How to Use Units Digits to Avoid Doing Painful Calculations on the GMAT

StudentDuring the first session of each new class I teach, we do a quick primer on the utility of units digits. Imagine I want to solve 130,467 * 367,569. Without a calculator, we are surely entering a world of hurt. But we can see almost instantaneously what the units digit of this product would be.

The units digit of 130,467 * 367,569 would be the same as the units digit of 7*9, as only the units digits of the larger numbers are relevant in such a calculation. 7*9 = 63, so the units digit of 130,467 * 367,569 is 3. This is one of those concepts that is so simple and elegant that it seems too good to be true.

And yet, this simple, elegant rule comes into play on the GMAT with surprising frequency.

Take this question for example:

If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digit of n^3?

A) three
B) four
C) six
D) nine
E) ten

Surely, you think, the solution to this question can’t be as simple as cubing the easiest possible numbers to see how many different units digits result. And yet that’s exactly what we’d do here.

1^3 = 1

2^3 = 8

3^3 = 27 à units 7

4^3 = 64 à units 4

5^3 = ends in 5 (Fun fact: 5 raised to any positive integer will end in 5.)

6^3 = ends in 6 (Fun fact: 6 raised to any positive integer will end in 6.)

7^3 = ends in 3 (Well 7*7 = 49. 49*7 isn’t that hard to calculate, but only the units digit matters, and 9*7 is 63, so 7^3 will end in 3.)

8^3 = ends in 2 (Well, 8*8 = 64, and 4*8 = 32, so 8^3 will end in 2.)

9^3 = ends in 9 (9*9 = 81 and 1 * 9 = 9, so 9^3 will end in 9.)

10^3 = ends in 0

Amazingly, when I cube all the integers from 1 to 10 inclusive, I get 10 different units digits. Pretty neat. The answer is E.

Of course, this question specifically invoked the term “units digit.” What are the odds of that happening? Maybe not terribly high, but any time there’s a painful calculation, you’d want to consider thinking about the units digits.

Take this question, for example:

A certain stock exchange designates each stock with a one, two or three letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be replaced and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes? 

A) 2,951
B) 8,125
C) 15,600
D) 16,302
E) 18,278 

Conceptually, this one doesn’t seem that bad.

If I wanted to make a one-letter code, there’d be 26 ways I could do so.

If I wanted to make a two-letter code, there’d be 26*26 or 26^2 ways I could do so.

If I wanted to make a three-letter code, there’d be 26*26*26, or 26^3 ways I could so.

So the total number of codes I could make, given the conditions of the problem, would be 26 + 26^2 + 26^3. Hopefully, at this point, you notice two things. First, this arithmetic will be deeply unpleasant to do.  Second, all of the answer choices have different units digits!

Now remember that 6 raised to any positive integer will always end in 6. So the units digit of 26 is 6, and the units digit of 26^2 is 6 and the units digit of 26^3 is also 6. Therefore, the units digit of 26 + 26^2 + 26^3 will be the same as the units digit of 6 + 6 + 6. Because 6 + 6 + 6 = 18, our answer will end in an 8. The only possibility here is E. Pretty nifty.

Takeaway: Painful arithmetic can always be avoided on the GMAT. When calculating large numbers, note that we can quickly find the units digit with minimal effort. If all the answer choices have different units digits, the question writer is blatantly telegraphing how to approach this problem.

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 written by him here.

How to Approach Difficult GMAT Problems

SAT/ACTMy students have a hard time understanding what makes a difficult GMAT question difficult. They assume that the tougher questions are either testing something they don’t know, or that these problems involve a dizzying level of complexity that requires an algebraic proficiency that’s simply beyond them.

One of my main goals in teaching a class is to persuade everyone that this is not, in fact, how hard questions work on this test. Hard questions don’t ask you do to something you don’t know how to do. Rather, they’re cleverly designed to provoke an anxiety response that makes it difficult to realize that you do know exactly how to solve the problem.

Take this official question, for example:

Let a, b, c and d be nonzero real numbers. If the quadratic equation ax(cx + d) = -b(cx +d) is solved for x, which of the following is a possible ratio of the 2 solutions?

A) –ab/cd
B) –ac/bd
C) –ad/bc
D) ab/cd
E) ad/bc

Most students see this and panic. Often, they’ll start by multiplying out the left side of the equation, see that the expression is horrible (acx^2 + adx), and take this as evidence that this question is beyond their skill level. And, of course, the question was designed to elicit precisely this response. So when I do this problem in class, I always start by telling my students, much to their surprise, that every one of them already knows how to do this. They’ve just succumbed to the question writer’s attempt to convince them otherwise.

So let’s start simple. I’ll write the following on the board: xy = 0. Then I’ll ask what we know about x or y. And my students shrug and say x or y (or both) is equal to 0. They’ll also wonder what on earth such a simple identity has to do with the algebraic mess of the question they’d been struggling with.

I’ll then write this: zx + zy = 0. Again, I’ll ask what we know about the variables. Most will quickly see that we can factor out a “z” and get z(x+y) = 0. And again, applying the same logic, we see that one of the two components of the product must equal zero – either z = 0 or x + y = 0.

Next, I’ll ask if they would approach the problem any differently if I’d given them zx = -zy – they wouldn’t.

Now it clicks. We can take our initial equation in the aforementioned problem: ax(cx +d) = -b(cx+d), and see that we have a ‘cx + d’ on both sides of the equation, just as we’d had a “z” on both sides of the previous example. If I’m able to get everything on one side of the equation, I can factor out the common term.

Now ax(cx +d) = -b(cx+d) becomes ax(cx +d) + b(cx+d) = 0.

Just as we factored out a “z” in the previous example, we can factor out “cx + d” in this one.

Now we have (cx + d)(ax + b) = 0.

Again, if we multiply two expressions to get a product of zero, we know that at least one of those expressions must equal 0. Either cx + d = 0 or ax + b = 0.

If cx + d = 0, then x = -d/c.

If ax + b = 0, then x = -b/a.

Therefore, our two possible solutions for x are –d/c and –b/a. So, the ratio of the two would simply be (-d/c)/(-b/a). Recall that dividing by a fraction is the equivalent of multiplying by the reciprocal, so we’re ultimately solving for (-d/c)(-a/b). Multiplying two negatives gives us a positive, and we end up with da/cb, which is equivalent to answer choice E.

Takeaway: Anytime you see something on the GMAT that you think you don’t know how to do, remind yourself that the question was designed to create this false impression. You know how to do it – don’t hesitate to dive in and search for how to apply this knowledge.

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 written by him here.

How to Reach a 99th Percentile GMAT Score Using No New Academic Strategies

Pump UpLast week I received an email from an old student who’d just retaken the GMAT. He was writing to let me know that he’d just received a 770. Of course, I was ecstatic for him, but I was even more excited once I considered what his journey could mean for other students.

His story is a fairly typical one: like the vast majority of GMAT test-takers, he enrolled in the class looking to hit a 700. His scores improved steadily throughout the course, and when he took the test the first time, he’d received a 720, which was in line with his last two practice exams. After he finished the official test, he called me – both because he was feeling pretty good about his score but also because a part of him was sure he could do better.

My feeling at the time was that there really wasn’t any pressing need for a retake: a 720 is a fantastic score, and once you hit that level of success, the incremental gains of an improvement begin to suffer from the law of diminishing returns. Still, when you’re talking about the most competitive MBA programs, you want any edge you can get. Moreover, he’d already made up his mind. He wanted to retake.

Part of his decision was rooted in principle. He was sure he could hit the 99th percentile, and he wanted to prove it to himself. The problem, he noted, was that he’d already mastered the test’s content. So if there was nothing left for him to learn, how did he jump to the 99th percentile?

The answer can be found in the vast body of literature enumerating the psychological variables that influence test scores. We like to think of tests as detached analytic tools that measure how well we’ve mastered a given topic. In reality, our mastery of the content is one small aspect of performance.

Many of us know this from experience – we’ve all had the experience of studying hard for a test, feeling as though we know everything cold, and then ending up with a score that didn’t seem to reflect how well we’d learned the material. After I looked at the research, it was clear that the two most important psychological variables were 1) confidence and 2) how well test-takers managed test anxiety. (And there’s every reason to believe that those two variables are interconnected.)

I’ve written in the past about how a mindfulness meditation practice can boost test day performance. I’ve also written about how perceiving anxiety as excitement, rather than as a nefarious force that needs to be conquered, has a similarly salutary effect. Recently I came across a pair of newer studies.

In one, researchers found that when students wrote in their journals for 10 minutes about their test-taking anxiety the morning of their exams, their scores went up substantially. In another, the social psychologist Amy Cuddy found that body language had a profound impact on performance in all sorts of domains. For example, her research has revealed that subjects who assumed “power poses” for two minutes before a job interview projected more confidence during the interview and were better able to solve problems than a control group that assumed more lethargic postures. (To see what these power poses look like, check out Cuddy’s fascinating Ted talk here.) Moreover, doing power poses actually created a physiological change, boosting testosterone and reducing the stress hormone Cortisol.

Though her research wasn’t targeted specifically at test-takers, there’s every reason to believe that there would be a beneficial effect for students who practiced power poses before an exam. Many teachers acquainted with Cuddy’s research now recommend that their students do this before tests.

So the missing piece of the puzzle for my student was simply confidence. His strategies hadn’t changed. His knowledge of the core concepts was the same. The only difference was his psychological approach. So now I’m recommending that all of my students do the following to cultivate an ideal mindset for producing their best possible test scores:

  1. Perform mindfulness meditation for the two weeks leading up to the exam.
  2. Reframe test-day anxiety as excitement.
  3. Spend 10 minutes the morning of the test writing in a journal.
  4. Practice two minutes of power poses in the waiting room before sitting for the exam and between the Quant and Verbal section.

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 written by him here.

Don’t Swim Against the Arithmetic Currents on the GMAT Quant Section

MalibuWhen I was a child, I was terrified of riptides. Partially, this was a function of having been raised by unusually neurotic parents who painstakingly instilled this fear in me, and partially this was a function of having inherited a set of genes that seems to have predisposed me towards neuroticism. (The point, of course, is that my parents are to blame for everything. Perhaps there is a better venue for discussing these issues.)

If there’s a benefit to fears, it’s that they serve as potent motivators to find solutions to the troubling predicaments that prompt them. The solution to dealing with riptides is to avoid struggling against the current. The water is more powerful than you are, so a fight is a losing proposition – rather, you want to wait for an opportunity to swim with the current and allow the surf to bring you back to shore. There’s a profound wisdom here that translates to many domains, including the GMAT.

In class, whenever we review a strategy, my students are usually comfortable applying it almost immediately. Their deeper concern is about when to apply the strategy, as they’ll invariably find that different approaches work with different levels of efficacy on different problems. Moreover, even if one has a good strategy in mind, the way the strategy is best applied is often context-dependent. When we’re picking numbers, we can say that x = 2 or x = 100 or x = 10,000; the key is not to go in with a single approach in mind. Put another way, don’t swim against the arithmetic currents.

Let’s look at some questions to see this approach in action:

At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women, and children at the picnic, how many men were there, in terms of x?

A) x/2
B) x/3
C) x/4
D) x/5
E) x/6

The moment we see “x,” we can consider picking numbers. The key here is contemplating how complicated the number should be. Swim with the current – let the question tell you. A quick look at the answer choices reveals that x could be something simple. Ultimately, we’re just dividing this value by 2, 3, 4, 5, or 6.

Keeping this in mind, let’s think about the first line of the question. If there are 3 times as many adults as children, and we’re keeping things simple, we can say that there are 3 adults and 1 child, for a total of 4 people. So, x = 4.

Now, we know that among our 3 adults, there are twice as many women as men. So let’s say there are 2 women and 1 man. Easy enough. In sum, we have 2 women, 1 man, and 1 child at this picnic, and a total of 4 people. The question is how many men are there? There’s just 1! So now we plug x = 4 into the answers and keep going until we find x = 1. Clearly x/4 will work, so C is our answer. The key was to let the question dictate our approach rather than trying to impose an approach on the question.

Let’s try another one:

Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in February, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. On which month were sales closes to the sales in January?

A) February
B) March
C) April
D) May
E) June

Great, you say. It’s a percent question. So you know that picking 100 is often a good idea. So, let’s say sales in January were 100. If we want the month when sales were closest to January’s level, we want the month when sales were closest to 100, Sales in February were 10% greater, so February sales were 110. (Remember that if sales increase by 10%, we can multiply the original number by 1.1. If they decrease by 10% we could multiply by 0.9, and so forth.)

So far so good. Sales in March were 15% less than in February. Well, if sales in Feb were 110, then the sales in March must be 110*(0.85). Hmm… A little tougher, but not insurmountable. Now, sales in April were 20% greater than they were in March, meaning that April sales would be 110*(0.85)*1.2. Uh oh.  Once you see that sales are 10% less in May than they were in April, we know that sales will be 110*(0.85)*1.2*0.9.

Now you need to stop. Don’t swim against the current. The arithmetic is getting hard and is going to become time-consuming. The question asks which month is closest to 100, so we don’t have to calculate precise values. We can estimate a bit. Let’s double back and try to simplify month by month, keeping things as simple as possible.

Our February sales were simple: 110. March sales were 110*0.85 – an unpleasant number. So, let’s try thinking about this a little differently. 100*0.85 = 85.  10*0.85 = 8.5. Add them together and we get 85 + 8.5 = 93.5.  Let’s make life easier on ourselves – we’ll round up, and call this number 94.

April sales are 20% more than March sales. Well, 20% of 100 is clearly 20, so 20% of 94 will be a little less than that. Say it’s 18. Now sales are up to 94 + 18 = 112. Still not close to 100, so we’ll keep going.

May sales are 10% less than April sales. 10% of 112 is about 11. Subtract 11 from 112, and you get 101. We’re looking for the number closest to 100, so we’ve got our answer – it’s D, May.

Takeaway: Don’t try to impose your will on GMAT questions. Use the structural clues of the problems to dictate how you implement your strategy, and be prepared to adjust midstream. The goal is never to conquer the ocean, but rather, to ride the waves to calmer waters.

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 written by him here.

GMAT Tip of the Week: Exit the GMAT Test Center…Don’t Brexit It

GMAT Tip of the WeekAcross much of the United Kingdom today, referendum voters are asking themselves “wait, did I think that through thoroughly?” in the aftermath of yesterday’s Brexit vote. Some voters have already admitted that they’d like a do-over, while evidence from Google searches in the hours immediately following the poll closures show that many Brits did a good deal of research after the fact.

And regardless of whether you side with Leave or Stay as it corresponds to the EU, if your goal is to Leave your job to Stay at a top MBA program in the near future, you’d be well-served to learn a lesson from those experiencing Brexit Remorse today.

How can the Brexit aftermath improve you GMAT score?

Pregrets, Not Regrets (Yes, Brexiters…we can combine words too.)
The first lesson is quite simple. Unlike those who returned home from the polls to immediately research “What should I have read up on beforehand?” you should make sure that you do your GMAT study before you get to the test center, not after you’ve (br)exited it with a score as disappointing as this morning’s Dow Jones.

But that doesn’t just mean, “Study before the test!” – an obvious tip. It also means, “Anticipate the things you’ll wish you had thought about.” Which means that you should go into the test center with list of “pregrets” and not leave the test center with a list of regrets.

Having “pregrets” means that you already know before you get to the test center what your likely regrets will be, so that you can fix them in the moment and not lament them after you’ve seen your score. Your list of pregrets should be a summary of the most common mistakes you’ve made on your practice tests, things like:

  • On Data Sufficiency, I’d better not forget to consider negative numbers and nonintegers.
  • Before I start doing algebra, I should check the answer choices to see if I can stop with an estimate.
  • I always blank on the 30-60-90 divisibility rule, so I should memorize it one more time in the parking lot and write it down as soon as I get my noteboard.
  • Reading Comprehension inferences must be true, so always look for proof.
  • Slow down when writing 4’s and 7’s on scratchwork, since when I rush they tend to look too much alike.
  • Check after every 10 questions to make sure I’m on a good pace.

Any mistakes you’ve made more than once on practice tests, any formulas that you know you’re apt to blank on, any reminders to yourself that “when X happens, that’s when the test starts to go downhill” – these are all items that you can plan for in advance. Your debriefs of your practice tests are previews of the real thing, so you should arrive at the test center with your pregrets in mind so that you can avoid having them become regrets.

Much like select English voters, many GMAT examinees can readily articulate, “I should have read/studied/prepare for _____” within minutes of completing their exam, and very frequently, those elements are not a surprise. So anticipate in the hour/day before the test what your regrets might be in the hours/days immediately following the test, and you can avoid that immediate remorse.

Double Cheque Your Work
Much like a Brexit vote, you only get one shot at each GMAT problem, and then the results lead to consequences. But the GMAT gives you a chance to save yourself from yourself – you have to both select your answer and confirm it. So, unlike those who voted and then came home to Google asking, “Did I do the right thing?” you should ask yourself that question before you confirm your answer. Again, your pregrets are helpful. Before you submit your answer, ask yourself:

  • Did I solve for the proper variable?
  • Does this number make logical sense?
  • Does this answer choice create a logical sentence when I read it back to myself?
  • Does this Inference answer have to be true, or is there a chance it’s not?
  • Am I really allowed to perform that algebraic operation? Let me try it with small numbers to make sure…

There will, of course, be some problems on the GMAT that you simply don’t know how to do, and you’ll undoubtedly get some problems wrong. But for those problems that you really should have gotten right, the worst thing that can happen is realizing a question or two later that you blew it.

Almost every GMAT examinee can immediately add 30 points to his score by simply taking back those points he would have given away by rushing through a problem and making a mistake he’d be humiliated to know he made. So, take that extra 5-10 seconds on each question to double check for common mistakes, even if that means you have to burn a guess later in the section. If you minimize those mistakes on questions within your ability level, that guess will come on a problem you should get wrong, anyway.

Like a Brexit voter, the best you can do the day before and day of your important decision-making day is to prepare to make the best decisions you can make. If you’re right, you’re right, and if you’re wrong, you’re wrong, and you may never know which is which (the GMAT won’t release your questions/answers and the Brexit decision will take time to play out). The key is making sure that you don’t leave with immediate regrets that you made bad decisions or didn’t take the short amount of time to prepare yourself for better ones. Enter the test center with pregrets; don’t Brexit it with regrets.

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.

How to Simplify Percent Questions on the GMAT

stressed-studentOne of the most confounding aspects of the GMAT is its tendency to make simple concepts seem far more complex than they are in reality. Percent questions are an excellent example of this.

When I introduce this topic, I’ll typically start by asking my class the following question: If you’ve completed 10% of a project how much is left to do?  I have never, in all my years of teaching, had a class that was unable to tell me that 90% of the project remains. It’s more likely that they’ll react as though I’m insulting their collective intelligence. And yet, when test-takers see this concept under pressure, they’ll often fail to recognize it.

Take the following question, for example:

Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24 min 18 sec, she had completed 10% of her exercise session. The readout indicated which of the following when she had completed 40% of her exercise session.

(A) 10 min. 48 sec.
(B) 14 min. 52 sec.
(C) 14 min. 58 sec.
(D) 16 min. 6 sec.
(E) 16 min. 12 sec.

Hopefully, you’ve noticed that this question is testing the same simple concept that I use when introducing percent problems to my class. And yet, in my experience, a solid majority of students are stumped by this problem. The reason, I suspect, is twofold. First, that figure – 24 min. 18 sec. – is decidedly unfriendly. Painful math often lends itself to careless mistakes and can easily trigger a panic response. Second, anxiety causes us to work faster, and when we work faster, we’re often unable to recognize patterns that would be clearer to us if we were calm.

There’s interesting research on this. Psychologists, knowing that the color red prompts an anxiety response and that the color blue has a calming effect, conducted a study in which test-takers had to answer math questions – the questions were given to some subjects on paper with a red background and to other subjects on paper with a blue background. (The control group had questions on standard white paper.) The red anxiety-producing background noticeably lowered scores and the calming blue background boosted scores.

Now, the GMAT doesn’t give you a red background, but it does give you unfriendly-seeming numbers that likely have the same effect. So, this question is as much about psychology as it is about mathematical proficiency. Our job is to take a deep breath or two and rein in our anxiety before we proceed.

If Dara has completed 10% of her workout, we know she has 90% of her workout remaining. So, that 24 min. 18 sec. presents 90% of her total workout. If we designate her total workout time as “t,” we end up with the following equation:

24 min. 18 sec. = 0.90t

Let’s work with fractions to solve. 18 seconds is 18/60 minutes, which simplifies to 3/10 minutes. 0.9 is 9/10, so we can rewrite our equation as:

24 + 3/10 = (9/10)t
(243/10) = (9/10)t
(243/10)*(10/9) = t
27 = t

Not so bad. Dara’s full workout is 27 minutes long.

We want to know how much time is remaining when Dara has completed 40% of her workout. Well, if she’s completed 40% of her workout, we know she has 60% of her workout remaining. If her full workout is 27 minutes, then 60% of this value is 0.60*27 = (3/5)*27 = 81/5 = 16 + 1/5, or 16 minutes 12 seconds. And we’ve got our answer: E.

Now, let’s say you get this problem with 20 seconds remaining on the clock and you simply don’t have time to solve it properly. Let’s estimate.

Say, instead of 24 min 18 seconds remaining, Dara had 24 minutes remaining (so we know we’re going to underestimate the answer). If that’s 90% of her workout time, 24 = (9/10)t, or 240/9 = t.

We want 60% of this, so we want (240/9)*(3/5).

Because 240/5 = 48 and 9/3 = 3, (240/9)*(3/5) = 48/3 = 16.

We know that the correct answer is over 16 minutes and that we’ve significantly underestimated – makes sense to go with E.

Takeaway: Don’t let the question-writer trip you up with figures concocted to make you nervous. Take a breath, and remember that the concepts being tested are the same ones that, when boiled down to their essence, are a breeze when we’re calm.

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 written by him here.

GMAT Tip of the Week: The Least Helpful Waze To Study

GMAT Tip of the WeekIf you drive in a large city, chances are you’re at least familiar with Waze, a navigation app that leverages user data to suggest time-saving routes that avoid traffic and construction and that shave off seconds and minutes with shortcuts on lesser-used streets.

And chances are that you’ve also, at some point or another, been inconvenienced by Waze, whether by a devout user cutting blindly across several lanes to make a suggested turn, by the app requiring you to cut through smaller streets and alleys to save a minute, or by Waze users turning your once-quiet side street into the Talladega Superspeedway.

To its credit, Waze is correcting one of its most common user complaints – that it often leads users into harrowing and time-consuming left turns. But another major concern still looms, and it’s one that could damage both your fender and your chances on the GMAT:

Beware the shortcuts and “crutches” that save you a few seconds, but in doing so completely remove all reasoning and awareness.

With Waze, we’ve all seen it happen: someone so beholden to, “I must turn left on 9th Street because the app told me to!” will often barrel through two lanes of traffic – with no turn signal – to make that turn…not realizing that the trip would have taken the exact same amount of time, with much less risk to the driver and everyone else on the road, had he waited a block or two to safely merge left and turn on 10th or 11th. By focusing so intently on the app’s “don’t worry about paying attention…we’ll tell you when to turn” features, the driver was unaware of other cars and of earlier opportunities to safely make the merge in the desired direction.

The GMAT offers similar pitfalls when examinees rely too heavily on “turn your brain off” tricks and techniques. As you learn and practice them, strategies like the “plumber butt” for rates and averages may seem quick, easy, and “turn your brain off” painless. But the last thing you want to do on a higher-order thinking test like the GMAT is completely turn your brain off. For example, a “turn your brain off” rate problem might say:

John drives at an average rate of 45 miles per hour. How many miles will he drive in 2.5 hours?

And using a Waze-style crutch, you could remember that to get distance you multiply time by rate so you’d get 112.5 miles. That may be a few seconds faster than performing the algebra by thinking “Rate = Distance over Time”; 45 = D/2.5; 45(2.5) = D; D = 112.5.

But where a shortcut crutch saves you time on easier problems, it can leave you helpless on longer problems that are designed to make you think. Consider this Data Sufficiency example:

A factory has three types of machines – A, B, and C – each of which works at its own constant rate. How many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

(1) 7 Machine As and 11 Machine Bs can produce 250 widgets per hour

(2) 8 Machine As and 22 Machine Cs can produce 600 widgets per hour

Here, simply trying to plug the information into a simple diagram will lead you directly to choice E. You simply cannot separate the rate of A from the rate of B, or the rate of B from the rate of C. It will not fit into the classic “rate pie / plumber’s butt” diagram that many test-takers use as their “I hate rates so I’ll just do this trick instead” crutch.

However, those who have their critical thinking mind turned on will notice two things: that choice E is kind of obvious (the algebra doesn’t get you very close to solving for any one machine’s rate) so it’s worth pressing the issue for the “reward” answer of C, and that if you simply arrange the algebra there are similarities between the number of B and of C:

7(Rate A) + 11(Rate B) = 250
8(Rate A) + 22(Rate C) = 600

Since 11 is half of 22, one way to play with this is to double the first equation so that you at least have the same number of Bs as Cs (and remember…those are the only two machines that you don’t have “together” in either statement, so relating one to the other may help). If you do, then you have:

14(A) + 22(B) = 500
8(A) + 22(C) = 600

Then if you sum the questions (Where does the third 22 come from? Oh, 14 + 8, the coefficients for A.), you have:

22A + 22B + 22C = 1100

So, A + B + C = 50, and now you know the rate for one of each machine. The two statements together are sufficient, but the road to get there comes from awareness and algebra, not from reliance on a trick designed to make easy problems even easier.

The lesson? Much like Waze, which can lead to lack-of-awareness accidents and to shortcuts that dramatically up the degree of difficulty for a minimal time savings, you should take caution when deciding to memorize and rely upon a knee-jerk trick in your GMAT preparation.

Many are willing (or just unaware that this is the decision) to sacrifice mindfulness and awareness to save 10 seconds here or there, but then fall for trap answers because they weren’t paying attention or become lost when problems are more involved because they weren’t prepared.

So, be choosy in the tricks and shortcuts you decide to adopt! If a shortcut saves you a minute or two of calculations, it’s worth the time it takes to learn and master it (but probably never worth completely avoiding the “long way” or knowing the general concept). But if its time savings are minimal and its grand reward is that, “Hey, you don’t have to understand math to do this!” you should be wary of how well it will serve your aspirations of scores above around 600.

Don’t let these slick shortcut waze of avoiding math drive you straight into an accident. Unless the time savings are game-changing, you shouldn’t make a trade that gains you a few seconds of efficiency on select, easier problems in exchange for your awareness and understanding.

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.

How to Simplify Sequences on the GMAT

SAT/ACTThe GMAT loves sequence questions. Test-takers, not surprisingly, do not feel the same level of affection for this topic. In some ways, it’s a peculiar reaction. A sequence is really just a set of numbers. It may be infinite, it may be finite, but it’s this very open-endedness, this dizzying level of fuzzy abstraction, that can make sequences so difficult to mentally corral.

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

Take this question for example:

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

I. 4
II. -1
III. -5

A) I only
B) II only
C) III only
D) I and II
E) II and III

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

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

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

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

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

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

The sequence a1, a2, a3, . . , an of n integers is such that ak = k if k is odd and ak = -ak-1 if k is even. Is the sum of the terms in the sequence positive?

1) n is odd

2) an is positive

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

a1 is the first term in the sequence. We’re told that ak = k if k is odd. Well, 1 is odd, so now we know that a1 = 1. So far so good.

a2 is the second term in the sequence. We’re told that ak = -ak-1 if k is even. 2 is even, so a2 = -a2-1 , meaning that a2 = -a1. Well, we know that a1 = 1, so if a2 = -a1 then a2 = -1.

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

Let’s keep going.

a3 is the third term in the sequence. Remember that ak = k if k is odd. 3 is odd, so now we know that a3 = 3.

a4 is the fourth term in the sequence. Remember that ak = -ak-1 if k is even. 4 is even, so a4 = -a4-1 , meaning that a4 = -a3We know that a3 = 3, so if a4 = -a3 then a4 = -3.

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

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

We’re asked about the sum:

After one term, we have 1.

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

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

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

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

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

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

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

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

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

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

You’re Fooling Yourself: The GMAT is NOT the SAT!

StudentWhile a fair number of GMAT test takers study for and complete the exam a number of years into their professional career (the average age of a B-school applicant is 28, a good 6-7 years removed from their undergraduate graduation), you may be one of the ambitious few who is studying for the GMAT during, or immediately following, your undergraduate studies.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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