GMAT Challenge Question: Solve this stats problem, STAT!

Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and T. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of T if J is negative?

(A) -2
(B) 0
(C) 1
(D) 2
(E) 5

Please include your answers in the comments field and we'll be back later today with the solution!


UPDATE: Solution.

This problem demonstrates a helpful note about statistics problems - quite often the key to solving a stats problem is something other than stats: number properties, divisibility, algebra, etc. The statistics nature of these problems is often just a way to make a simpler problem look more difficult.

Here, the phrase "factor of 34" should stand out to you, as there are only four factors of 34, so you can narrow down the possibilities pretty quickly to 1, 2, 17, and 34. And because the number in question must be an exponential term that becomes a factor of 34, it's even more limited: 2, 17, and 34 can only be created by one integer exponent - "itself" to the first power.

The base of that exponent is going to be the median of Set A, and because we know that the median of Set A will be 3 (a negative term for variable J means that 3 will be the middle term), the question becomes that much clearer. 3^W can only be a factor of 34 if it's set equal to 1, and the only way to do that is for W to be 0. REMEMBER: anything to the power of 0 is equal to 1, a great equalizer on the GMAT!

Therefore, the correct answer is 0.

Plan on taking the GMAT soon? See how Veritas Prep's GMAT prep courses can help you break 700. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Tip of the Week: Let 'er Rip

10-10-10. The date has been plastered all over the streets of Chicago on billboards, storefront signs, flyers and posters. On that repetitive date, approximately 40,000 people will take part in one of the world's most repetitive activities -- the Chicago Marathon. A marathon is not unlike the GMAT -- a task for which you prepare for months, agonize the night before, and hope to complete successfully in under four hours, for many. And, on both the GMAT and the marathon, the worst thing that you can do is think too much.

Your author will be among the 40,000 runners, so in a break from journalistic norm I may switch to first-person here. (As a side note, I took the opportunity last night to visit our Chicago GMAT course and picked up a memorable quote from instructor extraordinaire Frankie Beecroft: "You have to get as good at taking this test as they are at making it." Brilliant.) In any marathon that I've ever run, the smartest thing I did was turn my conscious mind off, and I'm convinced that it's the best way to take the GMAT.

Like the marathon, the GMAT is a repetitive activity -- you're studied for hours, taken multiple practice tests, and turned yourself into a creature of habit, subconsciously performing operations like "it's a weaken question so I'll focus on finding the conclusion and the logical flaw" or "that sentence leads with a description so the modifier may be misplaced." But on test day, just as marathoners tend to do on race day, you'll be tempted to think about anything and everything other than the problem in front of you: "This question looks too easy, so I must be doing poorly"; "I need to calculate my pace-per-question"; "What's the shortcut that I read about a month ago, and does it even apply to this problem?" Your conscious mind, if let to run free, will overwhelm your subconscious -- the part of your mind that already knows what to do.

My worst ever marathon experience was the first six miles of the Boston Marathon, a race that I had trained for years to qualify for and for which I had subsequently trained harder than for any other I had done. This was a dream come true...and for those first six miles I thought of nothing else other than calculating split times, worrying about where the next mile marker would come, second-guessing my hydration and nutrition strategies, etc. It was excruciating...at the end of hundreds of miles and several months of training, I was thinking about this race like I were a toddler taking his first step, completely overthinking and overanalyzing each step and each breath. Finally in the sixth mile, I had to take control of my conscious mind and put it in its place -- a well-conditioned athlete in the first quarter of the race, I stopped and walked for a full minute to get control of my mind and start fresh.

I had to let my body do what I had trained it to, because at that point frantic thinking could only hurt me.

On the GMAT, you'll likely need to do the version of the same. You've trained your mind to recognize common problem types and concepts, and you probably can do them in your sleep (admit it -- we've all dreamed in Data Sufficiency form at least once). Let yourself do that -- rely on your internal pacing clock that you've developed over several practice tests and do a self-check every 10 problems or so to make sure that you're on pace. Relax and keep your conscious thought solely on the areas that you've preordained to be important -- double-checking common mistakes, interpreting problems that look unique, etc.

Ultimately, test day, like race day, is just the final lap of a long process -- by that point, the best thing you can do is to stay out of your own way and let your mind and body do what you've trained them to do. If you do find yourself thinking too much about anything and everything other than the problem, take a mental "walk" and remind yourself that your training needs to take over. Save your conscious stress for truly difficult decisions, like "Harvard or Wharton?"

Plan on taking the GMAT soon? See how Veritas Prep's GMAT prep courses can help you reach your maximum potential on the test. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Tip of the Week: Punting For Field Position

What a weekend this will be! (Author's note: you're looking at about a paragraph of pure football content; not a fan? You can probably skip a paragraph and just pick up the GMAT tips, but trust me when I say that this paragraph is going somewhere). Perhaps the Ali-Frazier of the current era will take place tomorrow evening in Tuscaloosa, with #1 Alabama taking on #7 Florida.

Just down the dial, two of the early-season's most impressive teams, Oregon and Stanford, will do battle in the Pac 10's matchup of the season. Stanford's coach, Jim Harbaugh, will take part in a weekend that prominently features several members of Quarterback U, Michigan: Heisman frontrunner Denard Robinson will get back on track after an injury-shortened game last week, and the NFL's Monday Night Football showcase will feature Robinson's predecessors Tom Brady and Chad Henne quarterbacking their respective teams. Are you excited yet?

The answer may well be no, as if you're applying to business schools this fall you may be swamped in applications (perhaps to Stanford itself, with the deadline coming next week) and GMAT preparation. But if you're looking for an excuse to take a study/essay break and watch some football this weekend, the slate of huge games can actually teach you a valuable strategic lesson as you ready yourself for battle with the GMAT:

Sometimes you have to punt for field position.

The term "punt" has become synonymous, at least in some connotations, with "quit", but in football (as it can be on the GMAT) it's actually a very strategic type of quitting. Coaches will elect to punt the ball away to the opposing team in order to gain valuable field position -- the space that the team will need in order to be able to score on the next possession.

This strategy can work wonders for you on the GMAT, a test that quite often limits its version of "field position" -- in this case time -- giving you precious little of the resource that you may need most. In at least some cases, you'll likely need to guess ("punt") and move on so that you have time available for future questions. Punting on the GMAT can take on at least a couple of strategic forms:

Necessary Punting
There will almost certainly be questions that you simply cannot solve in 2-3 minutes, and after that duration of time you'll need to cut your losses, guess, and save your time and mental energy for the next question. At an average of 2 minutes per math question and 1:45 for each verbal question, wasting an extra minute per question on a handful of questions can severely impact your ability to finish the exam on time. In addition to the severe penalties for leaving questions blank (it's almost always worse than guessing), you're losing opportunities to answer questions that you could likely answer correctly. What's even more troubling is the impact that running behind on time can have on multiple questions - when you rush, you're exponentially more likely to make careless mistakes and miss questions that you should answer correctly.

Accordingly, you'll want to develop an internal clock - much like that of a top quarterback like Brady or Henne - that lets you know when you're starting to approach that 2-minute mark (taking practice tests is crucial for developing this skill). Then, when your internal clock lets you know that you're starting to push that 2-minute threshold, take a second to analyze your situation. If you think that within 30 seconds or so you'll have the right answer - it's just a matter of finishing the calculations or double-checking your work - then by all means finish the question...it's like 4th-and-short in the opponents' territory! However, if you assess that it's more than likely that you'll still be working without a finish line - you're in 4th-and-long territory - you'll want to make an educated guess, punt, and save your time for the remaining questions.

Quick Punt
This type of punting - you'll see it in college football when a quarterback lines up in the shotgun on a makeable 4th down but then punts out of that formation to catch the defense without a returner - can be more strategic and a little less intuitive.

The "quick punt" strategy is one that you should consider employing if you know that timing will be a significant factor for you on the test. If you're resigned to having to rush, the quick punt strategy can help you win the "field position" or time battle. Here's how you can employ this strategy:

- Plan to "punt" on a predetermined number of questions (1 out of every 10 or 1 out of every 12...basically 1/4 or 1/3 of the test) and consider those punts to be assets - you own them and can feel free to use them at your discretion.

- When you see a question that looks difficult or time-consuming, use your punt within the first 30 seconds or less of looking at it so that you can bank nearly the full two minutes to spread over the rest of that section. This way, you have more time available for the questions that you know you can answer correctly. And because you've already predetermined that you'd guess, you psychologically don't have to feel like you've quit or failed - you've just strategically deployed an asset.

- The advantages? That extra time will allow you to relax a bit and not worry about pacing. You'll reduce your stress level and give yourself extra time to avoid those working-too-quickly errors. And because of the adaptive nature of the GMAT, it's quite likely that the questions you identify as "puntworthy" are those that you would have answered incorrectly, anyway. You're sacrificing minimal accuracy and giving yourself extra time. Furthermore, there's a 20% chance or more that you'll get that question right based on your guess, and a not-insignificant chance that that question is an unscored, experimental question, so you may not lose at all on this strategy.

As has been discussed in this space previously, the GMAT tests not only your ability to answer individual questions correctly but also your ability to manage the entire project of taking the test. By strategically electing to punt on a handful of questions, you can demonstrate your capacity for managing aggressive deadlines and workloads, and those skills are highly sought by business schools and employers. Punting isn't always "quitting" -- it's a part of the game, and if you learn to play it effectively you can maximize your chances of winning.

Do you want to reach your maximum potential on the GMAT? A Veritas Prep GMAT prep course is just what you need. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Challenge Question: Prime Time

It's time again for another GMAT challenge question, and this one focuses on one of the quantitative section's favorite themes: prime factors.

Please submit your answers in the comments field, and check back later today for the solution and a more-thorough explanation of prime factors!

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

(A) 7
(B) 11
(C) 13
(D) 17
(E) 19

UPDATE: Solution!

While it's quite common for students to simply look at the numbers 12!, 11!, and 10! and recognize that the highest naturally-occurring prime number is 11, it's important to recognize that this is an addition problem - the numbers 12!11! and 11!10! are combined to create a new number that may well have a higher prime factor than its factorial components.

When adding large numbers like factorials and exponents, as we discussed in this space last week, it's often quite helpful to factor out common terms. In this case, it's particularly important, because our entire goal is to break out the large sum into prime factors so that we can determine which is biggest. Each term has a common 11!, so by factoring that out we can get from:

12!11! + 11!10!

to

11! (12! + 10!)

Now, 12! includes a 10! - it's essentially 12 * 11 * 10!, so we have a common 10! within the parentheses that can also be factored out, going from:

11! (12*11*10! + 10!)

to

11!10! (12*11 + 1)

At this point, the largest prime factor must be either the 11 outside the parentheses or a factor of the number within it, so it's necessary to check the number within. 12*11 + 1 = 132 + 1 = 133. 133 is the product of 7*19, so 19 is a prime factor of 12!11! + 11!10!, and therefore the largest prime factor. Accordingly, E is the correct answer.

Plan on taking the GMAT soon? See how Veritas Prep's GMAT prep courses can help you reach your maximum potential on the test. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Tip of the Week: Change You Can Believe In

If it's the autumn of an even-numbered year, change is in the air, or at least in the hot air of the politicians seeking election in November. Noting, evidently, that most people are unhappy, politicians repeat the word change more than any other (with the exception of John McCain, who in 2008 used the word "Petraeus" slightly more than he used "change", but it was close!). Browse the political ads and stump speeches on YouTube and you won't get too specific an idea of what each candidate promises, but, by George, they'll certainly repeat the word "change" until you want to change the channel.

If you've clicked off of the Brown-vs.-Whitman or O'Donnell-vs.-sanity ads long enough to view this post, you're probably looking to change your GMAT score and your MBA candidacy. If so, you're in luck, because if there's one thing you can be sure of on the GMAT, it's change. Ratios, mixtures, proportions -- they're all GMAT problem types that focus on change.

And if you focus on that change in each problem, the change becomes the key to unlocking the entire problem - literally change you can believe in and should depend on. And, with a nod to Hillary Clinton, yes, this change post is one you can certainly Xerox if you'd like to. We don't mind.

How can an emphasis on change improve your GMAT score?

Consider the question:

The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

(A) 1.5
(B) 3.0
(C) 3.9
(D) 4.0
(E) 6.0

As with any problem, you should start with what you know. You know that, if the average of 5 numbers is 6.8, then the sum of those numbers is 5*6.8 or 34. Similarly for the new total, if the average is 9.2, then the sum of those five numbers is 5*9.2 or 46.

So we have:

Old total: 34
New total: 46

When problems involve a change - ratio problems in which a certain number is added or subtracted and the ratio changes; mixture problems in which something is added to or subtracted from the solution and the mixture changes, etc. - the key to solving them is typically the change itself. Almost always, the change is expressed in two ways:

x is added and the new ratio becomes...
one of the numbers is multiplied by 3 and the average becomes...

When you're given two ways to mathematically express that change, use those two ways to set up an equation - you can then solve for a variable that links the past to the present (or the present to the proposed future, depending on how the question is asked) and that solution will allow you to fill in the entire puzzle.

In this case, we know that "multiplying one number by 3" also "increases the sum by 12". Since the only number that changes is that number that is multiplied by 3, we know that the multiplying by 3 is the same as adding 12 to that number. So, mathematically, we can say that:

3x = x + 12
2x = 12
x = 6

Therefore, the number in question - that which is multiplied by 3 and in doing so is also added to 12 - is 6, and the correct answer is E.

Use change as your "anchor" in problems that emphasize a change in ratios, proportions, or any other elements of a mixture. By expressing the change in two ways, you'll have an equation that will translate to both the initial and the final mixtures, and therefore will be able to answer any question that the GMAT asks about any part of the relationship. If politicians can use change as their platform to try to get to Washington, you can certainly use change as your springboard to Boston, Palo Alto, Evanston, or the other b-school campus of your choice.

Plan on taking the GMAT soon? Our online GMAT courses run all the time, to suit YOUR schedule. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Tip of the Week: Exponents the Denard Robinson Way

People talk about him the way they talk about Chuck Norris or the Most Interesting Man In The World:

When Denard Robinson scored a touchdown in the 2-minute drill the clock actually read 2:05*

Human reaction time can't use a stopwatch fast enough to time Denard Robinson in the 40, so they have to time him in the 50. And his time is still zero.

Defenses have stopped trying to tackle Denard Robinson; they simply want to hug him.

Maybe it's because Denard Robinson, quarterback of the Michigan Wolverines, is the most interesting man in the world. At least for now - in the past two weeks he's vaulted to the top of nearly everyone's Heisman Trophy rankings and topped the trends list on Google and Twitter. He broke several school records in his first game of the season, then broke them again in the second. With all due respect to the Dos Equis guy, sharks really should have a week dedicated to Denard Robinson. So, naturally, a guy like that should be able to teach you a thing or two about the GMAT, right?

("If Denard Robinson took the GMAT, he'd score 801, but he doesn't have to because any school lucky enough to admit him would waive that requirement and simply name their school the Robinson School of Business")

It seems like every few years in college football there's a player like Denard - Reggie Bush, Percy Harvin, etc. - who can play virtually any position on the field and is a constant threat to score each time he touches the ball. Maybe they line up at receiver, or go in motion. Maybe they line up in the backfield, or step up under center or take a direct snap. Wherever that player is, he's dangerous - he's versatile enough to hurt you running, catching, throwing, and the offense can hide him in different positions to keep you guessing.

For those players, the defense always has to look for where they line up as soon as the huddle breaks, calling out by jersey number "There's 16" and ensuring that everyone knows where he is.

The GMAT has such a "player" -- a game changer that is as versatile and easy to hide as the greatest college football players of all time. That number is 0, and much like a safety or middle linebacker, you should always be looking for where 0 lines up on any given question.

0 is a complete game changer:

• Multiply anything by 0 and you get 0.


• Divide 0 by anything and you get 0.


• Add or subtract 0 and nothing changes.


• You cannot divide by 0 because it's undefined (although the Chuck Norris/Most Interesting


• Man quotes will lead you believe that some special person can divide by 0)


• Take anything to the exponent of 0 (e.g. 6^0) and you get 1.


• 0 is the only number that is neither positive nor negative; multiply it by -1 and it stays 0.

0 is easy to hide:

• 0 is neither positive nor negative, so "x is positive" excludes 0 but "x is non-negative" includes 0.


• 0 is an even number, but the only even without an opposite (e.g. 2 and -2)


• 0 is a multiple of every integer (that integer * 0 = 0)


• 0 literally means "nothing", so it's easy to forget about.

Because of all this, 0 carries all the traits of a dominant college football multi-threat, and you should never fail to consider 0 on any problem. Yesterday's challenge question in this space relied heavily on properties of 0:

For integers x, y, and z, if (3^x)(4^y)(5^z) = 3,276,800,000 and x + y + z = 15, what is the value of xy/z?

3,276,800,000 is clearly even, so it could definitely be a multiple of 4. And it ends in 0, so it is definitely divisible by 5. But the sum of its digits do not equal a multiple of 3:

3 + 2 + 7 + 6 + 8 + 0... = 26

So the number is NOT divisible by 3. In problems like these with multiple prime bases and exponents, finding a base that is not represented in the overall number is a godsend. Because that number is not divisible by 3, the 3^x term cannot equal a multiple of 3. The only way for that to happen is for x to be 0, as that would make that term 3^0, which equals 1. That factors out that term, leaving 4^y * 5^z = 3,276,800,000.

Now, solving that problem could still prove difficult (although there's a way to do it fairly easily if you look at it the right way...more on that in a second), but we don't need to. Because we know that x = 0, and the question asks for xy/z, that means that we have a 0 in the numerator:

0*y/z =

And that makes the entire term 0. Therefore, the correct answer is 0.

Two footnotes:

1) Even with 4^y * 5^z = 3,276,800,000 there is a quick way to solve it. In order to end with exactly five 0s, this number needs to be divisible by exactly five 10s (10^5). You could even write it as: 32,768 * 10^5. The only way to have exactly five 10s is to have exactly five pairings of 2*5 (the prime factors of 10), so z must equal 5.

2) Denard's finishing the two-minute drill with 2:05 left means he runs faster than the speed of light. Think about it.

Learn to love (and respect) the number 0, and just like a football coach you can game plan to defend against the versatile-and-dangerous game changer that the GMAT loves to feature. As for Big Ten defensive coordinators...maybe you should consult your MBA students for tips on defending Denard Robinson. (Number of times he's tied his shoelaces? Zero.)

Are you studying for the GMAT? Be sure to compare us to other GMAT courses and see why more people choose Veritas Prep every year. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Challenge Question: Your Opponent is the Exponent

It's time again for another Veritas Prep Challenge Question. Once again you'll find that exponents will play a fairly significant role in this question. Stay tuned to the GMAT Tip of the Week post tomorrow for an explanation of this question and a quick checklist for everything you need to know about GMAT exponents.

For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,000 and x + y + z = 15, what is the value of xy/z?

(A) undefined
(B) 0
(C) 3
(D) 5
(E) 15

Please submit your answers in the comments field, and check back tomorrow morning for an explanation and some critical exponent strategies.

Plan on taking the GMAT soon? We have GMAT prep courses starting around the world next week!. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Tip of the Week: Remainder

Chances are that you haven't used a remainder in years. Remainders in division are pretty much just placeholders for kids who haven't yet learned about mixed numbers or decimals yet; as soon as you learn what to do with the remainder, you tend to never explicitly touch a remainder again...until you take the GMAT.

Consider the problem 11/3. 3*3 is 9, but then there are 2 left over that won't divide evenly. So in this case, 11/3 = 3 remainder 2.

But by now you've figured out that you can divide that remaining 2 by 3, either as a mixed number:

3 2/3

Or as a decimal:

2/3 = .6667, so 11/3 = 3.6667

As with many concepts the GMAT tests, your ability to use all three ways of dealing with numbers that are not evenly divisible will be important -- you'll need to stay mentally flexible to see problems from multiple angles, and often times the GMAT will test the conceptual (e.g. remainders) applications of these problems more so than it will test the "calculational" (decimals), plug-and-chug methods to which you've become accustomed. To celebrate Back-To-School week for most school districts around the US, let's take you back to elementary school to show you how the GMAT will test remainders.

Sometimes the GMAT will simply test the concept of a remainder. Consider the question:

If 13,333 - n is divisible by 11, and 0 <> n is the remainder of that problem

Now, because we don't care about the quotient of this problem -- the question solely asks for the remainder, we simply need to determine what's left over when we divide 13333 by 11. The fastest way to do that is to simply subtract large multiples of 11 from 13333 to see what's left. We can do this because of the rule a (x + y) = ax + ay. If we're trying to divide a number like, say 51 by 3, we can break apart that 51 into 21 and 30 so that we have 7*3 + 10*3, which equals 3(7+10) = 3*17 = 51. In this case, we can break apart 13,333 by taking off large multiples of 11:

13333 - 11000 = 2333
2333 - 2200 = 133
133 - 121 = 12
12 - 11 = 1

The remainder, then, is 1.

Another way that the GMAT will test remainders goes back to the concept at the beginning of this post. The remainder of a division problem is what you would typically just divide back into the problem to determine the decimals:

25/4 = 6 remainder 1.
Divide that 1 back by 4 to get .25, so the answer is 6.25. The remainder provides the data after the decimal point, and the quotient gives you the number to the left of the decimal point.

Consider this problem (which appears courtesy of GMAC):

When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Going back to the concept of the remainder, the remainder of 9 is what will give us that .12 after the decimal place. The answer to the division problem x/y is either:

96 remainder 9
or
96.12

Therefore, when the remainder of 9 is divided back over y, we get .12. Mathematically, this means that:

9/y = .12
9 = .12y
900 = 12y (multiplying both sides by 100 to eliminate the need to deal with decimals can make calculation much easier!)
900/12 = y
300/4 = y (factor out the 3)
75 = y

The correct answer is B.

The GMAT is famous for testing you on concepts that you've long forgotten, and remainders are a favorite example of that. Understanding the concept of remainders -- what they are, how they're calculated, and how they can be turned into fractions/decimals -- can be quite useful on this test, so as you study take a glance back at your elementary school years and hopefully your knowledge of remainders will remain.

Are you studying for the GMAT? Be sure to compare us to other GMAT courses and see why more people choose Veritas Prep every year. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Tip of the Week: Data Sufficiency the Newton Way

Few two-syllable proper nouns connote brilliance quite like Newton: Sir Isaac, obviously; the Newton Hills along the Boston Marathon course that lead to Boston College; the Newton unit of force; even Las Vegas lounge singer Wayne Newton is supposedly quite intelligent.

Perhaps, however, no Newton has displayed the kind of GMAT brilliance that Nabisco brought us with the introduction and expansion of the world's most beloved Newton:

The Fig Newton.

The beloved Fig Newton has been a staple of the snack-and-light-dessert market for nearly a century (and is based on an ancient recipe that has been delicious for centuries). It has inspired a great many spinoffs, including the not-quite-as-good play-on-words competitor from Newman's Own, the Fig Newman.

Fig Newtons have grown into one of the most powerful brand names in the snack food industry, and as such are something for any aspiring brand manager to consider. How, specifically, can Fig Newtons help you on the GMAT?

Data Sufficiency questions rely on your ability to consider all of the potential options. Consider the question:

Is x > y/z?

1) xz > y

2) x^2 > y/z

Statement 1 looks awfully tempting, as one could simply divide by z on both sides to arrive at exactly x > y/z. However, this is not necessarily the case -- if z were negative, then dividing by z would require the > inequality sign to be flipped to <. Accordingly, the statement can give either answer: Yes or No.

Plugging in quick numbers can demonstrate this point even more clearly. If x = 3, y = 2, and z = 1, then statement 1 yields:

Is x >y/z?
3 > 2/1 ----> YES

But if x and z were negative, statement 1 is still satisfied (-3 * -1 = 3, which is greater than 2), and that would yield:

-3 <> NO

We need to consider the possibility of negative numbers (and nonintegers, and 0...numbers with unique properties) whenever looking at Data Sufficiency questions. Which is what the brand managers at Fig Newton did to expand that brand significantly. Is there anything particularly spectacular about the Fig? Or was it the packaging, the cookie type, the size and texture, etc. that drove such demand? Nabisco rolled out Apple Newtons (a natural with the Newton tie-in), Strawberry Newtons, Raspberry Newtons, and did so to substantial success. The Newton family considered all of the options and didn't allow itself to be pigeonholed into one type of Newton, the same way that you, on Data Sufficiency questions, need to consider all allowable numbers and not allow yourself to focus specifically on one type.

Statement 2, similarly, does not guarantee a positive or negative value for x, and continues to allow itself to support both answers. The answer to this question is thus E -- even given both statements, we cannot eliminate the possibility of negative values for x, y, and z, and therefore need to recognize that both answers to the main question are possible.

Learn from the experts at Fig Newton -- when you consider the entire array of possibilities, you enable yourself to be capable of higher success...be it on Data Sufficiency questions, in the snack food markets, or in physics.

Are you studying for the GMAT? We have classes starting worldwide next week! Be sure to compare us to other GMAT courses and see why more people choose Veritas Prep every year. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Challenge Question: Too Many Twos

Right at this second it's September 2nd, with 2 days until the college football season starts, once again with too many teams in the Big Ten. In honor of all of these twos and toos, we present you a GMAT problem that features too many twos:

What is the value of 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8?

(A) 2^9
(B) 2^10
(C) 2^11
(D) 3(2^10)
(E) 3(2^11)

Please post your answers in the comments field and we'll post the solution later today!

Afternoon Update:

Great solutions, everyone. This question brings up an important point about exponents - we only have a few "core competencies" when it comes to performing with algebra, and those are:

-Multiplying/dividing exponents with common bases
-Finding patterns (units digits, relationships between adding/subtracting common terms, etc.)
-Setting common bases equal to equate exponents

Outside of that, there's very little that we can do without the use of a calculator. So, in order to take advantage of what we do well, we should find ways when we see exponents to:

-Find common bases
-Multiply (using factorization to turn addition/subtraction into multiplication)

Here, we're asked to add several terms together...that's not something that we do well with exponents. However, by blending our abilities to factor terms (to get to multiplication) and to see patterns, we can attack this question relatively efficiently:

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

Combine the 2s to be 4, or 2^2, and you have:

2^2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

Now we can add them together, and we have 2(2^2), or 2^3, simplifying the entire statement to:

2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

Notice that we'll be able to combine two more terms, the two 2^3 terms, to be 2(2^3) or 2^4, leaving:

2^4 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

By now hopefully you've seen a pattern (patterns come up frequently in exponent questions) - the first two terms will add to the third, and then adding those will add to the fourth:

2^4 + 2^4 (the first two) = 2^5 (so now we have two of the third term):

2^5 + 2^5 + 2^6 + 2^7 + 2^8

Do that again and we'll have:

2^6 + 2^6 + 2^7 + 2^8

If we repeat the pattern, we'll end up with:

2^8 + 2^8 = 2(2^8) = 2^9. Therefore, the correct answer is A.

When approaching exponent problems, keep your core competencies in mind: factor, multiply, find common bases, and look for patterns. These strategies will help you turn complicated problems into efficient solutions.

Plan on taking the GMAT soon? We have GMAT prep courses starting around the world next week!. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Tip of the Week: Some Means Anything-But-None

You can't talk about probability without mentioning Las Vegas, and with the football gambling season looming it seems time for a probability-themed post with a gambling lead. As the football season approaches, you may well be placing your futures bets, noting that Alabama is a 9:2 favorite to win the collegiate national championship and that Indianapolis is a 13:2 favorite to win the Super Bowl.

The interesting thing about those futures bets is that when you select, say, Alabama, the sports book gets "everyone else". Will Alabama defend its title? Possibly, but the football season has so many hurdles (LSU, Auburn, the SEC championship game, the BCS championship game, injuries, Nick Saban leaving mid-season for another job...) that "everyone else" is a pretty good bet. Most seasons, a team that loses one game is eliminated from contention for the national championship, so a team would have to go undefeated in order to win. In a 12-game season, even if a team is 90% likely to win each game, that corresponds to:

9/10 * 9/10 * 9/10.... probability of going undefeated. For 12 games, the calculation would be (9/10)^12 = <30% chance of going undefeated.

And that's with a 90% chance of winning each game. Sure, Alabama will be favored against LSU, Auburn, and some of its other SEC opponents, but maybe it only has a 60% chance of winning those big games. That puts the undefeated odds down considerably (even with a returning Heisman winner).

How can this help you on the GMAT? As we've talked about, the opposite of "Alabama wins the national championship" is "anyone else wins the national championship", and that setup of complementary events (one and only one of those options will occur) allows you to tackle difficult problems with some insightful ease.

Here's an example of a GMAT problem that might test this subject:

Alabama is undefeated with four games remaining, with two at home and two away. If it has a 75% chance of winning its home games and a 50% chance of winning its away games, what is the probability that Alabama loses at least one of its last four games?

This question could get quite involved, as "at least one" loss has many permutations:

Loses the first and wins the next three (which would correspond to 1/4 * 3/4 * 1/2 * 1/2)
Loses the first and the last and wins the middle two (1/4 * 3/4 * 1/2 * 1/2)
Wins the first three and loses the last (3/4 * 3/4 * 1/2 * 1/2)
Loses all four (1/4 * 1/4 * 1/2 * 1/2)
Etc.

Each of the above corresponds to one sequence via which Alabama would lose at least one game, and you could drive yourself crazy (particularly if you bleed Crimson) thinking of all the possible ways to lose at least one game.

However, you can also look at it this way (through Crimson colored glasses):

If Alabama does NOT lose "at least one game" that means that it wins them all. And it's easier (and more fun for Bama fans) to calculate the odds of winning them all:

There is only one sequence that works - Win-Win-Win-Win:
3/4 * 3/4 * 1/2 * 1/2 = 9/64 chance that Alabama wins the rest.

Because there's a 100% chance that "something" happens, and we can divide that 100% into two comprehensive categories: "Alabama goes undefeated" or "Alabama loses at least one game", then we can take 100% and subtract "undefeated" to get "loses at least one":

1 - 9/64 = 55/64 probability that Alabama loses at least one of its last four games.

When you see questions that ask for the probability of "at least one" occurrence, the easiest way to calculate them is to calculate the probability of "no" occurrences and then subtract that from 100%. There are several sequences that could give you "at least one" (just the first, just the last, all of them, etc.) but only one that gives you "none" (all nones), so use that strategy to make quick, efficient work of probability questions on the GMAT.

What is your probability of missing at least one question on the math section of the GMAT? Well, it's 1 - getting-them-all-right, and the odds of your getting them all right just went up after reading this post!

Are you studying for the GMAT? Be sure to compare us to other GMAT courses and see why more people choose Veritas Prep every year. And, as always, be sure to find us on Facebook and follow us on Twitter!

Read More >>

GMAT Challenge Question: The Red Stapler

Studying for the GMAT does not have to be a chore -- it can certainly be made enjoyable through fun challenge problems! That's why we try to keep things lighthearted (yet effective) when it comes to your GMAT preparation.

With that in mind, try today's Cheerful Challenge Problem, channeling your inner Peter Gibbons in your pursuit of an MBA to become the next Bill Lumbergh. Do it right, and you just may have The Bobs eating out of the palm of your hand. Check back later today for the answer to this problem!

GMAT Critical Reasoning Question

Milton: I believe that you have my red stapler.

Boss: Yeah…we switched from the Swingline to the Boston staplers some time ago. So I am just going to have to go ahead and confiscate this…

Milton: But I was told that I could keep this stapler, it is a better stapler and it does not jam.

Boss: Sorry, Milton. Oh and I’m going to have to ask you to go ahead and move your desk to the basement…

Milton and the Boss are committed to disagreeing about whether_______________

A) Milton should move his desk to the basement.

B) The red Swingline stapler jams less.

C) Milton should be allowed to keep his red stapler.

D) The company previously switched to Boston staplers.

E) Milton needs to go ahead and come in on Saturday.


What do you think? Post your response (along with an explanation!) in the comments field below, and we'll add the solution later today!


UPDATE: SOLUTION

This is a unique variation of an Inference question, as the question asks for the subject on which the two parties must be in disagreement. They may well disagree on each of the answer choices, but only one of them is definite based on the passage.

The correct answer is C, as both parties mention the stapler, and each has a different opinion. Milton provides reasons that he should be allowed to keep it, and his boss denies him that opportunity and takes it. Because both parties explicitly express an opposite opinion about Milton's ability to keep his stapler, they must be in disagreement about it.

As in any Inference problem, the other answers could be true, but are not necessarily true. It's very likely that Milton does not want to come in on Saturday (who would?) and that he wouldn't want to move his desk to the basement, but because there is no explicit evidence of either, neither is correct. Correct Inference answers on the GMAT must be true, so use that burden of proof to your advantage as you approach these questions on the exam.

Follow these and other steps to GMAT success, and you may one day be in a position to have as many as...four people working directly under you (or get a high-paying consulting job at McKinsey or Bain & Company as one of the Bobs).

Plan on taking the GMAT soon? Take a a look at our new, lower prices on Veritas Prep online GMAT courses. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Tip of the Week: Get Flexible

At Veritas Prep we're big believers in the idea of flexibility. As we discussed in our take on the new version of the GMAT that's coming in 2012, business schools want to see how well you can think, not how well you can memorize idioms. That's why our 42-hour GMAT course trains you in the higher-order thinking skills and "mental agility" you need to do well no matter what type of question you face on the real exam.

Flexibility also matters in how you prepare for the exam. Deciding on Day One that you're just going to keep taking practice tests until you "get it," or that you're going to mow down practice GMAT problems until your eyes hurt, will only set you up for failure. That's why Veritas Prep gives you the most flexible options for GMAT prep in the industry.

What do we mean? Let us count the ways!

One year of membership for all GMAT students.
When you enroll for a Veritas Prep class (in-person or online), you're a member for 12 months from the start of your course. Did you sign up in July for a class starting on September 7? Then you have access to EVERYTHING for 12 months from September 8, so you in fact have more than one full year of membership!

You can attend two full-length, live courses during your membership period.
When you enroll in an in-person GMAT course, included in your membership is the ability to take two in-person courses in a 12-month period. Did you take the course but don't still don't feel ready to take the GMAT? Did your job get in the way, and you weren't able to complete the course? No problem... Just call us and we'll gladly put you in another course of that same type, no questions asked.

Unlimited access to our GMAT preparation resources for one year.
No one offers a longer membership, no one else offers all of the following resources: 15 practice tests, seven diagnostic midterms, Veritas Prep On Demand™ pre-recorded lessons, instructor-manned phone support, and MBA admissions workshops, all included in your membership.

Prepare for the GMAT any way you choose.
Not sure whether you want to do an in-person or online course. No problem. Enroll in any in-person Veritas Prep GMAT course, and you already have access to our online Veritas Prep on Demand™ course. Decide that you'd rather do Live Online? Great... Just call us and we'll put you in any upcoming Live Online GMAT course! Or, start with an online course, and if you decide you really need in-person prep, let us know and you can upgrade to any in-person class!

Flexibility matters. That's why we give you the most flexible GMAT preparation in the industry, period.

Plan on taking the GMAT soon? Take a look at our new, lower prices on Veritas Prep online GMAT courses. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Tip of the Week: Put the Critic in Critical Reasoning

Admit it: you're a critical person. When you drive, you criticize the others on the road. When you're in a long line at a store or DMV, you criticize the way the establishment runs things. When you're at the airport, you criticize the way that others dress and act. No need to deny it -- like anything, being critical is a matter of interpretation as to whether it's a good or bad thing. Critical person? Bad. Critical thinker? Harvard material. And on the GMAT, it pays to embrace your inner critic.

One of the least-used but most-useful ways of doing so takes place on Critical Reasoning questions that ask you to identify an assumption that an author makes when constructing an argument. True, the correct answer will strengthen, and not weaken, the author's conclusion, but we're much better at criticizing than we are at defending, and when given the option we should probably choose the former.

Consider this argument and question:

When it rains for more than an hour immediately before or during a baseball game, the game is canceled. Therefore, tomorrow's game is sure to be canceled.

The author of the argument above assumes which of the following?

(A) The manager of the home team has already begun planning his pitching rotation around the impending cancellation.

(B) The ticket office has issued a statement to ticketholders regarding the rain check policy.

(C) It will rain for an extended period of time leading up to tomorrow's scheduled game time.

Looking at the answer choices, each seems to be a good reason to believe the conclusion, that the game will be cancelled. If, according to choice A, the manager is already planning for a cancellation, it seems quite likely that the game is doomed. If, according to choice B, the ticket office has begun its preparations for a cancellation, it's also likely that the game won't be played. But neither of these is a correct answer for an assumption that the author makes, regardless of whether they would aid his case if they were true.

An assumption is a missing premise -- one upon which the author's argument depends. This fact can help you to navigate answer choices, as if the correct answer is required in order to believe the author's argument, if it weren't true then the argument would fail to hold. Accordingly, you can quickly turn these questions into opportunities to be critical, something you do quite well!

To use what we call the Assumption Negation Technique, which allows you to convert these assumption questions into Weaken questions, take each answer choice and negate it, making it an opposite statement. When done so, the correct answer will directly contradict the author's conclusion, while the others will fall safely out of scope. To negate these answer choices:

(A) The manager of the home team has NOT begun planning his pitching rotation around the impending cancellation.

WRONG: Whether or not the manager has begun to prepare for the cancellation has no bearing on whether it will rain enough for the game to be cancelled. The manager may have many reasons not to have begun that prep, most of which are unrelated to the weather.

(B) The ticket office has NOT issued a statement to ticketholders regarding the rain check policy.

WRONG: Again, whether the ticket office has begun preparing for a cancellation -- or whether it even has a rain check policy to begin with -- has no bearing on whether the game will be cancelled.

(C) It will NOT rain for an extended period of time leading up to the game's scheduled start time.

CORRECT: Our only basis for concluding that the game will be canceled is the rainout policy described in the argument. If it were true that it would not rain, we'd have no way to conclude anything about the game. This demonstrates that choice C is essential to the author's argument; without it, the argument is meaningless.

By using these opportunities to allow yourself to be more critical, you can answer these questions from a position of your own natural strength -- as a critic. When faced with assumption questions on the GMAT, see them as opportunities to do what you do best -- be critical. After all, that's the name of the game (which will not be canceled).

Plan on taking the GMAT soon? Compare us to the competition and see why more people choose Veritas Prep every year. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

Understanding the GMAT Scoring Algorithm

As you likely know, the GMAT is a computer-adaptive test (CAT), in which your score is calculated by an algorithm that provides you with harder questions (and higher score returns) when you answer previous questions correctly, and with easier questions (and lower returns) when you've answered previous questions incorrectly.

Through this method, the GMAT can ascertain your ability level in a relatively short period -- 37 math and 41 verbal questions -- and provide you with an immediate score upon completion of the test. On the flip side -- and unintentionally -- the GMAT can cause you a great deal of stress as you try to find ways to better understand and game its scoring system. To save you that stress, here are some important things you should know about GMAT scoring:

1) Good news: You can get a lot of questions wrong and still do well!

The job of the GMAT scoring algorithm is to determine your ability level by asking you questions that begin to close in on it. Think of how you'd play a game of 20 Questions as you attempt to zero in on the historical figure that your "opponent" has selected:

Was this person famous in the era BC? (No -- too early)

Was this person famous before the Middle Ages? (No -- still too early)

Was this person famous before the Declaration of Independence? (Yes -- 1776 is too late)

Was this person famous before 1600? (Yes -- 1600 is still too late)

Did this person become famous before 1500? (Yes -- now we're getting close to that period between around 1300-1500)

Was this person famous in the late 1400s? (Yes -- now we're getting close to really knowing the answer)

Was this person famous for something that happened in the 1490s? (Yes)

Is it Christopher Columbus in 1492? (Yes -- once you get to the 1490s, you can be pretty sure that you're talking Columbus. We've managed to narrow down our assessment of the figure in question by getting some "yes" and "no" answers)

Essentially, that's what the GMAT is trying to do with the questions it feeds you. "Is this person above a 700? Yes." "Is this person above a 750? No." Because the test needs to get those "no" answers at the upper limit of your ability, it will continue to feed you harder questions that you will likely answer incorrectly as it tests your upper threshold, and at the lower end it will feed you easier questions to test your minimum ability.

The upshot for you? You're supposed to answer a fair number of questions incorrectly. Everyone does. Akil over at BellCurves wrote up a pretty extensive analysis of official practice test scores that demonstrated some trends in the ways that scores are calculated. If you don't want to sort through the dense analysis to draw your own conclusion, know this: those scoring in the 46-50 scaled score range on the quant section (the upper limit of high scores) answered between 21 and 26 of the 37 math questions correctly. You can score well above the 90th percentile on math and miss more than a dozen questions! (And if you're good enough at math to do that, you'll note that it equates to your missing roughly a third of the questions)

2) The first ten questions are no more important than the last ten.

The Graduate Management Admissions Council goes as far as to spell this out clearly in the Official Guide for GMAT Review and on its blog, but the rumors still persist. Let's go back to the game of 20 questions; if it's that easy for you or I to correctly guess "Christopher Columbus" in just 20 questions, why does the GMAT need 37 or 41 to determine your score? After all, GMAC is run by a sophisticated team of statisticians and psychometricians.

The answer? The GMAT needs to account for false positives and false negatives. In a game of 20 questions, it's in unbelievably poor form to lie about the answer to a question, but on the GMAT you'll "lie" about your ability whenever you guess correctly or make a silly mistake and answer incorrectly. The test needs to account for that, and so more questions are needed.

Going back to Columbus, say that the 20 questions proprietor had forgotten that catchy rhyme "In 1492 Columbus sailed the ocean blue", and tried to estimate your line of time-sensitive questioning by thinking "Jamestown was in the early 1600s, so Columbus must have reached the Americas in the 1500s." He'd have answered your question "before 1500?" as "no". But your subsequent questions -- "was he an explorer/sponsored by the Spanish crown/etc." -- would eventually bear out that the answer to the pre-1500 question was false.

The GMAT knows that you'll have some false positives/negatives in your answers, and accordingly it's equipped to filter through those. And, accordingly, it can't make any major decisions about your ability level that early in the test. If you're taking the GMAT soon, hopefully you're studying probability concepts thoroughly enough to recognize this -- 1 out of every 525 test-takers who guesses blindly on the first four questions will get them all right. The GMAT can't hand that person a 700-ish score on the basis of pure guessing and then some mediocrity for the rest of the test. With well over 200,000 GMATs taken per year, the overseers of the test (statisticians to boot) know that they'll see quite a few tests that include sets of 3-4 consecutive correct guesses, and the algorithm is set up to mitigate those and accurately reflect your scores.

3) Knowing how the scoring algorithm works neither significantly impacts your score nor excuses you from having to answer questions correctly!

Of the time that most examinees spend preparing for the GMAT, among the least-value-added is the time beyond that first, say, 20 minutes that they spend thinking about the scoring algorithm. Consider this quote from Dr. Eileen Talento-Miller, one of the chief psychometricians behind the GMAT, in her blog post about guessing on the exam:

"And because no one knows what item you would have gotten next if you don’t complete the items at the end, then there is no good way to estimate how that would affect your score."

If the creators of the exam are willing to admit that they're unsure how they'd game the test, it's unlikely that you'll somehow crack the code on your own. The psychometricians at GMAC are tasked by business schools with, above all else, the job of ensuring that the test is a valid assessment of a student's performance. Quite frankly, they do that incredibly well, and so even if they did spot an opportunity to beat the system, rest assured that they'd identify and correct it before you would have the opportunity to use it.

The GMAT measures your score differently, but not entirely differently, than Omega measures the results of the Olympic 100 meter dash. Like GMAC, Omega has a job to ensure that the results of the race accurately reflect the performances of the athletes. Usain Bolt, the fastest man alive and defending Olympic sprint champion, could spend hours understanding the nuances of electronic timing, the ways in which a second is calculated, etc., but in the end he'll only defend his championship and potentially lower his world record if he simply runs faster than everyone else.

In fact, Omega and the international track & field governing bodies have even instituted a system that punishes runners who try to beat the system. As it is scientifically understood as impossible for an athlete to react to the starter's pistol in less than 0.10 second, any athlete who tries to time the start and begins his motion after the gun but before that natural reaction time has elapsed is charged with a false start (notably, 1992 Olympic champion Linford Christie was disqualified from defending his title in 1996 under this rule). When the stakes are high, those who perform the assessment of your performance have greater incentive to validate that numerical assessment than you have to beat the system.

Accordingly, like Bolt, you can spend your time much more effectively by preparing to succeed than by trying to fully understand the nuances of how you'll be assessed. Ultimately, you should trust that the scoring system will accurately value your performance, and that the only thing you can control is that performance itself.

Are you preparing for the GMAT? Take a look at Veritas Prep's GMAT prep courses and GMAT books, now available for individual purchase. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Photo courtesy of William Warby, under a Creative Commons license.

Read More >>

GMAT Tip of the Week: Cinderella Man

Who forms pyramids and raps circles around square lyricists?

Eminem, Cinderella Man.

Eminem's latest (and greatest?) album, Recovery, has defied convention in many ways:

• Few rappers have enjoyed success well into their 30s or more than a decade into their careers, but Eminem has led the Billboard charts now five weeks and counting.


• In the digital age, few artists can even sell full albums anymore, but Recovery sold more albums in its first week than any album since 2008.


• In between aggressive, venomous lyrics that need to be rewound to be fully appreciated, Eminem also provides listeners with an insider knowledge of some of the GMAT's unconventional geometry questions.

With his lyric "who forms pyramids and raps circles around square lyricists", the world's greatest inside-out rhyme pattern rapper isn't merely calling out the world's other emcees, but also calling attention to one of the GMAT's favorite inside-out Geometry question formats, those that wrap circles around squares and vice versa.

The GMAT loves to ask questions about:

A circle inscribed in a square

and

A square inscribed in a circle

This allows the exam to test your ability to link together seemingly disparate concepts. But much like a top emcee, you can blend together unique concepts to achieve financial success.

When a square is inscribed inside a circle:

The diagonal of the square is the same length as the diameter of the circle, which also means that the diameter of the circle / diagonal of the square takes the "x * squareroot 2" side of the 45-45-90 triangle that it creates with two sides of the square. Divide the diameter by the square root of 2 and you have the length of the side of the square.

In this case, just having one piece of information allows you to solve for everything else. Given the area or circumference of the circle, you can find the radius and then the diameter, and use the diameter to acquire the lengths of the sides of the square. Given the area or perimeter of the square and you can find the diagonal, use that as the diameter of the circle, and find out whatever you need to know about the circle that way.

When a circle is inscribed inside a square:

The diameter of the circle is the same as the length of a side of the square. This may make things even easier than the square-inside-circle setup. Once you have the area, circumference, or radius of the circle, you can find the diameter and therefore a side of the square. Or, if given information about the square, you can then find the length of a side, equate it to the diameter, and use that to unlock the numerical properties of the circle.

Circles and squares are perfect shapes because they're perfectly symmetrical: find one piece of information about either and you know about the entire thing. Because of this, they're great shapes for the GMAT to use to test your ability to link together concepts, and these one-inscribed-in-another questions have long been favorite geometry question fodder. Learn to wrap circles around squares and squares around circles and you'll be testing circles around the GMAT in no time. The next step after that? Echoing Eminem's "Hi, My Name Is..." at business school orientation.

Are you preparing for the GMAT? Take a look at Veritas Prep's GMAT prep courses and GMAT books, now available for individual purchase. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Tip of the Week: Data Sufficiency the Nikola Tesla Way

If you've used electricity in your life, you're undoubtedly familiar with Thomas Edison, and likely pay your electric bills to a company named in his honor. (And if you're reading this, you're using an electronic device, so you are familiar with Edison. Q.E.D.) You may not, however, be as familiar with a man perhaps even more responsible for the electricity you're using to view this blog post: Nikola Tesla.

Tesla, who apprenticed for Edison, helped to make Edison's Direct Current (DC) electrical transmission more efficient and therefore more marketable, but then, against Edison's conservative wishes, branched out on his own to create an even-more efficient electrical system, Alternating Current (AC). (And, in doing so, gave way to the name for one of history's greatest bands, AC/DC...and whose electrical system did they list first?)

Despite Edison's reluctance (and massive anti-AC public relations campaigns to preserve his technology's profitability), Tesla's AC technology won out, essentially because the AC system was more efficient and more flexible. AC technology allows for changes in voltage without the need of expensive conversion machines, and allows electricity to be transported across longer distances. Essentially, Edison's DC systems were "brute force" systems, whereas Tesla's AC was efficient and adaptable, and in the end efficient-and-adaptable won out in the "War of the Currents," the same way that it will for you on the GMAT. How?

Tesla's great advantage was that he could take electricity and adapt it to the required situation. AC allowed low-power items to receive low levels of power, and for higher-power items to receive the higher levels of required power, all from the same source. Electricity, through Tesla, could adapt to the required situation.

The same is true of GMAT Data Sufficiency questions, and in particular those that feature algebra with multiple variables. These questions often provide you with information in an inconvenient fashion, giving you a choice to be made: do you "brute force" them by plugging in a series of values, or do you attack them efficiently-and-adaptably, fitting the information provided to the situation at hand?

Consider this question:

For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?

1) a/b = 3/5

2) a and b have no common factors greater than 1

At first glance, Statement 1 seems to require quite a bit of work to be useful, as all of the provided information is in terms of a, and the question at hand only involves b and c. Plugging in values of a, b, and c using the 3:5 ratio between a and b could be extremely time-consuming and frustrating.

However, the information provided in the question and in statement 1 can be fitted nicely to the question:

a/(b-c) = 1
a/b = 3/5
What is (b-c)/b?

Taking the first statement and multiplying both sides by the denominator, we find that:

a = (b-c)

Knowing that, we can simply replace (b-c) in the question with a, since we know that the two quantities are equal:

What is a/b?

At this point, the question asks for exactly what statement 1 provides:

a/b = 3/5

So the first statement is sufficient.

By approaching this one like Tesla, valuing flexibility and using the algebra to fit our assets to the question, we can make quick, efficient work of this statement without much effort.

Statement 2 is not sufficient. Simply knowing that a and b have no common factors greater than 1 does not tell us which is which. Since we're asked for a/b, we'd need to know which value is the numerator and which is the denominator, and the statement does not provide for that. Potential values include:

a = 3, b = 5 (both primes, so they don't have any common factors)
b = 5, a = 3 (the same values, but as no order was specified we could simply invert them)

Accordingly, the correct answer is A, as statement 1 alone, but not statement 2, is sufficient.

Ultimately, the GMAT is a test of how you manage resources and solve problems, and few minds in world history have done that better than Nikola Tesla. Train yourself to think that way, fitting your algebraic assets to the Data Sufficiency question stems, and you'll demonstrate to business schools that you have what it takes to be successful (and to rock bands like AC/DC and Tesla that you know where they're coming from).

Are you preparing for the GMAT? Take a look at Veritas Prep's GMAT prep courses and GMAT books, now available for individual purchase. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Tip of the Week: GMAT Composure the Andy Schleck Way

One of the most compelling dramas in all of sports took place yesterday in the Tour de France, with Andy Schleck and Alberto Contador -- the two leaders of the race, which ends Sunday -- matching each other's yeoman efforts pedal-for-pedal up one of the world's most intimidating mountain roads, the Col de Tourmalet. Through the fog, up grades of over 10%, surrounded by fans waving flags and cowbells, and well ahead of every other rider in the race, the two riders -- separated after two weeks and thousands of miles by only eight seconds -- put on a battle for the ages.

While winning the respect and admiration of the world, Schleck also won the day although he may have lost the Tour in the process (history suggests that Contador, who owns the eight-second advantage, will extend that lead significantly in tomorrow's Individual Time Trial, the last real opportunity for the riders to separate themselves). And he was able to do it by employing the exact kind of poise that you may need on the GMAT.

Just two days earlier, Schleck proved himself the stronger man in the mountains, at least for that day, attacking Contador with a massive burst of speed and appearing to be on the verge of extending his 31-second lead at the time. Pushing to extend his lead, he flipped a switch on his handlebars to change into a larger gear, and the unthinkable happened -- his chain slipped of the ring in the process, and his bike cruised idly to a stop, leaving him to fix the mechanical problem with his heart beating near its maximum of around 200 beats per minute and his lifelong dreams escaping before his eyes nearly as frantically.

The same may happen to you on test day -- in the midst of a hard problem, you may find that a calculation yields a number unlike any of the answer choices, or that you can't find a way to isolate a variable in a calculation, or that none of the answer choices seems to match with the conclusion of a Critical Reasoning problem. Like Schleck, you may feel the pressure of months of hard work slipping away from you in the blink of an eye, while the clock ticks ever louder giving you less and less time to right the wrong and get back on track. Unlike Schleck's situation, however, a rare gear malfunction that happened at the exact worst moment in one of the unluckiest events in all of cycling, mistakes are bound to happen for you on the GMAT -- you almost certainly will encounter some kind of stress-turned-panic one at least one question.

So how can you react to such a situation? Like Andy Schleck did. Amidst all the chaos and pressure, with his heart beating out of his chest and his lungs craving oxygen at high altitude, Schleck calmly rotated his pedals, threaded the chain onto the sprockets, turned the crank to ensure that it was in place, hopped back on his bike and went back to work. In GMAT terms, he calmly assessed the problem, went back through the same motions he had done thousands of times before, and focused on the task in front of him with little thought about the panic behind him. The result? An event that could have lost him minutes of time only cost him about 30 seconds, and allowed him to take part in yesterday's epic duel with everything on the line and a chance to win the greatest endurance race in the world.

On the GMAT, you'll make mistakes, you'll feel pressure, and you'll see time slipping away. How you manage the situation is what determines your success, and the best way to manage the situation is to go back to the basics. Identify the question you're being asked, think of the strategies that work on those problems, and follow your work calmly to see where you may have been in error. If you can't get back on track efficiently, know that there are multiple battles -- 37 math and 41 verbal -- to be fought, and that you may simply need to limit your time losses on one problem to be ready to fight on the next. Keep your cool and prove to the test -- and those who view your scores -- that you can calmly and efficiently manage stressful situations, and like Schleck you can continue on to bigger and more rewarding challenges with the respect of those around you.

Preparing for the GMAT? Take a look at Veritas Prep's GMAT prep courses and GMAT books, now available for individual purchase. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Tip of the Week: Roll Out Those Lazy Days of Summer

Now that the World Cup is over and the majority of the world's population has forgotten again about the Southern Hemisphere, it's safe to say that most of us are enjoying the middle of summer. Summer is more than just a season between the solstice in June and the equinox in September; it's a state of mind and a way of life. Close your eyes and just think of "summer" -- just the notion of it implies to most of us a sense of happiness, relaxation, and comfort. Take Christmas carols out of the mix and summer is easily the most musically-written-about season of all. Admit it -- you have DJ Jazzy Jeff & The Fresh Prince's "Summertime" in your head right now!

Summer, and the music that it inspires, can teach us about how to succeed on the GMAT and in other pursuits. Peak performance tends to come when stress levels are lower, when we feel calm and confident, and when we're enjoying a positive frame of mind. Since summer is generally associated with all of those feelings, embracing our inner summertime can be instrumental in achieving peak performance. As Nat King Cole wrote it, we should "roll out those lazy, hazy, crazy days of summer..." Here's how:

Focus on the lazy!

The GMAT, like life itself, will try to encourage you to work too hard. Also like life itself, however, the GMAT will reward you for finding a simpler, easier way. The key to that is telling yourself that you don't want to work too hard, and that you can find a way to be lazy (which, if you're smart about it, is just another word for "efficient").

Consider this tough Data Sufficiency problem:

What is the remainder when integer n is divided by 10?

1) The tens digit of 11^n is 4

This statement is a tough one -- at first glance it looks impossible, as we're pretty good with units digit properties but don't have very many (if any) hard-and-fast rules for digits to the left of that. It almost seems as though you have two choices: either assume that "n could be anything so there's no way that this works," or start multiplying out 11 after 11 to see if you find a pattern. The multiplication sounds just awful -- after 11^1 as 11 and 11^2 as 121, those values get big in a hurry, and multiplication can be incredibly time consuming.

But does it have to be? After all, this is the GMAT, a carefully-written test that rewards efficient (or just plain lazy) ingenuity. You can't simply assume that "statement 1 doesn't work because n could be anything" -- the GMAT's authors specifically wrote that statement for a reason, and they're not apt to give you a "throwaway." But you also don't have to mindlessly grind out calculations, either -- the authors want to give you that option, but they also write these carefully enough to give you an out if you're clever (or lazy) enough to look for it. Here's that out:

Multiplying by 11 is the same as multiplying by 10 and adding that to the original number (11 = 10+1).

Watch how the exponents of 11 increase:

11^1 = 11
11^2 = 11*10 + 11 * 1 = 110 + 11 = 121
11^3 = 121*10 + 121*1 = 1210 + 121 = 1331
11^4 = 1331*10 + 1331 = 13310 + 1331 = 14641
11^5 = 14641*10 + 14641 = 146410 + 14641 = 161051
and so on...

Notice any patterns?

First, hopefully you've found that multiplying by 11s was easier than expected -multiplying by 10 just means adding a 0 on the end of the initial number, and then adding that original number back in to account for the 11th value.

The units digit is always 1, which should stand out but also be expected (when multiplying two numbers that end in 1 you'll always get a number that ends in 1).

The tens digit is also interesting though -- look at how it increases: 11, 121, 1331, 14641, 161051. The tens digits go from 1, 2, 3, 4, 5.... in lockstep with the value of n, the exponent.

Here is where the GMAT provides you with another decision point. You can either assume that this pattern will continue (not a terrible assumption since it's worked for five values of n in a row, albeit all single-digit values of n which may make them too similar to be proof of an infinite pattern) or try to prove it to yourself. Proving it may seem to take too much math -- we can continue the process we've been doing to make the multiplication easier, but the bigger the numbers get the more time-consuming and error-prone that process will be. Is there an easier way?

Go back to the process we've used for multiplication by 11:

Multiply by 10 -- which means just add a 0 on the end -- and then add the original number back.

Well, every "original" number we have to multiply by 11 has a units digit of 1, which means that when we add the zero on the end of that number it will end in 10, and have a units digit of 10. When we add that back to the original number, then, we're simply increasing the tens digit by adding 1. This pattern will hold infinitely -- we're going to add 1 each time to the tens digit, which means that whenever n ends in a 4, then the tens digit will be a 4. Therefore, the statement is sufficient.

Note that you don't need to (and probably shouldn't) memorize this rule! There's a process for identifying unique number properties when they arise:

Three-Step Process for Unique Number Properties

1) Identify that you are being tested on Number Properties: When a question deals with incredibly large values (or potential values), you're likely to be able to use a number property; when a number asks about units digits, tens digits, etc., you're almost certainly being tested on number properties.

2) Look for a pattern: When you've identified that you're likely to need to use a number property, try to find a pattern using smaller numbers that you can extrapolate to larger ones.

3) Determine why: Once you've identified a pattern, time permitting, try to reason why the pattern holds. If you don't have time, but you've established a recurring pattern, you may need to simply assume that it's much more likely than not that it will continue. But if you can afford the time, and definitely during your homework when time isn't a factor, try to rationalize the reason for the pattern.

The more that you embrace this method, the easier it becomes, and the lazier (er, more efficient) you can be. Finding patterns, and in doing so finding ways to accomplish difficult tasks quickly, is a highly-rewarded thought process on the GMAT, as it is in life. Embrace that summertime spirit of relaxation and calm, and enjoy the rewards that laziness can bring.

Are you preparing for the GMAT? Take a look at Veritas Prep's GMAT prep courses and GMAT books, now available for individual purchase. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>

GMAT Tip of the Week: Problem Solving the LBJ Way

There are big decisions in life, and then there are BIG DECISIONS. You'll make some pretty important decisions on the GMAT, so you should want to consider the methodology of how to best make these choices. And few of those BIG DECISIONS can compete with some of those made by one of the world's most prominent figures of the last century, LBJ.

Lyndon Baines Johnson (what, you were expecting another LeBron James article today?) in his nearly six years as U.S. President was tasked with some absolutely huge decisions: how to deal with the Vietnam conflict, what to do about the growing need for civil rights reform, how to put a man on the moon... "The Sixties" are remembered as a monumentally revolutionary decade in American and world history, and LBJ presided over the vast majority of it, making big decision after big decision.

How, other than the timely LBJ/LeBron James made-you-look reference, is this relevant to your GMAT studies?

Much like your situtation on the GMAT, most of LBJ's was inherited - the questions facing him were not as much part of an agenda of his choosing, but rather issues that were thrust upon him. He took office after the assassination of John F. Kennedy, inheriting the task of bolstering a nation in shock. At the time he took office, the conflict in Vietnam was already underway with thousands of U.S. troops on the ground; Kennedy's guarantee of a man on the moon by the end of the decade had already been made; racial tensions were reaching a head in the aftermath of Brown v. Board of Education and with the evolution of multiple powerful civil rights groups and leaders.

Johnson, like you as a GMAT examinee, had no choice but to answer the questions that faced him. And, like you should on test day, he did so by taking the issues and making them his own, pushing for, among other things, a "Great Society" agenda to leave office better than he found it. On the GMAT, you will undoubtedly face problems that you simply wish not to, but as LBJ found the best way to handle them is to make them your own.

Consider the problem:

&$ * $& = &@&

In the multiplication problem above, &, $, and @ represent different, nonzero digits, and the product of & and $ is less than 10. What is the value of the two-digit number &$?

A) 11
B) 12
C) 13
D) 21
E) 31

Tricky, eh? Like taking office and having to confront civil rights and a growing military conflict all at once...

The keys to these problems are to make them your own by writing down what you know. Here, we can start with a couple quick things that we know to get started:

1) We're dealing with unique digits, which means that choice A, 11, isn't a possibility, so at least that's out of the way.

2) We're dealing with individual digits, and not numbers, so they're probably testing some kind of number property - and one that we know they test a lot when looking at individual digits in multiplication is a unit's digit property. Stacking the multiplication vertically can help to better gauge that:

&$
$&
_____
&@&

With the unit's digit rule in mind, we know that multiplying $ * & leaves us with &. In other words, multiplying & by $ keeps it the same. What number, when multiplied, keeps the other the same? 1. So now we know that the $ is 1, making our problem:

&1
1&
____
&@&

Since the problem is asking for &$, and we know that $ is 1, then we also know that choices B and C, which put the 1 in the tens place and not the units, are incorrect. Now we're down to two choices: 21 and 31.

We need to replicate that repeating digit, so it may just make sense to multiply out our options:

21 * 12 = 252 (replicates that repeat)
31 * 13 = 403 (does not replicate the repeat)

So 21 * 12 is the problem that works, and we know that our answer has to end in 1, so it must be 21, or choice D.

Often times, the GMAT will create a uniquely complex situation for you, and your best option is to make decisions by breaking out the complexity into smaller steps of your own. If you can unpack both the things that you know and your GMAT "guiding principles" (like number properties), you can take these complicated situations that you inherit and turn them into logical, systematic decisions.

Are you preparing for the GMAT? Take a look at Veritas Prep's GMAT prep courses and GMAT books, now available for individual purchase. And, as always, be sure to subscribe to this blog and to follow us on Twitter!

Read More >>