The post Quarter Wit Quarter Wisdom: Cyclicity of Units Digits on the GMAT appeared first on Veritas Prep Blog.

]]>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 = 1__6__

2^5 = 3__2__

2^6 = 6__4__

2^7 = 12__8__

2^8 = 25__6__

2^9 = 51__2__

2^10 = 102__4__

…

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 = 2__7__

3^4 = 8__1__

3^5 = 24__3__

3^6 = 72__9__

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 = 4__9__

7^3 = 34__3__

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 = 6__4__

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

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

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]]>The post Is Technology Costing You Your GMAT Score? appeared first on Veritas Prep Blog.

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

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

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]]>The post What to Do if You're Struggling with GMAT Solutions appeared first on Veritas Prep Blog.

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

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]]>The post You Can Do It! How to Work on GMAT Work Problems appeared first on Veritas Prep Blog.

]]>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, R_{a. }Similarly, we’ll designate the rate for pump B as R_{b,}and the rate for pump C as R_{c.}

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:

R_{a }+ R_{b} = 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:

R_{a }+ R_{c} = 2/3.

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

R_{b}+ R_{c} = 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 R_{a }+ R_{b }+ R_{c}, 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 R_{a }+ R_{b }+ R_{c} on one side of an equation? First, let’s line our equations up vertically:

_{ }R_{a }+ R_{b} = 5/6.

R_{a }+ R_{c} = 2/3.

R_{b}+ R_{c} = 1/2.

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

2R_{a }+ 2R_{b }+ 2R_{c} = 5/6 + 2/3 + 1/2. This simplifies to:

2R_{a }+ 2R_{b }+ 2R_{c} = 5/6 + 4/6 + 3/6 = 12/6 or 2R_{a }+ 2R_{b }+ 2R_{c } = 2.

Dividing both sides by 2, we’ll get: R_{a }+ R_{b }+ R_{c } = 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**, **YouTube**, **Google+ **and **Twitter**!

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

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]]>The post Don't Panic on the GMAT! appeared first on Veritas Prep Blog.

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

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]]>The post Use Number Lines on the GMAT, Not Memory! appeared first on Veritas Prep Blog.

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

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

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]]>The post GMAT Tip of the Week: Movember and Moving Your GMAT Score Higher appeared first on Veritas Prep Blog.

]]>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.*

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]]>The post GMAT Tip of the Week: Trick or Treat appeared first on Veritas Prep Blog.

]]>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.*

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]]>The post How to Solve Tough GMAT Quant Problems by Blending Strategies appeared first on Veritas Prep Blog.

]]>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**!

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]]>The post How “Back to the Future” Can Help Your GMAT Score! appeared first on Veritas Prep Blog.

]]>**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 30^{th} 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.*

The post How “Back to the Future” Can Help Your GMAT Score! appeared first on Veritas Prep Blog.

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