The post How to Use Units Digits to Avoid Doing Painful Calculations on the GMAT appeared first on Veritas Prep Blog.

]]>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 Facebook, YouTube, Google+ and Twitter!*

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

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]]>The post How to Approach Difficult GMAT Problems appeared first on Veritas Prep Blog.

]]>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 Facebook, YouTube, Google+ and Twitter!*

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

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]]>The post How to Reach a 99th Percentile GMAT Score Using No New Academic Strategies appeared first on Veritas Prep Blog.

]]>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 99^{th} 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 99^{th} 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:

- Perform mindfulness meditation for the two weeks leading up to the exam.
- Reframe test-day anxiety as excitement.
- Spend 10 minutes the morning of the test writing in a journal.
- 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 Facebook, YouTube, Google+ and Twitter!*

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

The post How to Reach a 99th Percentile GMAT Score Using No New Academic Strategies appeared first on Veritas Prep Blog.

]]>The post Don’t Swim Against the Arithmetic Currents on the GMAT Quant Section appeared first on Veritas Prep Blog.

]]>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.

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

The post Don’t Swim Against the Arithmetic Currents on the GMAT Quant Section appeared first on Veritas Prep Blog.

]]>The post GMAT Tip of the Week: Exit the GMAT Test Center…Don’t Brexit It appeared first on Veritas Prep Blog.

]]>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, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post How to Simplify Percent Questions on the GMAT appeared first on Veritas Prep Blog.

]]>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.

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

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]]>The post GMAT Tip of the Week: The Least Helpful Waze To Study appeared first on Veritas Prep Blog.

]]>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, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

The post GMAT Tip of the Week: The Least Helpful Waze To Study appeared first on Veritas Prep Blog.

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

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

Take this question for example:

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

*I. **4*

*II. **-1*

*III. **-5*

*A) **I only*

*B) **II only*

*C) **III only*

*D) **I and II*

*E) **II and III *

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

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

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

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

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

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

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

*1) **n is odd*

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

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

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

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

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

Let’s keep going.

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

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

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

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

We’re asked about the sum:

After one term, we have 1.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

*By Brian Galvin.*

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

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