4, 8, 6, 2, 4, 8, 6, 2, 4 … and so on

So what will 2^11 end with? The pattern tells us that two full cycles of 2-4-8-6 will take us to 2^8, and then a new cycle starts at 2^9. 

2-4-8-6

2-4-8-6

2-4

The next digit in the pattern will be 8, which will belong to 2^11. 

In fact, any integer that ends with 2 and is raised to the power 11 will end in 8 because the last digit will depend only on the last digit of the base. 

So 652^(11) will end in 8,1896782^(11) will end in 8, and so on…

A similar pattern exists for all units digits. Let’s find out what the pattern is for the rest of the 9 digits. 

Units digit 3:

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

3^5 = 243

3^6 = 729

The pattern here is 3, 9, 7, 1, 3, 9, 7, 1, and so on…

Units digit 4:

4^1 = 4

4^2 = 16

4^3 = 64

4^4 = 256

The pattern here is 4, 6, 4, 6, 4, 6, and so on… 

Integers ending in digits 0, 1, 5 or 6 have the same units digit (0, 1, 5 or 6 respectively), whatever the positive integer exponent. That is:

1545^23 = ……..5

1650^19 = ……..0

161^28 = ………1

Hope you get the point.

Units digit 7:

7^1 = 7

7^2 = 49

7^3 = 343

7^4 = ….1 (Just multiply the last digit of 343 i.e. 3 by another 7 and you get 21 and hence 1 as the units digit)

7^5 = ….7 (Now multiply 1 from above by 7 to get 7 as the units digit)

7^6 = ….9

The pattern here is 7, 9, 3, 1, 7, 9, 3, 1, and so on…

Units digit 8:

8^1 = 8

8^2 = 64

8^3 = …2

8^4 = …6

8^5 = …8

8^6 = …4

The pattern here is 8, 4, 2, 6, 8, 4, 2, 6, and so on…

Units digit 9: 

9^1 = 9

9^2 = 81

9^3 = 729

9^4 = …1

The pattern here is 9, 1, 9, 1, 9, 1, and so on…

Summing it all up:

1) Digits 2, 3, 7 and 8 have a cyclicity of 4; i.e. the units digit repeats itself every 4 digits.

Cyclicity of 2: 2, 4, 8, 6

Cyclicity of 3: 3, 9, 7, 1

Cyclicity of 7: 7, 9, 3, 1

Cyclicity of 8: 8, 4, 2, 6

2) Digits 4 and 9 have a cyclicity of 2; i.e. the units digit repeats itself every 2 digits.

Cyclicity of 4: 4, 6

Cyclicity of 9: 9, 1 

3) Digits 0, 1, 5 and 6 have a cyclicity of 1.

Cyclicity of 0: 0

Cyclicity of 1: 1

Cyclicity of 5: 5

Cyclicity of 6: 6

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTube, 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!

Is Technology Costing You Your GMAT Score?

Veritas Prep GMAT Prep Books on iPadI recently read Sherry Turkle’s Reclaiming Conversation: The Power of Talk in a Digital Age. While the book isn’t about testing advice, per se, its analysis of the costs of technology is so comprehensive that the insights are applicable to virtually every aspect of our lives.

The book’s core thesis – that our smartphones and tablets are fragmenting our concentration and robbing us of a fundamental part of what it means to be human – isn’t a terribly original one. The difference between Turkle’s work and less effective screeds about the evils of technology is the scope of the research she provides in demonstrating how the overuse of our devices is eroding the quality of our education, our personal relationships, and our mental health.

What’s amazing is that these costs are, to some extent, quantifiable. Ever wonder what the impact is of having most of our conversations mediated through screens rather than through hoary old things like facial expressions? College students in the age of smartphones score 40% lower on tests measuring indicators of empathy than college students from a generation ago. In polls, respondents who had access to smartphones by the time they were adolescents reported heightened anxiety about the prospect of face-to-face conversations in general.

Okay, you say. Disturbing as that is, those findings have to do with interpersonal relationships, not education. Can’t technology be used to enhance the learning environment as well? Though it would be silly to condemn any technology as wholly corrosive, particularly in light of the fact that most schools are making a concerted effort to incorporate laptops and tablets in the classroom, Turkle makes a persuasive case that the overall costs outweigh the benefits.

In one study conducted by Pam Mueller and Daniel Oppenheimer, the researchers compared the retention rates of students who took notes on their laptops versus those who took notes by hand. The researchers’ assumption had always been that taking notes on a laptop would be more beneficial, as most of us can type faster than we can write longhand. Much to their surprise, the students who took notes by hand did significantly better than those who took notes on their laptops when tested on the contents of a lecture a week later.

The reason, Mueller and Oppenheimer speculate, is that because the students writing longhand couldn’t transcribe fast enough to record everything, they had to work harder to filter the information they were provided, and this additional cognitive effort allowed them to retain more. The ease of transcription – what we perceive as a benefit of technology – actually proved to be a cost. Even more disturbing, another study indicated that the mere presence of a smartphone – even if the phone is off – will cause everyone in its presence to retain less of a lecture, not just the phone’s owner.

I’ve been teaching long enough that when I first started, it was basically unheard of for a student’s attention to wander because he’d been distracted by a device. Smartphones didn’t exist yet. No one brought laptops to class. Now, if I were to take a poll, I’d be surprised if there were a single student in class who didn’t at least glance at a smartphone during the course of a lesson. One imagines that the same is true when students are studying on their own – a phone is nearby, just in case something important comes up. I’d always assumed the presence of these devices was relatively harmless, but if a phone that’s off can degrade the quality of our study sessions, just imagine the impact of a phone that continually pings and buzzes as fresh texts, emails and notifications come in.

The GMAT is a four-hour test that requires intense focus and concentration, so anything that hampers our ability to focus is a potential drag on our scores. There’s no easy solution here. I’m certainly not advocating that anyone throw away their smartphone – the fact that certain technology has costs associated with it is hardly a reason to discard that technology altogether. There are plenty of well-documented educational benefits: one can use a long train ride as an opportunity to do practice problems or watch a lecture. We can easily store data that can shed light on where we need to focus our attention in future study sessions. So the answer isn’t a draconian one in which we have to dramatically alter our lifestyles. Technology isn’t going anywhere – it’s a question of moderation.

Takeaways: No rant about the costs of technology is going to be terribly helpful without an action plan, so here’s what I suggest:

  • Put the devices away in class and take notes longhand. Whether you’re in a GMAT prep class, or an accounting class in your MBA program, this will benefit both you and your classmates.
  • If you aren’t using your device to study, turn it off, and make sure it’s out of sight when you work. The mere visual presence of a smartphone will cause you to retain less.
  • Give yourself at least 2 hours of device-free time each day. This need not be when you’re studying. It can also be when you’re out to dinner with friends or spending time with family. In addition to improving your interpersonal relationships, conversation actually makes you smarter.

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

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

What to Do if You’re Struggling with GMAT Solutions

stressed-studentOne of the most misleading parts of the whole GMAT experience is the process of reading the solution to a math problem in the Quant section. When you try the problem, you struggle, sweat, and go nowhere; when they explain the problem, they wave a snooty, know-it-all magic wand that clears everything up. But how did they think of that? What can you do to think like them (or barring that, where do they keep that magic wand, and how late do we have to break into their house to be sure they’re asleep when we steal it)?

The short answer is that they struggled just like you did, but like anybody else, they wanted to make it look easy. (Think of all the time some people spend preening their LinkedIn or their Instagram: you only ever see the flashy corporate name and the glamour shot, never the 5 AM wake up call or the 6 AM look in the mirror.) Solution writers, particularly those who work for the GMAC, never seem to tell you that problem solving is mostly about blundering through a lot of guesswork before hitting upon a pattern, but that’s really what it is. Your willingness to blunder around until you hit something promising is a huge part of what’s being tested on the GMAT; after all, as depressing as it sounds, that’s basically how life works.

Here’s a great example:

I haven’t laid eyes on it in thirty years, but I still remember that the rope ladder to my childhood treehouse had exactly ten rungs. I was a lot shorter then, and a born lummox, so I could only climb the ladder one or two rungs at a time. I also had more than a touch of childhood OCD, so I had to climb the ladder a different way every time. After how many trips up did my OCD prevent me from ever climbing it again? (In other words, how many different ways was I able to climb the ladder?)

A) 55       

B) 63       

C) 72       

D) 81        

E) 89

Just the thought of trying 55 to 89 different permutations of climbing the ladder has my OCD going off like a car alarm, so I’m going to look for an easier way of doing this. It’s a GMAT problem, albeit one on the level of a Google interview question, so it must have a simple solution. There has to be a pattern here, or the problem wouldn’t be tested. Maybe I could find that pattern, or at least get an idea of how the process works, if I tried some shorter ladders.

Suppose the ladder had one rung. That’d be easy: there’s only one way to climb it.

Now suppose the ladder had two rungs. OK, two ways: I could go 0-1 then 1-2, or straight from 0-2 in a single two step, so there are two ways to climb the ladder.

Now suppose that ladder had three rungs. 0-1, 1-2, 2-3 is one way; 0-2, 2-3 is another; 0-1, 1-3 is the third. So the pattern is looking like 1, 2, 3 … ? That can’t be right! Doubt is gnawing at me, but I’m going to give it one last shot.

Suppose that the ladder had four rungs. I could do [0-1-2-3-4] or [0-1-3-4] or [0-1-2-4] or [0-2-4] or [0-2-3-4]. So there are five ways to climb it … wait, that’s it!

While I was mucking through the ways to climb my four-rung ladder, I hit upon something. When I take my first step onto the ladder, I either climb one rung or two. If I climb one rung, then there are 3 rungs left: in other words, I have a 3-rung ladder, which I can climb in 3 ways, as I saw earlier. If my step is a two-rung step instead, then there are 2 rungs left: in other words, a 2-rung ladder, which I can climb in 2 ways. Making sense?

By the same logic, if I want to climb a 5-rung ladder, I can start with one rung, then have a 4-rung ladder to go, or start with two rungs, then have a 3-rung ladder to go. So the number of ways to climb a 5-rung ladder = (the number of ways to climb a 3-rung ladder) + (the number of ways to climb a 4-rung ladder). Aha!

My pattern starts 1, 2, 3, so from there I can find the number of ways to climb each ladder by summing the previous two. This gives me a 1-, 2-, 3-, … rung ladder list of 1, 2, 3, 5, 8, 13, 21, 34, 55, and 89, so a 10-rung ladder would have 89 possible climbing permutations, and we’re done.

And the lesson? Much like a kid on a rope ladder, for a GMAT examinee on an abstract problem there’s often no “one way” to do the problem, at least not one that you can readily identify from the first instant you start. Very often you have to take a few small steps so that in doing so, you learn what the problem is all about. When all else fails in a “big-number” problem, try testing the relationship with small numbers so that you can either find a pattern or learn more about how you can better attack the bigger numbers. Sometimes your biggest test-day blunder is not allowing yourself to blunder around enough to figure the problem out.

Congratulations: that’s the hardest GMAT problem you’ve solved yet! (And bonus points if you noticed that the answer choices differed by 8, 9, 9, and 8. I still have OCD, and a terrible sense of humor.)

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

You Can Do It! How to Work on GMAT Work Problems

Pump UpRate questions, so far as I can remember, have been a staple of almost every standardized test I’ve ever taken. I recall seeing them on proficiency tests in grade school. They showed up on the SAT. They were on the GRE. And, rest assured, dear reader, you will see them on the GMAT. What’s peculiar is that despite the apparent ubiquity of these problems, I never really learned how to do them in school. This is true for many of my students as well, as they come into my class thinking that they’re just not very good at these kinds of questions, when, in actuality, they’ve just never developed a proper approach. This is doubly true of work problems, which are just a kind of rate problem.

When dealing with a complex work question there are typically only two things we need to keep in mind, aside from our standard “rate * time = work” equation. First, we know that rates are  additive. If I can do 1 job in 4 hours, my rate is 1/4. If you can do 1 job in 3 hours, your rate is 1/3. Therefore, our combined rate is 1/4 + 1/3, or 7/12. So we can do 7 jobs in 12 hours.

The second thing we need to bear in mind is that rate and time have a reciprocal relationship. If our rate is 7/12, then the time it would take us to complete a job is 12/7 hours. Not so complex. What’s interesting is that these simple ideas can unlock seemingly complex questions. Take this official question, for example:

Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.

A) 1/3

B) 1/2

C) 2/3

D) 5/6

E) 1

So let’s start by assigning some variables. We’ll call the rate for p ump A, Ra. Similarly, we’ll designate the rate for pump B as Rb,and the rate for pump C as Rc.

If the time for A and B together to fill the tank is 6/5 hours, then we know that their combined rate is 5/6, because again, time and rate have a reciprocal relationship. So this first piece of information yields the following equation:

Ra + Rb = 5/6.

If A and C can fill the tank in 3/2 hours, then, employing identical logic, their combined rate will be 2/3, and we’ll get:

Ra + Rc = 2/3.

Last, if B and C can fill tank in 2 hours, then their combined rate will be ½, and we’ll have:

Rb+ Rc = 1/2.

Ultimately, what we want here is the time it would take all three pumps working together to fill the tank. If we can find the combined rate, or Ra + Rb + Rc, then all we need to do is take the reciprocal of that number, and we’ll have our time to full the pump. So now, looking at the above equations, how can we get Ra + Rb + Rc on one side of an equation? First, let’s line our equations up vertically:

 Ra + Rb = 5/6.

Ra + Rc = 2/3.

Rb+ Rc = 1/2.

 Now, if we sum those equations, we’ll get the following:

2Ra + 2Rb + 2Rc = 5/6 + 2/3 + 1/2. This simplifies to:

2Ra + 2Rb + 2Rc = 5/6 + 4/6 + 3/6 = 12/6 or 2Ra + 2Rb + 2Rc  = 2.

Dividing both sides by 2, we’ll get: Ra + Rb + Rc  = 1.

This tells us that the pumps, all working together can do one tank in one hour. Well, if the rate is 1, and the time is the reciprocal of the rate, it’s pretty obvious that the time to complete the task is also 1. The answer, therefore, is E.

Takeaway: the most persistent myth we have about our academic limitations is that we’re simply not good at a certain subset of problems when, in truth, we just never properly learned how to do this type of question. Like every other topic on the GMAT, rate/work questions can be mastered rapidly with a sound framework and a little practice. So file away the notion that rates can be added in work questions and that time and rate have a reciprocal relationship. Then do a few practice questions, move on to the next topic, and know that you’re one step closer to mastering the skills that will lead you to your desired GMAT score.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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

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

Don’t Panic on the GMAT!

Letter of RecommendationYou’ve made it. After months of study, mountains of flash cards, and enough time spent on our YouTube channel that you’re starting to feel like Brian Galvin is one of your roommates, you’re at the test center and the GMAT — not the essay or something, but the real GMAT, in all its evil glory, complete with exponents and fractions — is about to begin. You’re nervous but excited, and cautiously optimistic for the first question: maybe it’ll be something like “What’s (2²)³?” or a work rate problem about how long it’d take George Jetson to burn down a widget factory. You mostly remember these questions, so you click “Begin”, and this is what you see:

A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 200 that is both a prime and a palindrome. What is the sum of the digits of p?

A) 3

B) 4

C) 5

D) 6

E) 7

Thud.

I don’t know about you, but I’m petrified. I mean, yeah, I know what you’re saying — I’m the bozo who just dreamed up that question — but I don’t know where it came from, and I’m sort of thinking I might need to summon an exorcist, because I must be possessed by a math demon. What does that question even say? How the heck are we going to solve it?

This is such a common GMAT predicament to be in that I’m willing to bet that 99% of test takers experience it: the feeling that you don’t even know what the question is saying, and the sense of creeping terror that maybe you don’t know what any of these questions are saying. This is by design, of course. The test writers love these sort of “gut check” questions that test your ability to calmly unpack and reason out a cruel and unusual prompt. So many students take themselves out of the game by panicking, but like any GMAT question, once we get past the intimidation factor, the problem is simple at heart. Let’s try to model the process.

We’ll start by clarifying our terms. Palindrome, palindrome … what on earth is a palindrome!? Is that some sort of hovercraft where Sarah Palin lives? Where are our flash cards? Maybe we should just go to law school or open a food truck or something, this test is absurd.

Wait, the answer is right in front of us, in the very first line! “A palindrome is a number that reads the same back-to-front as it does front-to-back.” Phew, OK, and there are even some examples. So a palindrome is a number like 101, 111, 121, etc. Alright, got that. And it’s prime … prime, prime … OK, right, that WAS on a flashcard: a prime number is a number with exactly two factors, such as 2, or 3, or 5, or 7. So if we were to make lists of each of these numbers, primes and palindromes, we’d have

Primes: 2, 3, 5, 7, 11, 13, 17, 19, …

Palindromes: 101, 111, 121, 131, …

and we want the first number that’s greater than 200 that appears on both lists. OK!

Now let’s think of where to start. We know our number is greater than 200, so 202 seems promising. But that can’t be prime: it’s even, so it has at least three factors (1, itself, and 2). Great! We can skip everything that begins/ends with 2, and fast forward to 303. That looks prime, but what was it that Brian kept telling us about divisibility by 3 … ah, yes, test the sum of the digits! 3 + 0 + 3 = 6, and 6 divides by 3, so 303 also divides by 3.

Our next candidate is 313. This seems to be our final hurdle: a lot of quick arithmetic. That’s what the question is testing, after all, right? How quickly can you factor 313?

It sure seems that way, but take one last look at the answers. The GMAT tests efficiency as much as anything else, and it has a way of hiding easter eggs for the observant. Our largest answer is 7, and what’s 3+1+3? 7! So this MUST be the answer, and any time spent factoring 313 is wasted time.

We made it! In hindsight, that didn’t really feel like a math problem, did it? It was testing our ability to:

1) Remember a definition (“prime”)

2) Actually read the question stem (“a palindrome is…”)

3) Not panic, and try a few numbers (“202”? “303”?)

4) Realize that heavy calculation is for suckers, and that the answer might be right in front of us (“check the answers”)

So we just had to remember, actually read the directions, have the courage to try something to see where it leads, and look for clues directly around us. I don’t know about you, but if I were running a business, those are exactly the sort of skills I’d want my employees to have; maybe these test writers are on to something after all!

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

Use Number Lines on the GMAT, Not Memory!

SAT/ACTI’ve written in the past about how the biggest challenge on many GMAT questions is the strain they put on our working memory. Working memory, or our ability to process information that we hold temporarily, is by definition quite limited. It’s why phone numbers only contain seven digits – any more than that and most people wouldn’t be able to recall them. (Yes, there was a time, in the dark and distant past, when we had to remember phone numbers.)

One of the most simple and effective strategies we can deploy to combat our working memory limitations is to simply list out the sample space of scenarios we’re dealing with. If we were told, for example, that x is a prime number less than 20, rather than internalize this information, we can jot down x = 2, 3, 5, 7, 11, 13, 17, or 19. The harder and more abstract the question, the more necessary such a strategy will prove to be.

Take this challenging Data Sufficiency question, for example:

On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?

1) xyz < 0

2) xy <0

The reader is hereby challenged to attempt this exercise in his or her head without inducing some kind of hemorrhage.

So, rather than try to conceptualize this problem mentally, let’s start by actually writing down all the number line configurations that we might have to deal with before even glancing at the statements. We know that x and z are closer than x and y. So we could get the following:

x____z_______________________y

z____x_______________________y

Or we can swap x and y to generate a kind of mirror image

y______________________x_____z

y______________________z_____x

The above number lines are the only four possibilities given the constraints provided in the question stem. Now we have something concrete and visual that we can use when evaluating the statements.

Statement 1 tells us that the product of the three variables is negative. If you’ve internalized your number properties – and we heartily encourage that you do – you know that a product is negative if there are an odd number of negative elements in said product. In this case, that means that either one of the variables is negative, or all three of them are. So let’s use say one of the variables is negative. By placing a 0 strategically, we can use any of our above number lines:

x__0__z______________________y

z__0__x______________________y

y__0___________________x_____z

y__0___________________z_____x

Each of these scenarios will satisfy that first statement. But we only need two.

In our first number line, z is between x and y, so we get a YES to the question.

In our second number line, z is not between x and y, so we get a NO to the question.

Because we can get a YES or a NO to the original question, Statement 1 alone is not sufficient. Eliminate answer choices A and D.

Statement 2 tells us that the product of x and y is negative. Thus, we know that one of the variables is positive, and one of the variables is negative. Again, we can simply peruse our number lines and select a couple of examples that satisfy this condition.

In our first number line, z is between x and y, so we get a YES to the question.

In our third number line, z is not between x and y, so we get a NO to the question.

Like with Statement 1, because we can get a YES or NO to the original question, Statement 2 alone is also not sufficient. Eliminate answer choice B.

When testing the statements together, we know two pieces of information. Statement 1 tells us that either one variable is negative or all three are. Statement 2 tells us that, between x and y, we have one negative and one positive. Therefore, together, we know that either x or y is negative, and the remaining variables are all positive. Now all we have to do is peruse our sample space and locate these scenarios. It turns out that we can use the same two number lines we used when testing Statement 2:

In our first number line, z is between x and y, so we get a YES to the question.

In our third number line, z is not between x and y, so we get a NO to the question.

So even together, the statements are not sufficient to answer the question – the correct answer is E.

Takeaway: on the GMAT there’s no reason to strain your brain any more than is necessary. The more concrete you can make the information you’re provided on a given question, the more likely it is that you’ll be able to properly execute whatever math or logic maneuvers you’re asked to perform.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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

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

GMAT Tip of the Week: Movember and Moving Your GMAT Score Higher

GMAT Tip of the WeekOn this first Friday of November, you may start seeing some peach fuzz sprouts on the upper lips of some of your friends and colleagues. For many around the world, November means Movember, a month dedicated to the hopefully-overlapping Venn Diagram of mustaches and men’s health. Why – other than the fact that this is a GMAT blog – do we mention the Venn Diagram?

Because while the Movember Foundation is committed to using mustaches as a way to increase both awareness of and funding for men’s health issues (in particular prostate and testicular cancer), many young men focus solely on the mustache-growth facet of the month. And “I’m growing a mustache for Movember” without the fundraising follow-through is akin to the following quotes:

“I’m growing a mustache for Movember.”

“I’m running a marathon for lymphoma research.”

“I’m dumping a bucket of ice water over my head on Facebook.”

“I’m taking a GMAT practice test this weekend.”/”I’m going to the library to study for the GMAT.”

Now, those are all noble sentiments expressed with great intentions. But another thing they all have in common is that they’re each missing a critical action step in their mission to reach their desired outcome. Growing a mustache does very little to prevent or treat prostate cancer. Running a marathon isn’t what furthers scientists’ knowledge of lymphoma. Dumping an ice bucket over your head is more likely to cause pneumonia than to cure ALS. And taking a practice test won’t do very much for your GMAT score.

Each of those actions requires a much more thorough and meaningful component. It’s the fundraising behind Movember, Team in Training, and the Ice Bucket Challenge that advances those causes. It’s your effort to use your mustache, sore knees, and Facebook video to encourage friends and family to seek out early diagnosis or to donate to the cause. And it’s the follow-up to your GMAT practice test or homework session that helps you increase your score.

This weekend, well over a thousand practice tests will be taken in the Veritas Prep system, many by young men a week into their mustache growth. But the practice tests that are truly valuable will be taken by those who follow up on their performance, adding that extra step of action that’s all so critical. They’ll ask themselves:

Which mistakes can I keep top-of-mind so that I never make them again?

How could I have budgeted my time better? Which types of problems take the most time with the least probability of a right answer, and which types would I always get right if I just took the extra few seconds to double check and really focus?

Based on this test, which are the 2-3 content areas/question types that I can markedly improve upon between now and my next practice test?

How will I structure this week’s study sessions to directly attack those areas?

And then they’ll follow up on what they’ve learned, following the new week’s plan of attack until it’s time to again take the first step (a practice test) with the commitment to take the substantially-more-important follow-up steps that really move the needle toward success.

Taking a practice test and growing a Movember mustache are great first steps toward accomplishing noble goals, but in classic Critical Reasoning form, premise alone doesn’t guarantee the conclusion. So make sure you don’t leave the GMAT test center this November with an ineffective mustache and a dismal score – put in the hard work that has to accompany that first step, and this can be a Movember to Remember.

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.

GMAT Tip of the Week: Trick or Treat

ZombieinsteinOne 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.

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 and Google+, and Twitter!

By Brian Galvin.

How to Solve Tough GMAT Quant Problems by Blending Strategies

victorinox_mountaineer_lgI 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.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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 “Back to the Future” Can Help Your GMAT Score!

Back to the FutureAs 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.

3) Find Your Skateboard

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.

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 and Google+, and Twitter!

By Brian Galvin.

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

GMAT Tip of the WeekThe 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.”

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 and Google+, and Twitter!

By Brian Galvin.

Read the Last Piece First on the GMAT!

Make Studying FunWhen 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:

DG Graph 1

 

 

 

 

 

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:

DG Graph 2

 

 

 

 

 

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:

DG Graph 3

 

 

 

 

 

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.


DG Graph 4

 

 

 

 

 

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.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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

Pi to the 36th digitWhenever 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.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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

GMAT ReasoningThe 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.

3) Evaluate the answer choices using your speculated answer.

You want to carefully read all 5 answer choices. As you read the answers, compare them to the answer, or the outline of the answer, you speculated. Some answers are obviously incorrect – either they are too narrow in scope, too extreme to be always be true, or do not follow the criteria laid out in the stimulus. Eliminate these answers. For other answer choices that seem attractive, keep them as possibilities. Once you have read all of the answer choices, you can then compare your list of possible answers using the criteria that the correct answer must be always be true.

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

EssayIn 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)!

Pie ChartWhen 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.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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!

MBA Interview QuestionsAbout 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.

Answer choice E:  (4m-12)/[m(m-4)]

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.

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

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

MBA Applicant Evaluation WorkshopThere’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.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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?

No MathThe 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.

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

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

raviVeritas 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

Yoda ForceOnce 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.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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.

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

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

SciNotationIn 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.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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

Ron Point_GMAT TipsThe 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

Ron Point_GMAT TipsAs 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

Keep the PaceLet’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

Ron Point_GMAT TipsI’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

Ron Point_GMAT TipsIt 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.
E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

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

Ron Point_GMAT TipsEveryone 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!”

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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.