GMAT Tip of the Week: Data Sufficiency and The Imitation Game

GMAT Tip of the WeekWith Oscar weekend upon us, it’s only fitting that this week’s GMAT Tip comes courtesy of Alan Turing. Of course the brilliant math mind featured in Best Picture nominee The Imitation Game would crush GMAT Data Sufficiency. But the mere title of the film provides a GMAT tip that can help bring Data Sufficiency success to even us mere mortals who can’t quite use math to save Britain from peril. How can you use The Imitation Game to succeed on Data Sufficiency?

When you’re asked a Yes/No Data Sufficiency question that asks whether an algebraic relationship is true, play The Imitation Game. Which means: if you can get one of the statements to directly imitate the question, you can definitively get the answer “yes” and prove that it’s sufficient.

Consider a few examples of questions that make for great Imitation Game candidates:

Is x – y > a – b?

(1) x + b > a + y

Here you can try to imitate the question with the statement. You want the statement to look more like the question, where x and y are paired together on the left and a and b are paired together on the right. so subtract y from both sides (to get it from the right to the left) and subtract b from both sides (to move it to the right), and the statement becomes:

x – y > a – b

Which directly answers the question “yes” – the question asks if the relationship is true, and by using the statement to imitate the question you can get the statement to directly answer it.

If the product abc does not equal 0, does a/b = c?

(1) bc = a

Here you can again use the statement to imitate the question, dividing both sides by b to get c on its own (which you’re allowed to do since no values are 0), and you have your answer:

c = a/b

Sometimes you’ll be able to imitate the question to get a definite “no” answer, which is still sufficient:

Is x – y > a – b?

(1) a > x and y > b

Here you can combine the inequalities to get them all in to one inequality. By adding the inequalities together (which you can do since the signs point in the same direction), you have:

a + y > x + b

And then you want to imitate the question, which has a and b on one side and x and y on the other. So subtract y and b from both sides to get:

a – b > x – y

Which is the opposite of the question, and therefore says “no, x – y is not greater than a – b” providing you with sufficient information.

The real lesson here? When you’re being asked a yes/no question with lots of algebra, it pays to play The Imitation Game. See if you can get the statement to imitate the question, and you’ll often find that it directly answers the question.

But be careful! As the second example showed you, you need to be careful when diving into algebra that you don’t:

*Divide by a variable that could be 0
*Multiply or divide by a variable in an inequality if you don’t know the sign

Keep those two caveats in mind and you can imitate math legend Alan Turing while you play the Data Sufficiency Imitation Game. And the winner is…you.

GMAT Tip of the Week: The Corrupt Mechanic Explains Sentence Correction

GMAT Tip of the WeekYour parallelism knowledge is paramount. You’re a pro when it comes to pronouns. You relax when you see that the problem involves verb tense. You can’t find a modifier error that’s even moderately challenging anymore. You should be a Sentence Correction sensei. So why are Sentence Correction problems still such a problem?

You’re being taken for a ride by a corrupt mechanic.

Let’s explain. The GMAT testmakers are committed to testing the same concepts over and over again: Modifiers, Verbs, Pronouns, Parallel Structure, Logical Meaning… And at a certain point it’s difficult to make those concepts any harder; they are what they are. So the testmakers resort to a time-honored tradition among corrupt mechanics; when oil changes and tire rotations and front-end-alignments aren’t bringing in enough profit, what do corrupt mechanics do?

They fix things that don’t need to be fixed.

The corrupt mechanic never simply fixes, flushes, or replaces the part you came in asking about; he always “strongly recommends” that you add on another service. If you’re not careful, your $30 oil change becomes a several-hundred dollar outing and your car comes back with shiny new parts that replaced perfectly-functional components, all with a nice labor surcharge on top. As Seinfeld’s George Costanza put it:

Well of course they’re trying to screw you! What do you think? That’s what they do. They can make up anything; nobody knows! “Why, well you need a new Johnson rod in here.” Oh, a Johnson rod. Yeah, well better put one of those on!

Now, in defense of the GMAT testmakers, they’re not trying to steal your money for unnecessary services. But in their quest to reward the kinds of business skills that are associated with avoiding unnecessary expenses and wasted time on ineffective initiatives, the GMAT testmaker does act like a Corrupt Mechanic on Sentence Correction problems. By fixing problems that don’t need fixing, the testmaker steals your attention, not your money. And in doing so, the testmaker baits the unwitting into bad decisions, while also rewarding those who prioritize their Decision Points properly. Consider this example:

Immanuel Kant’s writings, while praised by many philosophers for their brilliance and consistency, are characterized by sentences so dense and convoluted as to pose a significant hurdle for many readers who study his works.

(A) so dense and convoluted as to pose
(B) so dense and convoluted they posed
(C) so dense and convoluted that they posed
(D) dense and convoluted enough that they posed
(E) dense and convoluted enough as they pose

To those who know their role in the GMAT, the verb difference along the right hand side of the answer choices should loom large. “Pose” (present) vs. “Posed” (past) is a very actionable decision and a very common decision on the test. Like an oil change or the replacement of brake pads, verb tense decisions are something you should do regularly! So what does the Corrupt Mechanic do? He takes something uncomfortable – the structure “so dense and convoluted as to…” – but that doesn’t need fixing, and it fixes it. And since that choice comes along the left-hand side, many of us go right along with that and eliminate A with a preference for the more-familiar structures in B and C, without ever realizing that we’ve been “Johnson rodded” into ignoring the ever-important verb tense decision at the ends of the choices.

That’s how the testmaker’s Corrupt Mechanic works in Sentence Correction. He changes things that didn’t need changing and dares you to accept those “repairs” as necessary. So how can you avoid these traps? Be a savvy customer. Know what you want before you start listening to the Corrupt Mechanic’s menu of possible changes; you want to make Verb, Modifier, Pronoun, and Parallelism decisions before you even listen to anything else. Make the common repairs first, and then with the choices that are left you can start to get creative with add-ons.

The GMAT testmakers act like Corrupt Mechanics when they write Sentence Correction problems, so beware that not every change is actually a necessary repair. It’s on you to determine which fixes truly need to be made, so stick to the recommended SC maintenance schedule – the errors most commonly tested – and you’ll avoid falling victim to the Corrupt Mechanic.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: All About That Base

GMAT Tip of the WeekIt’s Grammy Weekend here in Los Angeles. All local sports teams have cleared out of the LA Live / Staples Center / Nokia Theater area and local citizens are humming along to the song of the year nominees. How can you (Taylor) Swiftly make your GMAT Quant score (Ariana) Grande, even without the help of an expensive GMAT (Meghan) Trainor? The process isn’t So Fancy, so take that stress and Shake It Off. When you see exponent-based questions, the #1 thing you can do:

Be All About That Base.

What does that mean? Nearly every exponent rule you’ll learn requires common bases. For example:

So when you’re presented with an exponent problem, one question you should always ask yourself is “Can I get all these terms to have the same base?”. That step allows you to use the exponent rules you’ve memorized to solve complicated problems. Consider an example:

For integers a and b, 16^a = 32^b. Which of the following correctly expresses a in terms of b?

(A) = 2^b
(B) a = 4^b
(C) a = 2^5b-4
(D) a = 4^5b-4
(E) a = 2^5b

Here there’s only one exponential term, 32 to the b power. But if you recognize that both 32 and 16 are powers of 2, you can quickly transform the problem, coming up with:

2^4 * a = (2^5)^b

And that allows you to dive right into exponent rules. First deal with the parentheses on the right, using the third exponent rule in the list above so that that term becomes 2^5b. That means you have:

2^4 * a = 2^5b

Then to isolate a, you divide both side by 2^4, getting to:

a = 2^5b / 2^4

And now since your bases are the same, you can use the second exponent rule in the list above to subtract the exponents and get to:

a = 2^(5b – 4), matching answer choice C.

More important than this problem is the lesson: when problems deal with exponents, and particularly with non-prime bases (like 16 and 32), one of your first mantras should be “All About That Base (no treble).” See if you can get multiple terms to have the same base, and you can simplify the expression using common exponent rules. Then, with your monster GMAT quant score, Harvard can take its Blank Space and write your name…

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: The Super Bowl Provides Super GMAT Lessons

GMAT Tip of the WeekIt’s Super Bowl weekend, one of the busiest gambling weekends of the year. Maybe you’ll play a squares pool and end up with the dreaded 6:5 combination, maybe you’ll parlay three prop bets and lose on the third, and maybe you’ll bet on your team to win and lose both the game and your cash. How can you turn your gambling losses into investments?

Well, if you’re a GMAT student, you can think about what the odds mean in terms of probability and you can watch the announcers miss Critical Reasoning lesson after Critical Reasoning lesson. For example:

Probability

Before the last piece of confetti hits the turf on Sunday, oddsmakers will have posted their odds on next year’s winner. For example, New England and Seattle might open at 4:1, Green Bay might come in at 7:1, etc. And while you might look at those odds and think “if I bet $100 on the Packers I’ll win $700!” you should also think about what those mean. 7:1 for Green Bay is really a ratio: 7 parts of the money says that Green Bay will not win, and 1 part says that it will. So that’s a good bet if you think that Green Bay has a better than 1 out of 8 chance (so better than 12.5%) to win next year’s Super Bowl. And if those are, indeed, the odds (4:1 for two teams and 7:1 for another), Vegas is essentially saying that there’s a less than likely chance (1/5 + 1/5 + 1/8 = 52.5% chance that one of those two teams wins) that someone other than Green Bay, New England, or Seattle will win next year.

So consider what the probability of those bets means before you make them. Individually odds might look tempting, but when you consider what that means on a fraction or percent basis you might have a different opinion.

Probability #2

As you watch the Super Bowl, there’s a high likelihood that at some point the screen will start showing a line indicating the season-long field goal for either Steven Hauschka or Stephen Gostkowski (the Seattle and New England kickers…there’s a huge probability that someone named Steve will be incredibly important in this game!). And the announcers will use that line to say that it’s likely field goal range for that team to win or tie the game.

Where’s the flawed logic? If that’s the longest field goal he’s made all year, is it really likely that he’ll make another one from a similar spot with all that pressure? Or, in the case of a low-scoring game like many predict between these two elite defenses, how likely is either kicker to make two consecutive field goals from a relatively far distance?

Sports fans are pretty bad with that probability. Say that a kicker has been 70% accurate from over 50 yards. Is it likely that he’ll make two straight 50-yard field goals on Sunday (assuming he gets those attempts)? Check the math: that’s 7/10 * 7/10 or 49/100 – it’s less than likely that he makes both! Even a kicker with 80% accuracy is only 8/10 * 8/10 = 64% likely to make two in a row…meaning that fail to perform that feat 1 out of every 3 times he had the chance! Think of the probability while announcers talk about field goals as a near certainty on Sunday.

Critical Reasoning

The announcers on Sunday will try to use all kinds of data to predict the outcome, and in doing so they’ll give you plenty of opportunities to think critically in a Critical Reasoning fashion. For example:

“For the last 40 Super Bowls, the team with the most rushing yards has won (some massive percent) of them; it’s important for New England to get LeGarrette Blount rolling early.”

This is a classic causation/correlation argument. Do the rushing yards really win the game? It could very well be true (Weaken answer!) that teams that build a big lead and therefore want to run out the clock run the ball a lot in the second half (incomplete passes stop the clock; runs keep it going). Winning might cause the rushing yards, not the other way around.

Similarly, the announcers will almost certainly make mention at halftime of a stat like:

“Team X has won (some huge percentage) of games they were leading at halftime, so that field goal to put them up 13-10 looms large.”

Here the announcer isn’t factoring in a couple big factors in that stat:

-A 3-point lead isn’t the same as a 20-point lead; how many of those halftime leads were significantly bigger?
-You’d expect teams leading at halftime to win a lot more frequently; based on 30 minutes they may have shown to be a better team plus they now have a head start for the last 30 minutes. Over time those factors should bear out, but in this one game is a potentially-flukey 3-point lead significant enough?

Regardless of how you watch the game, it can provide you with plenty of opportunities to outsmart friends and announcers and sharpen your GMAT critical thinking skills. So while Tom Brady or Russell Wilson runs off the field yelling “I’m going to Disneyland!”, if you’ve paid attention to logical flaws and probability opportunities during the game, you can celebrate by yelling “I’m going to business school!”

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Learn from DeflateGate and Don’t Get Caught Unintentionally Cheating

GMAT Tip of the WeekIt’s Super Bowl week, and instead of Seattle’s miracle comeback over Green Bay or a fantastically-intriguing matchup between the longstanding dynasty in New England and the up-and-coming dynasty in Seattle, all anyone wants to talk about is DeflateGate. Did the Patriots knowingly underinflate or consciously deflate footballs? Did doing so provide a competitive advantage? Will/should they be punished?

Some will say it’s a heinous act committed by serial cheaters. Others will say it’s a minor violation and that “everybody does it.” And still others will say it’s an inadvertent mistake that happened to run afoul of a technicality. What does it mean for you, a GMAT aspirant?

Be careful about honest mistakes that could be construed as cheating!

While the NFL isn’t going to kick the Patriots out of the Super Bowl, the Graduate Management Admission Council won’t hesitate to cancel your score if you’re found to be in violation of its test administration rules. So beware these rules that honest examinees have accidentally violated:

1. You cannot bring “testing aids” into the test center.

Don’t bring an Official Guide, a test prep book, or study notes into the test center with you. You may want to have notes while you’re waiting to check in, but if you’re caught with “study material” in your hands during one of your 8-minute breaks – which has happened to students who were rearranging items in their lockers to grab an apple or a granola bar – you’ll be in violation of the rule, and GMAC has cancelled scores for this in the past. Don’t take that risk! Leave watches, cell phones, and study aids in your car or at home so that there’s no chance you violate this rule simply by having a forbidden item in your hand during a break.

2. You cannot talk to anyone about the test during your administration.

You’ll be at the test center with other people, and someone’s break might coincide with yours. Holding a restroom door or crossing paths near a drinking fountain, you might be tempted to socially ask “how is your test going?” or sympathetically mention “man these tests are hard.” But since those innocent phrases could be seen as “talking about the test” you would technically be in violation of the rule, and GMAC has cancelled scores for this in the past. Your 8-minute break isn’t the time to make new friends – don’t take the risk of being caught talking about the test.

You know that you’re not a cheater, but as most New Englanders feel today it’s very possible to be considered a cheater if you end up on the wrong side of a rule, however accidentally. Learn from the lessons of test-takers before you: avoid these common mistakes and ensure that the score you earn is the score you’ll keep.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Stop Trying to Re-Write the Verbal Section of the Test

GMAT Tip of the WeekWhich ineffective habit do nearly all GMAT aspirants have when it comes to studying for the verbal section?

Thou doth protest too much. Meaning:

We all think we can write verbal questions better than the authors of the test.

When it comes to GMAT verbal questions, we critique but don’t solve Critical Reasoning problems, we correct rather than solve Sentence Correction problems, and we try to write but don’t thoroughly read Reading Comprehension questions. And this hubris can be the death of your GMAT verbal score, even if it comes from a good place and a good knowledge base.

Wander into a GMAT class or scan a GMAT forum and you’ll see and hear tons of comments like:

“I feel like the question should say people and not individuals.”

“I would never use the word imply like that.”

“I don’t think that’s the right idiom.”

“I would have gotten it right if it said X…I think it should have said X.”

Or you’ll hear questions like:

“But what if answer choice D said and and not or?”

“If that word were different would my answer choice be right? And if so would it be more right than B?”

And while these questions often come from a genuine desire to learn, they more often come from a place of frustration, and they’re the type of hypothetical thinking that doesn’t lend itself to progress on this test. Even if it’s not always perfect, the GMAT chooses its words very carefully. When the word in the Reading Comprehension correct answer choice isn’t the word you were hoping it would be (but it’s close), they picked that word for a reason – it makes the problem more difficult. When none of the Sentence correction answer choices match the way you or your classmates would have phrased it, that’s not a mistake – that’s an intentional device to make you eliminate four flawed answers and keep the strange-but-correct one. The GMAT can’t always match your expectations, not just because doing so would make it too easy but also because it’s trying to test other critical-thinking skills. It has to test your ability to see less-clear relationships, to make logical decisions amidst uncertainty, to find the least of five evils, and it has to punish you for jumping to unwarranted conclusions.

GMAT verbal is constructed carefully, and as you study it you have to learn how to answer questions more effectively, not to write better questions. The only thing you get to write on test day is the AWA essay; everything else you must answer on the GMAT’s terms, not on your own, so as you study you have to resist the urge to protest the problem and instead learn to see the value in it.

So as you study, remember your mission. Your job isn’t to find a flaw with the logic of the question, but rather with the logic of the four incorrect answers. When you get mad at a wrong answer, use that energy to attack the next problem with the lessons you learned from that frustrating mistake. Take the GMAT as it is and don’t try to justify your mistakes or fight the test.

Save your writing energy for the AWA essay; on the verbal section, you only get to answer the problem in front of you. When you accept that the test is what it is and commit yourself to learning how to attack it through critical thinking and not just general angst, you’ll have a competitive advantage over most frustrated examinees. Think like the testmaker, but don’t try to be the testmaker.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: New Year, New You, New Study Plan

GMAT Tip of the WeekHappy New Year!  If you’re reading this on January 9, our publication date, and your New Year’s Resolution is still intact, you’re probably in the majority.  But within the next few weeks that will change… This week the gyms, yoga studios, pools, and health food stores of the world were packed with people for whom 2015 is the year to become great; by Valentine’s Day, however, Netflix usage, Frito-Lay sales, and Taco Bell drive through volume will be back to their normal levels, while GMAT class attendance will start to wane, too.

As a GMAT student who wants to make 2015 the year of the elite MBA acceptance letter, how can you be among the disappointingly-few who keep up this week’s excellence exuberance?

Keep it simple.

The problem with most New Year’s Resolutions and GMAT study plan’s is that they’re far too ambitious.  Hatched over eggnog and 7-10 days of paid vacation, these plans are destined to failure because they’re way too much for anyone to adhere to in the long term.  They often read like:

“I’ll get up 90 minutes before I normally do and study over a healthy breakfast, then after work three days a week I’ll go the library, and every Saturday I’ll take a practice test and spend Sunday mornings with a tutor reviewing it all.”

“I’ll take a leave of absence from work so that I can study 40-50 hours a week for three months, then I’ll take the GMAT in the spring and get a high score, then volunteer all summer to demonstrate my community service, then apply round 1 to Harvard/Stanford/Wharton, and maybe throw Yale or London Business School in the mix as a safety school.”

“I’ll turn off my smartphone and give up social media for the next few months, study at least 90 minutes a day, and….”

And the problem with those study plans? You’ll resent them within a week, just like most New Year’s Resolvers resent their no-carb / all-lettuce diets and overpriced gym memberships.  You have to come up with a study plan that:

1) You can fit in to your lifestyle so that you can keep to it.

This means that you factor in your hobbies and, yes, limitations.  If you’re not a morning person, you won’t keep to a schedule of studying every morning before work.  If you thrive on a good workout, giving up your soccer league or gym regimen completely won’t work either.  And friends, family, work functions, etc. are always important.

2) You can build on.

The best study plans are those that start a bit smaller and build into something more robust, like a “Couch to 5k (or marathon)” training program.  If you want to run a marathon, you start with a couple miles and build up to 18-20 milers as your body is ready for it.  If you want a 700 on the GMAT, you start with a handful of study sessions per week and build into longer sessions when they’re more purposeful and you know what you’re using the time to work on.

3) Focus on achievement, not activity.

Veritas Prep emphasizes the famous John Wooden quote “never mistake activity for achievement”, meaning that simply spending 4 hours studying Sentence Correction, for example, isn’t going to get the job done; it’s the quality of study that helps.  So hold yourself accountable for goals, not time spent.  Think in terms of “I want to do 25 SC problems focusing on major error categories first, then thinking of logical meaning second”

or “I’m going to practice applying right triangle principles to geometry problems” or “I’m going to do a timed drill to force myself to think more quickly.”  Give your study sessions themes and achievement goals, and they’ll not only be more productive but they’ll also be more fun.

So what does a productive, sustainable study schedule look like?

*It’s firm but flexible.  Plan to study at least 3 times per week, but let yourself move Tuesday’s session to Wednesday if you get tickets to a Tuesday concert or you work late and just need to blow off steam with a run.  You have to get those sessions in, but you don’t have to resent them or go through the motions just to stick to your (probably arbitrary) schedule.

*It’s achievement-driven.  Your study sessions have themes and goals, not just durations.

*It’s reasonable. Know yourself and your preferences and limitations.

Very few people can study for hours every day, so schedule something you can commit to – a few sessions per week, maybe two weeknights and one weekend morning, or something that you know you can hold yourself accountable to.

*It’s custom-built. Think about when you’ve been most successful in other academic pursuits and try to replicate that.  Do you study better in the morning?  In the evening?  With friends or music?  Alone?  After a good workout?   With a snack?  Build your plan around your own successes.

*It’s built to expand.  2-3 study sessions a week may very well not be enough for you, so be honest with yourself once you’ve up and running.  Do you need more time to master algebra?  Do you need to build in a class or On Demand program to supplement your practice?  Do you have enough time for practice tests?  Once you’re committed to a bsseline study regimen, you need to be honest with yourself about what you need, and at that point it’s often easier to bite the bullet and dive into something more intense.

But in the beginning, make sure you have a schedule/plan that you won’t quit before your neighbors even take their Christmas lights down.

January is a great time to make plans for self-improvement, but most of those plans never live to see February.  To ensure that your New YEAR’s Resolution to succeed on the GMAT isn’t limited to one month or less, resolve to plan on something that will last.  If you can do that, we’ll see you back in this GMAT Tip of the Week every Friday until you have that score you’re looking for.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: It’s Always Darkest Before Sunrise

GMAT Tip of the WeekWith the winter solstice behind us here in the Northern Hemisphere, you’re probably noticing that the daylight is starting to return; this week we begin the steady climb toward summertime and you’ll see a few extra minutes of daylight after work each week from here until June. For many GMAT applicants, the darkest days of the year in December and early January match with the darkest days of their admissions journey, hustling to post a competitive GMAT while also scrambling on essays for Round 2. But this, too, shall pass.

If your New Year’s Resolution is to make 2015 the year that you ace the GMAT, you can take a lesson from this time of year. The darkest points always give way to enlightenment, and that secret will get you through some very difficult GMAT problems. There are two very common structures for challenging GMAT quant problems:

1) It looks easy, but the last step or two are tricky.

2) It looks impossible, but once you’ve found the right foothold it gets easy quickly.

This post is all about #2, those problems where it looks incredibly dark right up until that moment that you reach enlightenment. Veritas Prep’s own Jason Sun recounts the first quant question en route to his official 780 score: “I stared at a nasty sequence problem for probably 45 seconds with my jaw open thinking ‘there’s no way to solve this’. Then I remembered the strategy of starting with small numbers and finding a pattern, and 10 seconds later the answer was obvious.”

That’s common on the GMAT, and step one for you is to realize that problems are designed to look like that. When things look darkest, have faith that they’ll clear up. Here are a few ways that that occurs on the GMAT.

Calculations look awful, but work themselves out before you get to the answer.

Consider this problem:

If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then
what is the value of a – d?

(A) 2
(B) 8
(C) 10
(D) 11
(E) 14

Upon first glance, 1155 and four variables might look really messy. But take the first step – you know it’s divisible b y 11 and that you have to factor it. 1100 is 11*100 and 55 is 11*5, so you have 11*105. And 105 is much easier to divide out since it ends in a 5. That’s 21*5, which is 7*3*5. Once you’ve factored it down, it’s 11*7*5*3, which are all prime, so when 1 has to be less than any of these, that’s exactly a, b, c, and d. You need the biggest minus the smallest, and 11-3 is 8. What may have looked like a big, intimidating number was actually not so bad once you took the first step. It’s always darkest before the light goes on.

The problem is abstract, but comes into focus when you test small numbers.

What is the units digit of 2^40?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 0

2^40 is an insanely large number. You’ll never be able to calculate it. But if you take the first few steps with small numbers, you’ll see a pattern:

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256

And since you only care about the units digits, you should see a pretty firm pattern emerging. 2, 4, 8, 6, 2, 4, 8, 6. If you repeat through this pattern, you’ll see that every 4th number is a 6, and since 2^40 will be the finish of the tenth run of that every-fourth-number cycle, the answer has to be 6. The GMAT loves to give you problems with big or abstract numbers that seem unfathomable, but if you test properties with small numbers you can often find a pattern or some other way to determine what you have.

It’s always the last place you look.

Another common theme is specific to geometry problems – the GMAT often constructs them so that a seemingly irrelevant piece of information (like the measure of a far, far away angle, or the area of a figure when you’re only solving for the length of one line) is crucial to the answer…it’s just that you don’t even consider filling in that piece of information that seems so far away from what you’re really trying to solve for. So FILL IN EVERYTHING! Even if it seems irrelevant, fill in every piece of information you can solve for and you’ll give yourself a better shot of finding that unlikely relationship that cracks the code.

You’re not supposed to be able to solve for it, but you can estimate or use answer choices.

Plenty of GMAT questions beg you to do some horrifying math, but if you look at the answer choices ahead of time you can see that they’re either spread incredibly far apart and ready to be estimated or they have easy-to-plug-in properties that allow you to just test them. It’s crucial to remember that the GMAT isn’t a test of pure math, but of problem solving using math. Heed this advice: if you think the calculations are too detailed to do in two minutes, you’re probably right. That’s when you should look to estimate or backsolve.

So if your GMAT study sessions are growing longer as the daylight does, keep this wisdom in mind. It always looks darkest before sunrise, and the same is true of many tough GMAT quant problems. As you struggle through practice problems, pay attention to all those times that the solution wasn’t nearly as bad as it seemed it would have to be upon first glance.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Serial and Sufficiency

Like most offices in the United States today, Veritas Prep’s headquarters had its fair share of water cooler and coffemaker discussions about yesterday’s final episode of the Serial podcast. Did Adnan do it? Did Jay set him up? Why does Don get a free pass based on a LensCrafters time-card punch? Does Best Buy have pay phones? The one answer we can give you is “we used MailChimp” so there’s that at least.

The other answer we can give you? Sarah Koenig would do pretty darned well on Data Sufficiency questions, where often it’s just as important to determine what you don’t know as it is to determine what you do. While the internet buzzed with theories certain that Adnan did it, that Jay did it, that a recently-released serial killer did it, Koenig was often ridiculed for being so noncommittal in her assessment of whether Adnan is guilty or not. But that’s an important mentality on Data Sufficiency questions, as one of the common ways that the GMAT will bait you is giving you information that seems overwhelmingly sufficient (The Nisha call! The phone was in Leakin Park!) but that leaves just enough doubt (Why did Jay’s story change so much?) that you can’t prove a definitive answer. And like the jury in the Serial case, we all have that tendency to jump to conclusions (“well if he didn’t kill her, who did?”) and filter out information that we don’t like (Christina Gutierrez’s performance…). This Serial-themed Data Sufficiency problem should exemplify (forgive the lack of subscript formatting, but a sequence problem in a Serial blog post seemed fitting):

The infinite (serial) sequence a1, a2, …, an, … is such that a1 = x, a2 = y, a3 = z,a4 = 3 and an = a(n-4) for n > 4. What is the sum of the first 98 terms of the sequence?

(1) x = 5

(2) y + z = 2

As people unpack the mystery in this problem, they start to see what’s going on. If an = a(n-4), then each term equals the term that came four prior. So the sequence really goes:

x, y, z, 3, x, y, z, 3, x, y, z, 3…

So although it looks like a pretty massive mystery, really you’re trying to figure out x, y, and z because 3 is just 3. And here’s a common way of thinking:

Statement 1 is not sufficient, but it gets you one of the terms. And Statement 2 is not sufficient but it gets you two more. So when you put them together, you know that the sum of one trip through the 4-term sequence is 5 + 2 + 3 = 10, so you should be able to extrapolate that to the whole thing, right? Just figure out how many trips through will get you to term 98 and you have it; like the Syed jury, you have the motive and the timeline and the cell phone records and Jay’s testimony, so the answer has to be C. Right?

But let’s interview Sarah Koenig here:

Sarah: The pieces all seem to fit but I’m just not so sure. Statement 2 looks really bad for him. If we can connect those dots for y and z, and we already have x, we should have all variables converted to numbers. Literally it all adds up. But I feel like I’m missing something. I can definitely get the sum of the first 4 terms and of the first 8 terms and of the first 12 terms; those are 10, and 20, and 30. But what about the number 98?

And that’s where Sarah Koenig’s trademark thoughtfulness-over-opinionatedry comes in. There is a giant hole in “Answer choice C’s case” against this problem. You can get the sequence in blocks of 4, but 98 is two past the last multiple of 4 (which is 96). The 97th term is easy: that’s x = 5. But the 98th term is tricky: it’s y, and we don’t know y unless we have z with it ( we just have the sum of the two). So we can’t solve for the 98th term. The answer has to be E – we just don’t know.

Now if you’ve heard yesterday’s episode, think about Dana’s “think of all the things that would have to have gone wrong, all the bad luck” rundown. “He lent his car and his phone to the guy who pointed the finger at him. That sucks for him. On the day that his girlfriend went missing. That’s awful luck…” And in real life she may be right – that’s a lot of probability to overcome. But on the GMAT they hand pick the questions. On this problem you can solve for the 97th term (up to 96 there are just blocks of 4 terms, and you know that each block sums to 10, and the 97th term is known as 5) or the 99th term (same thing, but add the sum of the 98th and 99th terms which you know is 2). But the GMAT hand-selected the tricky question just like Koenig hand-selected the Adnan Syed case for its mystery. GMAT Data Sufficiency questions are like Serial…it pays to be skeptical as you examine the evidence. It pays to think like Sarah Koenig. Unlike Jay, the statements will always be true and they’ll always be consistent, but like Serial in general you’ll sometimes find that you just don’t have enough information to definitively answer the question on everyone’s lips. So do your journalistic due diligence and look for alternative explanations (Don did it!). Next thing you know you’ll be “Stepping Out!!!” of the test center with a high GMAT score.

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Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

4 Questions To Ask Yourself On Min/Max GMAT Problems

GMAT Tip of the WeekMin/Max problems can be among the most frustrating on the GMAT’s quantitative section. Why? Because they seldom involve an equation or definite value. They’re the ones that ask things like “did the fisherman who caught the third-most fish catch at least 12 fish?” or “what is the maximum number of fish that any one fisherman caught?”. And the reason the GMAT loves them? It’s precisely because they’re so much more strategic than they are “calculational.” They make you think, not just plug and chug.

However…

There are three knee-jerk questions that you should plug (if not chug) into your brain to ask yourself every time you see a Min/Max problem before you ask that fourth question “What’s my strategy?”:

  1. Do the numbers have to be integers?
  2. Is zero a possible value?
  3. Are repeat numbers possible?

In the Veritas Prep Word Problems lesson we refer to these problems as “scenario-driven” Min/Max problems precisely because of the above questions. The scenario created by the problem drives the whole thing, related mainly to those three above questions. Consider these four prompts and ask yourself which ones can definitively be answered:

#1: “Four friends go fishing and catch a total of 10 fish. How many fish did the friend with the highest total catch?”

#2: “Four friends go fishing and catch a total of 10 fish. If no two friends caught the same number of fish, how many fish did the friend with the highest total catch?”

#3: “Four friends go fishing and catch a total of 10 fish. If each friend caught at least one fish but no two friends caught the same number, how many fish did the friend with the highest total catch?”

#4: “Four friends go fishing and catch a total of 10 pounds of fish. If each friend caught at least one fish but no two friends caught the same number, how many pounds of fish did the friend with the highest total catch?”

Hopefully you can see the progression as this set builds. In the first problem, there’s clearly no way to tell. Did one friend catch all ten? Did everyone catch at least two and two friends tied with 3? You just don’t know. But then it gets interesting, based on the questions you need to ask yourself on all of these.

With #2, two big restrictions are in play. Fish must be integers, so you’re only dealing with the 11 integers 0 through 10. And if no two friends caught the same number there’s a limited number of unique values that can add up to 10. But the catch on this one should be evident after you’ve read #3. Zero *IS* possible in this case, so while the totals could be 1, 2, 3, and 4 (guaranteeing the answer of 4), if the lowest person could have caught 0 (that’s where “min/max” comes in – to maximize the top value you want to minimize the other values) there’s also the possibility for 0, 1, 2, and 7. Because the zero possibility was still lurking out there, there’s not quite enough information to solve this one. And that’s why you always have to ask yourself “is 0 possible?”.

#3 should showcase that. If 0 is no longer a possibility *AND* the numbers have to be integers *AND* the numbers can’t repeat, then the only option is 1 (the new min value since 0 is gone), 2 (because you can’t match 1), 3, and 4. The highest total is 4.

And #4 shows why the seemingly-irrelevant backstory of “friends going fishing” is so important. Pounds of fish can be nonintegers, but fish themselves have to be integers. So even though this prompt looks very similar to #3, because we’re no longer limited to integers it’s very easy for the values to not repeat and still give wildly different max values (1, 2, 3, and 4 or 1.5, 2, 3, and 3.5 for example).

As you can see, the scenario really drives the answer, although the fourth question “What is my strategy?” will almost always require some real work. Let’s take a look at a couple questions from the Veritas Prep Question Bank to illustrate.

Question 1:

Four workers from an international charity were selling shirts at a local event yesterday. Did one of the workers sell at least three shirts yesterday at the event?

(1) Together they sold 8 shirts yesterday at the event.

(2) No two workers sold the same number of shirts.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient to answer the question asked
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Before you begin strategizing, ask yourself the three major questions:

1) Do the values have to be integers? YES – that’s why the problem chose shirts.

2) Is zero possible? YES – it’s not prohibited, so that means you have to consider zero as a min value.

3) Can the numbers repeat? That’s why statement 2 is there. With the given information and with statement 1, numbers can repeat. That allows you to come up with the setup 2, 2, 2, and 2 for statement 1 (giving the answer “NO”) or 1, 2, 2, and 3 (giving the answer “YES” and proving this insufficient).

But when statement 2 says on its own that, NO, the numbers cannot repeat, that’s a much more impactful statement than most test-takers realize. Taking statement 2 alone, you have four integers that cannot repeat (and cannot be negative), so the smallest setup you can find is 0, 1, 2, and 3 – and with that someone definitely sold at least three shirts. Statement 2 is sufficient with really no calculations whatsoever, but with careful attention to the ever-important questions.

Question 2:

Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000
(B) $41,667
(C) $42,000
(D) $50,000
(E) $60,000

Here ask yourself the same questions:

1) The numbers do not have to be integers.
2) Zero is theoretically possible (but probably constrained by the 20% difference restriction)
3) Numbers absolutely can repeat (which will be very important)
4) What’s your strategy? If you want the LOWEST possible single salary, then use your answer to #3 (they can repeat) and give the other 20 salaries the maximum. That way your calculation looks like:

x + 20(1.2x) = 1,050,000

Which breaks out to 25x = 1,050,000, and x = 42000. And notice how important the answer to #3 was – by knowing that numbers could repeat, you were able to quickly put together a smart strategy to minimize one single value.

The larger lesson is crucial here, though – these problems are often (but not always) fairly basic mathematically, but derive their difficulty from a situation that limits some options or allows for more than you’d think via integer restrictions, the possibility of zero, and the possibility of repeat values. Ask yourself these four questions, and your answer to the first three especially will maximize your efficiency on the strategic portion of the problem.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Today’s Date in Geometry History

GMAT Tip of the WeekToday is December 5, or in date form it’s 12/5. And if you hope to score 700+ on the GMAT, you should see those two numbers, 5 and 12, and immediately also think “13”!

Why?

There are certain combinations of numbers that just have to be top of mind when you take the GMAT. The quantitative section goes quickly for almost everyone, and so if you know the following combinations you can save extremely valuable time.

Based on Pythagorean Theorem, a^2 + b^2 = c^2, these four ratios come up frequently with right triangles:

a_______b________c
3_______4________5
5______12_______13
x_______x______x*(sqrt 2)___(in an isosceles right triangle)
x____x*(sqrt3)___2x________(in a 30-60-90 triangle)

These four ratios come up frequently when right triangles are present, so they’re about as high as you can get on the “should I memorize this?” scale. But just as important is using these ratios wisely and appropriately, so make sure that when you see the opportunity for them you keep in mind these two important considerations:

1) These “Pythagorean Triplets” are RATIOS, not just exact numbers.

So a 3-4-5 right triangle could also be a 6-8-10 or 15-20-25, and an isosceles right triangle could very well have dimensions a = 4(sqrt 2), b = 4(sqrt 2), and c = 8 (which would be one of the short sides 4(sqrt 2) multiplied by (sqrt 2) ). An average level question might pair 5 and 12 with you and reward you for quickly seeing 13, while a harder question could make the ratio 15, 36, 39 to reward you for seeing the ratio and not just the exact numbers you memorized.

Similarly, people often memorize the 45-45-90 and 30-60-90 triangles so specifically that the test can completely destroy them by making the “wrong” side carry the radical. If the short sides are 4 and 4, you’ll naturally see the hypotenuse as 4(sqrt 2). But if they were to ask you for the length of the hypotenuse and tell you that the area of the triangle is 4 (so 1/2 * a * b = 4, and with a equal to b you’d have 1/2 a^2 = 4, so a^2 = 8 and the short side then measures 2(sqrt 2)), it’s difficult for many to recognize that the hypotenuse could be an integer. So be careful and know that the above chart gives you *RATIOS* and not fixed numbers or fixed placements for the radical sign that denotes square root.

2) In order to apply these ratios, you MUST know which side is the hypotenuse.

In a classic GMAT trap, they could easily ask you:

What is the perimeter of triangle ABC?

(1) Side AB measures 5 meters.

(2) Side AC measures 12 meters.

And it’s common (in fact a similar problem shows that about 55% of people make this exact mistake) to think “oh well this is a 5-12-13, so both statements together prove that side BC is 13 and I can calculate that the perimeter is 30 meters.” But wait – 5 and 12 only lead to a third side of 13 when you know that 5 and 12 are the short sides. If you don’t know that, the triangle could fit the Pythagorean Theorem with 12 as the hypotenuse, meaning that you’re solving for side b:

5^2 + b^2 = 12^2, so 25 + b^2 = 144, and b then equals the square root of 119.

So while it’s critical that you memorize these four right triangle ratios, it’s just as important that you don’t fall so in love with them that you use them even when they don’t apply.

Important caveats aside, knowing these ratios is crucial for your ability to work quickly on the quant section. For example, a problem that says something like:

In triangle XYZ, side XY, which runs perpendicular to side YZ, measures 24 inches in length. If the longest side of the the triangle is 26 inches, what is the area, in square inches, of triangle XYZ?

(A) 100
(B) 120
(C) 140
(D) 150
(E) 165

Those employing Pythagorean Theorem are in for a fight, calculating a^2 + 24^2 = 26^2, then finding the length of a and calculating the area. But those who know the trusty 5-12-13 triplet can quickly see that if 24 = 12*2 and 26 = 13*2, then the other short side is 5*2 which is 10, and the area then is 1/2 * 10 * 24, which is 120. Knowing these ratios, this is a 30 second problem; without them it could be a slog of over 2 minutes, easily, with a higher degree of difficulty due to the extensive calculations. So on today of all days, Friday, the 5th day of the 12th month, keep that 13th in there as a lucky charm.

On the GMAT, these ratios will get you out of lots of trouble.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Why Are You Here?

GMAT Tip of the WeekThis week’s video post brings you a tip for taking a closer look at the data in Data Sufficiency. Is what you know about Data Sufficiency statements really sufficient? There are certain points of information that are necessary to know for Data Sufficiency, but knowing those doesn’t mean you have sufficient information to correctly solve the problem.

Watch this video to learn how you can find hidden hints within statements and how that can help you avoid any GMAT traps. You don’t want to leave any points on the table.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: The Most Common Wrong Answer to Any GMAT Problem

GMAT Tip of the WeekThe GMAT is more than just a math or verbal test – it’s a reasoning test.  And so it’s important to think not merely about content, but also about the strategy games that the authors of these questions play with that content.  One mantra to keep in mind is “Think Like the Testmaker”, reminding yourself to pay just as much attention to why the wrong answer you chose was tempting (how did the author trick you) as to why the correct answer was right.

Arguably the single most common trap the authors set for you is evident in this question, which we invite you to answer before you read the rest of this post:

Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 15 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?

(A) 3
(B) 6
(C) 7.2
(D) 7.8
(E) 9

Now, we don’t want to gloss over the math here but there’s plenty of opportunity to practice with word problems and ratios in other posts and resources, so let’s cut to the true takeaway here.  Most students will correctly arrive at the amount of chocolate used by employing a method similar to:

If the 36 ounces of dough are to be 80% of the total weight, then 36 = 4/5 * total.

That means that the total weight is 45 ounces, and so when we subtract out the 36 ounces of dough, there’s 9 ounces of chocolate in the cookies.

So…the answer is E. Right?

Wrong.  Go back and double-check the question – the question asks for how much chocolate is LEFT OVER, not how much is USED.  To be correct, you’d need to go back to the 15 original ounces of chocolate, subtract the 9 used, and correctly answer that 6 were left.

What’s the trap?  GMAT questions are frequently set up so that you can answer the wrong question.  If a question asks you to solve for y, it typically makes it easier to first solve for x…and then x is a trap answer.  If a question asks you to strengthen a conclusion, the best way to weaken it is likely to be an answer choice.  If a question asks for the maximum value, the minimum is going to be a trap.

The most common wrong answer to any problem on the GMAT is the right answer to the wrong question.

So take precaution – to avoid this trap, make sure that you:

  • Circle the variable for which you’re solving, or write down the question at the top of your work.
  • Jot a question mark at the top of your noteboard on test day, and tap it with your pen before you submit your answer to double check “did I answer the right question?”
  • Keep track of your units in word problems (minutes vs. seconds, amount used vs. amount remaining) and double check the units of your answer against the question
  • Make note of every time you make that mistake in practice, and as a more general tip be sure not to write off silly mistakes as just “silly mistakes”.  If you made them in practice, you’re susceptible to them on the test, so make a note to watch out for them particularly if you’ve made the same mistake twice.

Few outcomes are more disappointing than doing all the work correctly but still getting the question wrong. The GMAT doesn’t do partial credit, so on a question like this falling for the trap is just as bad as not knowing how to get started.  Get credit for what you know how to do – make sure you pause before you submit your answer to make sure that it answers the proper question!

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Sentence Correction in Real Life

GMAT Tip of the WeekTotes McGotes. FML. Sorry for partying. I know, right? Of the common phrases that have permeated pop culture and everyday conversation, easily one of the most common is, wait for it…

Wait for it.

And that one phrase can totes make your GMAT score supes high. Like, for real.

How?

Perhaps the best example comes from an all-staff email sent at Veritas Prep headquarters this week regarding the holiday vacation schedule. It began “With pumpkin spice season nearing its apex, it’s…” Seeing that introduction, multiple Veritas Prep staffers commented later that “it’s” after the comma made them nervous, as the possessive of “season” is its, not it’s (which grammatically means “it is”).

Now later in that sentence it became clear that the intention was “it is” (…”it’s time to start making holiday vacation plans.”), but the fact that so many Sentence Correction experts were on the edge of their seats just seeing that contraction “it’s” next to a possessive should demonstrate for you how to become great at Sentence Correction. To be efficient and effective with Sentence Correction, it’s helpful to anticipate what types of errors you might see, rather than simply sit back and wait for them to appear. Those who are most successful at Sentence Correction read sentences looking for signs of potential danger; they’re proactive as they search for likely Decision Points. For example, if you were to read the introduction:

Particularly for a leadership or management role, it is important that a candidate be both…

your senses should be heightened for parallel structure with “both X and Y,” number one, and secondly you should be acutely aware that the word “be” precedes the word “both,” so there is a very high likelihood that there will be an extraneous “be” after the word “and” to follow. In other words, when you see “both,” wait for it…where’s the “and,” and is the portion directly after it parallel to the first portion?

Correct:

(A) qualified to perform the duties of most subordinates and able to inspire subordinates to perform those duties at a higher level.

Incorrect:

(B) qualified to perform the duties of most subordinates and be able to inspire subordinates to perform those duties at a higher level.

While the grammar of this problem is crucial, true expertise comes from knowing where to focus your attention and expend your mental energy. Analyzing every word of every answer choice is exhausting, so the experts train themselves to see clues and “…wait for it” focusing back in on the parts of the sentence most highly correlated with errors. Clues can be:

Signals of parallel structure: both, either, neither, not only

Signals of verb tense: since, from, until

Signals of pronoun or subject/verb agreement: it, they, its, their

To train yourself to spot those clues that tell you to “wait for it…”, pay attention not only (wait for it…) to the grammatical reasons that an answer choice is right or wrong in your homework, but also (here it is…is it parallel?) to the signals outside the underline that required the application of that grammar. Sentence Correction is to an extent about “what do you know” but to really excel it also has to be about “what do you do” – the clues and signals that tell you what to look for and where to spend your time and energy.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Getting Specific About Reading Comprehension

GMAT Tip of the WeekPop quiz!

1) What is the VIN number on your car?

2) What is your health insurance policy number?

3) What day does Daylight Savings Time start this coming spring?

If you’re like most people, your answer to all three is “I’d have to look that up.” And if you’re like most successful GMAT test-takers, that should be your answer to most Reading Comprehension questions, too. Particularly for questions like:

1) According to the passage, researchers were able to make the startling discovery because ______________.

2) It can be inferred from the passage that were a roundworm’s cilia become unable to sense temperature, _____________.

3) According to the passage, the reason that the antigen-antibody theory had to be seriously qualified was that ______________.

The answers to these questions are likely too obscure for you to have remembered from your initial read of the passage, and the answer choices are likely too dense to match exactly something from your memory, anyway, so when Reading Comprehension questions ask for a detail, you should always return to the passage. Thinking strategically, this means that you should:

*Not read too closely on your first read. Since you have to go back for details, they’re not all that important to remember your first time out. PLUS the main reason that people waste time and struggle on Reading Comprehension passages/questions is that they spend too much time processing and worrying about details on their first read. Much like the questions at the beginning of this post, details are only important if they ask you about them, so you shouldn’t spend too much time trying to understand or remember them until they come up in a question.

*When you’re asked about a detail, pay specific attention to the question being asked. Many details from wrong answer choices will appear next to the keyword (maybe as a cause while the question is looking for an effect, etc.) so you’ll need that time you saved from not worrying about details to help you focus in on what’s important on the question.

*Read effectively your first time through to know where certain things are discussed so that you minimize the time it takes you to go back. Give yourself “titles” for each paragraph so that you know where, for example, details of the new theory are discussed or problems with the old system appear. You will have to go back, so your first read is really about getting organized for each of those battles.

In Reading Comprehension as in life, there are often too many details to be concerned with until you absolutely have to. Know that going in, and be ready to go back and look up whatever you need when you need to.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Derek Jeter and the Data Sufficiency Walkoff

GMAT Tip of the WeekIt all looked so obvious: a storybook ending preordained from the beginning, some early success and a bit of good fortune leading to a glorious success story. But wait! Then fate intervened, and the easiest part of all had something different to say. And only then was true glory to be had, a glory much greater than that inevitable win ripped away just moments ago.

Derek Jeter’s final game at Yankee Stadium?

Sure…but also some of the hardest Data Sufficiency problems you’ll see on test day.

For those who didn’t see, Derek Jeter’s final game in a home Yankee uniform finished in fairy tale fashion last night. The Captain delighted the crowd early with a double, then reached base again on an error, and was set to ride off into the sunset (well, if it hadn’t rained and been dark out) a hero with one final Yankee win. The crowd chanting his name in the top of the 9th inning, he nearly teared up as he looked at his storybook finish, but then…uncharacteristically, Yankee closer David Robertson allowed two home runs to tie the game, perhaps dooming the win but in the end giving the clutch shortshop an even greater chance at glory. And Jeter delivered, batting in the winning run in his final at bat in pinstripes, on the last pitch he’d ever see at Yankee Stadium.

The GMAT relevance? It followed a blueprint for one of the hardest Data Sufficiency structures that the GMAT writes. That blueprint goes:

Step One: Somewhat difficult statement that takes some work but “satisfies your intellect” as the 650-and-up crowd finally realizes why it’s sufficient. (i.e. Jeter’s double and reached-base-on-error to set up a Yankee win)
Step Two: A much easier statement that seems a mere formality to deal with, but that for the truly elite (i.e. Jeter) provides an opportunity to really shine (i.e. the blown save in the top of the 9th)
Step Three: The chance for the hero to deliver.

Consider this problem:

What is the value of integer z?

(1) z is the remainder when positive integer x is divided by positive integer (x – 1)

(2) x is not a prime number

Now look at statement 1. There’s a lot to unpack – the concept of remainder, the definitions of “positive integer x and positive integer (x – 1)”, the fact that x then can’t be 1 (or x-1 would be 0 and therefore prohibited), the fact that the two values being divided are consecutive integers. So it’s not surprising that, on their way to the trap answer selected by nearly 60% of respondents in the Veritas Prep Question Bank, many feel the glory when they unravel the variables and processes and think:

“Ah, ok. 5/4 would work and that’s 1 remainder 1. 10/9 would work and that’s 1 remainder 1. 100 divided by 99 would work and that’s 1 remainder 1. I get it…remainder is always 1.”

After all that work, statement 2 is as much a formality as a 2 run lead with no baserunners in the 9th inning. Piece of cake. So people start to hear that crowd chanting their name a-la “De-rek-Jeeeet-er”, they pat themselves on the back for the accomplishment, and they pick A. Without ever seeing the opportunity that statement 2 really should provide them:

“Wait…that’s not the script I want – it shouldn’t be that easy.”

Those who know the GMAT well – those Jeterian scholars who have honed their craft through practice and determination to go with the natural talent – look at statement 2 and think “why does this matter? Why would the author write such a mundanely-irrelevant statement? The question is about z and the statement is about x? Come on…”

And in doing so, they’ll ask “Why would a prime number matter? And what kind of prime numbers might change things?” And when you’re talking prime numbers, just like when you’re talking Yankee lore, you have to bring up Number 2. 2 is the only even prime number and it’s the lowest prime number. If you see the definition “prime” and you don’t consider 2, you’re probably making a mistake. So statement 2 here should be your clue to test x = 2 and realize:

2/1 = 2 with no remainder. Based on statement 1 alone the answer is almost always “remainder 1” but this one exception allows for a remainder of 0, proving that statement 1 is not sufficient. You need statement 2 to rule it out, making the answer C (for captain?).

The real takeaway here?

Even if you think you’ve “won” after statement 1, if statement 2 looks so much like a mere formality that it’s almost anti-climactic there’s a good chance it’s there as a clue. Ask yourself why statement 2 might matter – sometimes it will and sometimes it won’t, but it’s always worth checking in these cases – and you may find that the real “glory” you’re after requires you to take a step back from that “win” you thought you had earlier on.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: At (the very) Least You Should Know This About Probability

GMAT Tip of the WeekAh, autumn. The busiest GMAT season of the year as application deadlines and back-to-school nostalgia fill the air, and that season always coincides with Major League Baseball’s pennant races and playoffs. And whether you’re a baseball fan or not, as an aspiring MBA you’ll find a fair amount of overlap between the two, as both the GMAT (and business) and baseball prominently feature the art of probability.

Through that lens, let’s discuss one of the most helpful “tricks” to avoid some of the most time-consuming types of problems on the GMAT, and we’ll lead with a problem:

Whenever his favorite baseball team’s “closer” allows a hit, Sean becomes irate (just close out the game, Joe Nathan!). If the closer needs to get three outs to win the game, and each batter he will face has a .250 batting average (a 1/4 chance of getting a hit), what is the probability that he will give up at least one hit (assuming that there are no walks/errors/hit-batsmen)?

And for those not consumed with baseball, this question essentially asks “if outcome A has a 25% chance of occurring in any one event, what is the probability that outcome A will happen at least once during three consecutive events?”

Baseball makes for an excellent demonstration here, because if we take out the other “free base” situations, really only two things happen – a Hit or an Out. And since we need 3 Outs, we could have all kinds of sequences in which there is at least one hit:

Hit, Out, Out, Out

Out, Hit, Out, Out

Out, Out, Hit, Out

or episodes with multiple hits:

Out, Hit, Hit, Out, Out

Hit, Out, Hit, Out, Hit, Out

or even

Hit, Hit, Hit, Hit, Hit, Hit, Hit, Hit…(game called by mercy rule, Sean punches through his TV)

The GMAT-relevant point is this: when a problem asks you for the probability of “at least one” of a certain event occurring, there are usually several ways that at least one could occur. But look at it this way: the ONLY way that you don’t get “at least one” H is if all three Os come first. The opposite of “at least one” is “none.” And there’s only one way to get “none” – it’s “Not Event A” then “Not Event A” then “Not Event A”… as many times as it takes to finish out the number of events. In other words, in this baseball analogy, if there’s a 25% chance of a hit then there’s a 75% chance of “not a hit” or “Out”, allowing us to set up the ONLY sequence in which there isn’t at least one hit:

Out, Out, Out

Which has a probability of:

3/4 * 3/4 * 3/4

Do the math, and you’ll find that there’s a 27/64 probability of “not at least one hit” and you can then know that the other 37/64 outcomes are “at least one hit.”

To the baseball fan, that means “take it easy on your closer – .250 is a pretty lackluster batting average and that even takes out the chance of walks and errors, and even with *that* there’s a better-than-likely chance there will be baserunners in the 9th!”

To the GMAT student, this example means that when you see a probability question that asks for the probability of “at least one” you should almost always try to calculate it by taking the probability of “none” (which is just one sequence and not several) and subtract that from 1. So your process is:

1) Recognize that the problem is asking for the probability of “at least one” of event A.

2) Find the probability for “not A” in any one event

3) Calculate the probability of getting “not A” in all outcomes by multiplying the “not A” probability as many times as there are outcomes

4) Subtract that total from 1

(and #5 – make sure the problem doesn’t involve any unique probability-changing events like “if outcome A doesn’t happen in the first try then the probability increases to X% for the second try” – that kind of language is rare but does complicate things)

Probability factors into many autumn situations, so whether you’re a GMAT student or a baseball fan, if you know at least this one probability concept your autumn should be a lot less stressful!

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: 3 Essential Test Day Strategies

GMAT Tip of the Week

The GMAT is an intimidating test. Here are 3 strategies to help you succeed on test day:

1) Check your work and be thorough.

Because of the Item Response Theory powered adaptive scoring engine, the GMAT comes with a substantial “penalty” for missing questions below your ability level. As the test attempts to home in on your ability level, it knows that approximately 20% of the time when you completely guess on problems that are beyond your ability, you’ll guess correctly. So the system is designed to protect against “false positives.” So even if you don’t get that hard problem right “accidentally,” but rather by investing extra time at the expense of other problems, the algorithm will continue to hit you with hard enough problems to undo the benefit of your getting that one outlier problem right. The same isn’t as true for “false negatives’ – problems below your ability level that you get wrong. There, that’s all on you – and getting easy problems wrong hurts you more than getting hard problems right helps you. So while your energy and attention may well naturally go toward the problems you find the most challenging, you simply cannot afford more than 1-2 silly mistakes on test day. Those wrong answers give the computer substantial data that your ability is lower than you’d like it to be, and the system responds by showing you even easier questions to determine just “how low can you go?”.

So make sure that if you’re on the verge of getting a problem right, you leave no doubt. Whatever silly mistakes you’re susceptible to – solving for the wrong variable, answering in the wrong units, miscalculating certain cells on the multiplication table – take the extra 10 seconds to double check and solidify your work. Yes that may mean that you have less time available for other questions, but the biggest score-killer out there is the “leaky floor” via which you’re in such a hurry to save time for hard questions that you make mistakes on easier ones. If you know that you should get a problem right, you have to make sure that you do.

2) Know when to give up and guess.

By the same token, you can’t get stubborn on hard questions. Everyone misses problems on the GMAT – the adaptive algorithm ensures it, by continuing to throw you challenging problems to test the upper limit of your ability. If you’re doing the little things right – double checking your work, being patient to avoid careless errors – you’ll see hard problems throughout the test. And no one hard problem will determine your score – the test expects that you’ll miss several, and you know that you’ll guess correctly on at least a few, so you can’t afford to spend 3-4 minutes on a question particularly if you’re not likely to get it right anyway. Often you have to lose the individual battle to make sure that you win the war – if your conscience starts to tell you “you’re spending a lot of time on this problem” and you can’t see a direct path to the correct answer at that point, it’s wise to give up and strategically guess so that you save the time to work on problems that you can or should get right later.

3) Have a pacing plan – and make sure it comes with a Plan B.

One of the easiest ways – and a surprisingly common way – to waste time on the GMAT is to try to calculate your pace-per-question as you’re going through the test. Which is crazy if you think about it – if you’re that worried about how long you’re taking, why would you spend *extra* time doing additional math problems that don’t count? So have a pacing plan well before you enter the test center. For most, it will look similar to:

Quant Section
After question 10 you should have approximately 53 minutes left
After question 20, approximately 33 minutes left
After question 30, approximately 13 minutes left

Verbal Section
After question 10, approximately 56 minutes left
After question 20, approximately 37 minutes left
After question 30, approximately 18 minutes left

If you find that you have less than that amount left at any point, it’s certainly not time to panic, but it is time to start thinking of how you’ll earn that time back. And by a fair margin the better way to do it is NOT to start rushing (which leaves you vulnerable to silly mistakes on several problems) but rather to give yourself one “free pass” over that next set of 10 problems. There, if you see a problem that after 15-20 seconds just doesn’t look like it’s one you’d likely get right, then guess. That saves you the time and means that you’ll probably (but not definitely) get that problem wrong, but it also allows you to continue to be thorough on future problems and avoid those score-killing “leaky floor” mistakes.

Students often get in a hurry when they start to feel the pressure of the ticking clock, and that pressure and haste leads to multiple mistakes. If you strategically make one big mistake instead of several small ones, you’ll maximize the likelihood that that big mistake doesn’t matter (it’s on a crazy hard problem) because you’ve done the little things well enough to have earned monster problems that are assessing your ceiling.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: 4 Questions You Must Ask Everytime You Miss A Practice Problem

GMAT Tip of the Week“I have not failed. I’ve just found 10,000 ways that won’t work.” -Thomas Edison, speaking about mistakes.

If you study for the GMAT for any appreciable amount of time (and you should) you’ll make mistakes. And that’s a good thing. People love to track their study progress with all kinds of metrics: percent correct, time per question, hours spent, problems completed – but in the end the only numbers that matter are the numbers on your official score report. So whether you were 10 for 10 on your homework or 0 for 20, whether you took less than 2 minutes per problem or spent almost an hour trying to figure it out, the key “metric” to your study sessions should be “what did I learn from this?”. And you can learn a lot from the mistakes you made, whether they’re silly (“I forgot to convert hours to minutes”) or confusing (“why does it matter that health care quality improved in the last three decades?”). You just need to know which questions to ask about the questions you missed. And there are four questions you should ask yourself any time you miss a problem:

1) Why was the right answer right?

This one comes pretty naturally to people – there was a right answer, you didn’t see it, and you want to know how to see it in the future. But don’t just take the back-of-the-book’s word for it – ask yourself in your own words and logic why that answer was right. One of the most common study mistakes people make is that they accept the written solution as “THE” way to solve the problem, but don’t internalize how they’d do it themselves or how they’d apply that particular problem’s steps (first you factor the common term, then you combine like terms within parentheses…) to a bigger strategy (“When I see exponents with addition and subtraction, I usually have to factor so that I can apply the exponent rules that require multiplication.”)

So instead of just reading the steps that the book or forum post took to get that problem right, ask yourself strategically how you’d get a similar problem like that right in the future.

2) Why was my answer wrong?

This is where you can really start to learn from your mistakes – what did you do/see/think that led you into a wrong answer. Did you make a careless math error? Did you eliminate the right answer too quickly because it didn’t seem “perfect”? Did your answer look great in terms of subject-verb agreement but actually contain a tense error you weren’t aware of? Was it “probably true” but not “definitely true”? With a standardized, multiple choice test, most wrong answers are created carefully to elicit common mistakes, so you should see your wrong answers as a blueprint for the types of mistakes you may well make in the future. Where did you go wrong?

3) Why was my wrong answer tempting?

This is first question that not nearly enough students ask themselves. The GMAT is a master of misdirection, of methods to get you focusing on the wrong thing or feeling uncomfortable with the right answer or falling in love with the wrong one. Your answers to this question might include:

-Answer choice B just seemed so obvious that I didn’t really do the math – I dove straight for the bait.

-I solved for x but the question wanted y, and I was so happy to be done “doing math” that I stopped too early.

-Answer choice D was just like I’d write that sentence and the others didn’t feel right, so I totally missed the pronoun error in D.

-I didn’t consider negative numbers so I thought this was sufficient.

-I know in my heart that B is true, but there wasn’t enough evidence in the answer choice to support it…they baited me into picking something that was close but just not there.

4) Why didn’t I like the right answer?

This is another huge question that not enough people ask (or that they don’t ask frequently enough). For the previous question, the GMAT is “selling the wrong answer” and usually that’s paired with this one – “hiding the right answer” by making it look irrelevant or awkward. Your answers might include:

-Statement 2 didn’t really seem relevant at all so I didn’t spend any time considering how I might use it…but I guess if the units have to be positive integers I could have just used trial and error.

-I hated the sentence structure of answer choice A so much that I immediately eliminated it and never even considered the verb tenses.

-The first few words of this CR answer choice seemed way out of scope, so I eliminated without reading the whole thing.

-It seemed almost like a double-negative so I never really understood the answer choice.

And here’s the really big takeaway – people often get so caught up in learning rules, facts, formulas, etc. that they don’t realize that they have to learn “the test” and “themselves”. The mistakes you make in practice are perfect opportunities to see what kinds of mistakes you’ll make on the test. Sometimes it’s because you just didn’t know the rule or couldn’t finish the math, but often it’s because the test used your tendencies – assumptions, hasty mistakes, etc. – against you. Ask yourself all four of these questions – and especially #s 3 and 4, which people rarely do – and you’ll be a much more well-rounded test-taker when test day comes and mistakes actually do count against you.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Come On,Commas! 3 Reasons You Should Look Forward To Commas On Sentence Correction

GMAT Tip of the WeekAdmit it – perhaps your favorite thing about the social media revolution is that you’re (or is it “your”?) almost done having to think about punctuation ever again. Hashtags don’t allow for punctuation, and with only 140 characters to express your point of view or challenge three friends to dump water on their heads, who can afford to waste a character on a comma or semicolon?

But regardless of how you feel about punctuation in your own writing, you should look forward to seeing a certain type of punctuation on GMAT Sentence Correction questions. Why?

Commas are clues.

While you’re doing Sentence Correction problems, commas can alert you to three very important Decision Points or strategic uses:

1) Commas help you identify Modifier errors.

Consider this sentence, which comes straight from the Official Guide for GMAT Review:

Architects and stonemasons, huge palace and temple clusters were built by the Maya without the benefit of the wheel or animal transport.

That comma should jump off the screen at you – when a comma appears in the first 10 words of a sentence and is underlined or touches the underlined portion, there’s an incredibly high likelihood that you’re dealing with a Modifier error in at least a couple answer choices. Even more so, if the comma is at the beginning or end of the underline, that probability creeps up to almost 100% – most modifiers are set off by commas, and the most hard-and-fast rules for modifiers apply toward the beginnings of sentences (participial and appositive modifiers get to take some liberties toward the ends of sentences), so in a case like this you should be salivating when you see that comma after the third word and touching the underline. Since “Architects and stonemasons” is a modifier here, it has to logically be able to describe the next noun, and here it cannot (palaces and temple clusters can never be architects), so you have not only eliminated A but also identified the “game” in the sentence – now you have to go find a proper modifier or continue to eliminate flawed ones.

2) Commas signal nonessential modifiers, helping you lighten your load.

What if the sentence above were changed to:

Architects and stonemasons, the most respected of early Mayan craftsmen, were built without the benefit of the wheel or animal transport.

That comma in the same place still alerts you to a modifier, but in this case “the most respected of early Mayan craftsmen” can logically modify “Architects and stonemasons.” So you can’t eliminate this sentence. But since you have identified a *valid* modifier, you have another tool at your disposal – you can ignore it! We call this the “Use It or Lose It” modifier strategy. When you see a modifier, if you don’t “Use It” to eliminate the answer choice (because the modifier is flawed) then “Lose It” – that modifier just adds extra description that isn’t totally necessary to the meaning of the sentence, so you can stop reading at the first comma and start reading again at the second, making the sentence:

Architects and stonemasons were built without the benefit…

And there you should see the mistake – logically that doesn’t work, since architects aren’t “built.” The modifier in this iteration of the sentence is there to distract you from the subject of the sentence, but by identifying commas that set apart a valid modifier, you can lift out that part of the sentence and more quickly cut to the chase.

3) Commas signify lists (which in turn need to be parallel).

Consider another sentence from the GMAT Prep Question Pack:

Displays of the aurora borealis, or “northern lights,” can heat the atmosphere over the arctic enough to affect the trajectories of ballistic missiles, induce electric currents that can cause blackouts in some areas and corrosion in north-south pipelines.

In this sentence, look at that underlined comma next to “induce.” “Induce” is a verb and is not used here as a description, so that comma-verb combination should jump out at you as a clue. This may well be setting up a list of verbs that all stem from one subject or action, like “the race requires competitors to swim in frigid waters, bike across rugged terrain, and run along challenging trails” in which the list of verbs “swim, bike, and run” all must be parallel.

Here, notice that the verb prior to “induce” is “to affect” – this should show you that the displays of the northern lights heats the atmosphere enough to do at least two things:

*affect (the trajectories)
*induce (electric currents)
*and…anything else?

That comma before “induce” should have you on a hunt for that third item in the list, preceded by the word “and” – if you can’t find it, the sentence is wrong. You can’t say “Tonight I plan to exercise, eat dinner.” It has to be “…exercise, eat dinner, and (third verb)” or “…exercise and eat dinner.” So when you see that comma before the verb, you should check to see if you’re dealing with a list, and then make sure that the list is complete (with a connector like “and” or “or” before the last item) and parallel.

Commas may be going the way of bookstores and newspapers, a bit outdated for the social media generation, but at least on GMAT Sentence Correction they’re still important. So in your question for a GMAT score that’s well above “comma” it will pay to look for the comma.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: The 2 Most Important Lessons You Will Learn from Mrs. Doubtfire

GMAT Tip of the WeekFor those considering higher education this week, Robin Williams’ memory looms large. The lessons he taught in Dead Poets’ Society and Good Will Hunting have made their way around the internet more quickly and in more contexts than even Williams’ genie character from Aladdin could throw out references.

But for GMAT test-takers, perhaps the greatest lessons a Robin Williams character can teach come from Mrs. Doubtfire.

 

Mrs. Doubtfire Lesson One: Look at Verbs! 

Why was Mrs. Doubtfire even called Mrs. Doubtfire? Fans of the movie will remember – when Williams’ character was on the phone applying to be the nanny for his children, he needed a fake name and looked at the newspaper on the table. The San Francisco Chronicle headline that caught his eye: Police Doubt Fire Was Accidental.

And your favorite movie from your childhood could have been called “Mrs. Firewas” or “Mrs. Accidental” or even “Mrs. Crumrise” (trivia question: what was the name of the author of that article?). But Robin Williams – once an English teacher at a New England prep school, then a professor at MIT – knew what GMAT test-takers need to know on Sentence Correction:

Look for the verb.

He looked for the verb – “doubt” – and hence movie history was made. Mrs. Doubtfire became an instant classic, and if you’d like to meteorically rise to prominence at elite New England schools like so many Williams characters, you, too, should learn to look for the verb. Why? Because verbs come with two extremely common and extremely actionable GMAT decision points: verb tense and subject-verb agreement. You can become an expert on those two items much more easily than you can become an expert on other, more nuanced facets of grammar, so look for the verb first. For example:

So devastating the fire, so specific its victim, that police doubt the fire was accidental.

(A) So devastating the fire, so specific its victim, that police doubt the fire was accidental.

(B) The fire was so devastating and had such a specific victim that police doubts the fire was accidental.

(C) So devastating was the fire and its specific victim that police doubted it is accidental.

(D) So devastating the fire, so specific its victim, that police had doubted it accidentally.

(E) The fire was so devastating, its victim so specific, that police doubts it was accidental.

If you read this sentence from left to right, you may well dislike the initial wording (So X, So Y, that…) and try to fix that. But you’re likely not an expert on “unique grammatical structures” – the structure in the original sentence is, indeed, valid (called anaphora). But you don’t need to know that, either – if you look to the verbs (doubt/doubts/doubted and was/is) toward the right hand side of each answer choices, you’ll notice that B and E screw up the subject-verb agreement and C and D botch the tense/timeline. The verb decisions are much easier to make than the structure decision, and if you use the verbs properly the only structure left is A. So learn from Mrs. Doubtfire – look for the verb!

Mrs. Doubtfire Lesson Two: GMAT Questions Often Dress In Drag (or at least in disguise).

Just as Robin Williams donned a mask, wig, and dress in order to appear more kind, friendly, and nurturing, so many GMAT questions are designed to look calming and “easy” when in fact they’re quite difficult. So while your instinct when you see an “easy” problem may well be to rush through it and create some doubt about how you’re performing on the computer-adaptive test, make sure you keep Mrs. Doubtfire in the back of your mind – the question that seems like Mary Poppins might actually be a little darker and scarier (like Williams’ character in One Hour Photo). Paraphrasing Williams’ Good Will Hunting co-star Matt Damon in his Rounders role “if you can’t spot the sucker in the first short while, you probably are the sucker.” Meaning that easy questions – those you might see as absolutely no problem and be able to answer in 30 seconds or so – may deserve a second look. Behind that comforting exterior might well be a trickier question (or your ex-husband who hates Pierce Brosnan).

Consider as an example:

Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate?

(A) 32.5%
(B) 34%
(C) 35%
(D) 36%
(E) 37.5%

If your mind immediately thought “the average of 30% and 40% is 35% – C!” you’re not alone…but you may be falling for the old Mrs. Doubtfire routine, mistaking a more-difficult question for one that’s sweet, nurturing, and easy. Because Mork & Mindy don’t earn the same amount, their average must be weighted, meaning that the correct answer is A (since Mindy’s income carries 3/4 of the weight, the weighted average will be 3/4 of the way toward her income). And the lesson – when a GMAT question seems a bit too easy, don’t merely assume that it’s easy and that you’re doing poorly. Think about Mrs. Doubtfire playing soccer in the park and Aerosmith singing “Dude Looks Like Lady” (or “Hard Looks Like It’s Easy”…same rhythm) and see if you’re falling for a hard problem disguised as an easy one.

Robin Williams will be remembered for the many ways he inspired us and the many lessons he taught us. While, sadly, you won’t be able to have a conversation with him on a park bench in Boston Common, remembering his Mrs. Doubtfire character on the GMAT will help you on your quest to find similarly-inspiring professors of your own.

Thank you, O’ Captain.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: 5 Words to Recognize Before You Start a Sentence Correction Problem

GMAT Tip of the WeekAfter you read this post about what to look for before you begin reading a Sentence Correction problem, you’ll be an SC expert since this strategy will tell you when to shift your focus from whatever it’s on to timeline and tense. Ready to get started?

So much of Sentence Correction mastery comes not from “learning more things” but from “recognizing when you can use the things you do well.” And one of the major themes you do know how to do well is recognize the timeline of events when you need to choose between different verb tenses. But, like many GMAT test takers, you’ve probably experience some trouble with two major Sentence Correction themes:

-How do you know that it’s a verb tense problem? (really, how do you know what type of problem it is)
-How do you choose a correct verb tense once you’ve identified that?

The answer very frequently lies outside the underlined portion and answer choices, and your clues can often be found in these words:

Since

Example: Since 1992, when Ross Perot ran for election as a third-party presidential candidate, …
“Since” indicates that something started in the past and has continued into the present, so you’ll want a corresponding verb tense like “has been”.

When

Example: The Republican stronghold on the White House lasted until 1992, when Bill Clinton…
“When” often indicates a turning point or beginning/ending event, helping you organize the timeline of events.

Before

Example: Before Australia become known as Australia, it had been known as the antipodes…
“Before” is a major indicator of timeline, letting you know that an event came prior to another. “Before” is often instrumental when you need to know whether the past-perfect tense (“had visited”) is in play (which is allowable when one event happened before another past-tense event).

After

Example: Human beings couldn’t have existed until well after dinosaurs, whose lifestyles would have drastically altered the current ecology of the planet, became extinct.
“After” is similar to “before” in its ability to help you quickly determine the order of events.

From

Example: Schembechler’s tenure lasted from 1969, when the fresh-faced young coach arrived to little fanfare, to 1989, when his retirement shocked many in the community.
“From” indicates a timespan, and one which typically has an endpoint that would call for past tense. “From” is your signal to look for the beginning and end of a time period to determine when/if it started and when/if it has yet ended.

BONUS: Dates
Dates, like 1985 and 1492, are easy to spot on the GMAT – words almost always contain a combination of TALL and short letters, but dates are always numbers in sequence. When you see that a Sentence Correction problem includes a date – particularly a 4-digit year – there’s a high likelihood that verb tense will come into play. So start thinking about what that date signifies (the beginning? the end?) and how that would affect the verb tense.

Overall, these words (and dates) can provide you with a massive clue as to how to read the sentence. When you see that timeline is likely in play, you’re not reading the sentence just hoping to find an error, you’re actively in “attack mode” looking for verb tenses and events and making sure that they’re consistent with the time markers elsewhere in the sentence. The more proactive you can be as you read these sentences, the better, so train your mind to look for words that signal timeline and you’ll have much of your job in mind before you begin the sentence so that there will be plenty to celebrate after you finish the test.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Instagram Your Way To Sentence Correction Success

GMAT Tip of the WeekAs our attention spans get shorter, the GMAT’s verbal section gets harder. Admit it – at some point in the verbal section of your latest practice test, and maybe earlier in that section than you’d like to admit, you just got bored, or at least lost in all the reading.

Open to a random page (let’s pick 691) in the verbal section of the Official Guide for GMAT Review’s new 2015 edition and you’ll find that you have to read about:

-The illustrator Beatrix Potter
-Marconi’s invention of the radio
-Proton-induced X-ray emission
-The cost to run nuclear power plants

And while you may even find 1-2 of these topics interesting, at a certain point they distract your mind from its ultimate job – get these Sentence Correction questions right! How can you overcome these way-longer-than-140-characters sentences in today’s Twitter age? Think about Instagram and take a 3-5 second “snapshot” of each problem before you actually read it.

What does a snapshot entail? It’s different from normal “reading” in that you’re not starting from left to right, top to bottom; in fact, there’s no one starting point overall. It’s looking at a problem in its entirety and getting a sense for “what’s up” before you actually do begin reading. You’re looking for clues:

  • Obvious differences between answer choices (“Decision Points”)
  • The presence of different pronouns in the answer choices (if 2 say “its” and 3 say “they”, you’re working with a pronoun error somewhere and you should immediately be looking for singularity/plurality in the referent)
  • The presence of different verbs in the answer choices (“was” vs. “were” means you’re looking for singular/plural as you read; “was” vs. “is” vs. “has been” means you’re looking for a timeline)
  • Comparison language (more, less, better, etc.) in the answer choices or the original sentence (which tells you that you’re looking for a parallel comparison)
  • The beginning of a “must-be parallel” construction (“both” or “either” or “not only” – in these cases, you know that you’re dealing with parallelism)
  • Easy indicators of a modifier as part of the underline in the original sentence (if a comma touches the underline in the first 10 words, or the sentence starts with “Unlike,” you’re almost always dealing with a modifier decision)

While this isn’t a completely comprehensive list, it should serve the purpose of getting you to think this way:

Within the first 3-5 seconds you look at a Sentence Correction problem, take a quick mental snapshot of the whole sentence and see if you can figure out what you’re looking for when you do dig in to read. On most problems, there’s a clue (or more than one) from a first glance, meaning that you don’t have to read the entire original sentence from scratch – you get to go in looking for something specific (what’s the timeline? what’s the subject and is it singular or plural? what two items are being compared?). And when you do that, you’re much less likely to get lost in the sentence or have to reread just to figure out what’s going on. You’re using the first few seconds to draw your eye to what is most likely important so that when you do read you’re in “attack mode” looking for something specific.

Consider this example, which appears courtesy the GMATPrep Question Pack:

Unlike many other countries, Thailand’s commercial crafts are influenced both by ancient beliefs and tradition and have remained relatively unchanged over the years.

(A) many other countries, Thailand’s commercial crafts are influenced both by
(B) many other countries, commercial crafts in Thailand have as an influenced both by
(C) the commercial crafts of many other countries, in Thailand they are influenced both by
(D) the commercial crafts of many other countries, those of Thailand are influenced by both
(E) in many other countries, Thailand’s commercial crafts have as an influence both

What does your initial snapshot show you? You should quickly notice a couple things:

1) The first word “Unlike” almost always signifies a modifier decision, and the comma after “countries” is another huge modifier clue (it’s a comma after the 4th word and it’s underlined). You should immediately be thinking “Modifier”

2) Even if you didn’t notice that, look at the differences between the first few words in each answer choice: “many other countries” vs. “the commercial crafts of many other countries” – that, again, should scream “modifier” (or “comparison”), as the change in “noun” vs. “something that belongs to a noun” tends to make you pick which one one those you need.

3) Or if you look down the right hand side, you’ll see that parallelism marker “both” and differences between answer choices “both by” and “by both” – that’s another huge indicator of what you may need to read for.

So before you know that this problem is about commercial crafts, Thailand, and influences, your initial snapshot should have you thinking “What subject works best with this modifier ‘Unlike’?” and “where should ‘by’ go?”. And now you’re in attack mode – the comparison/modifier is about boats/crafts in different countries, not the countries themselves, so you need the construction in C and D. And the non-underlined portion doesn’t have a “by” next to “tradition” so “both by ancient beliefs and (you need “by” here) tradition” isn’t parallel. So the answer has to be D, and if you took a mental snapshot your work was already cut out for you well before you started reading.

So steal a page from Instagram – take a quick snapshot of each Sentence Correction question before you start reading, and train yourself to recognize common clues in those snapshots so that you’re always reading with a purpose. Sentence Correction problems can go up to 56 words, but if you use your snapshot to read strategically you’ll usually find that well fewer than 140 characters really matter.

Take a Sentence Correction snapshot on test day, and your next big decision will be what filter to use when posting a snapshot of your 700+ score report.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: 5 Questions To Ask When Preparing For Your GMAT Retake

GMAT Tip of the WeekIf you’re taking the GMAT with the intent of applying to a top-tier business school, there’s a relatively fair chance that you’ll end up having/wanting to retake the GMAT. Which may sound horrible, but it’s true – in fact, several top schools note that their average students take the test more than twice, so if you see a frustrating score pop up during your first, second, or even third attempt don’t let yourself get too down. Rest assured that:

-Schools only care about your highest score

-A frustrating GMAT performance can be a fantastic teaching tool to help you maximize the score on your applications

They key to bouncing back from a poor performance is to analyze it soon after you took the exam, and to do so in a way that helps you address all the items that contributed to a rough outing. To do that, you should ask yourself these five questions within a few days of having taken the test:

1) Did you have any pacing issues?

And to follow up more closely: Did you have to rush/guess/not-finish? Did you end with more time left than you thought you would? In either case, you didn’t pace yourself optimally, and you can learn from that. If you felt rushed the entire time, ask yourself why – did you spend far too much time on any one question? Were you just sluggish from the beginning and can’t account for the time? Did you make mistakes and have to go back to restart problems? Whatever the reason for a pacing problem, you now know what you need to address. If you need to get quicker, try timing yourself on practice sets to both get used to working more quickly and learn which mistakes you make when you’re rushing, so that you can avoid them. If you wasted too much time on just a couple questions, note their setup/content (involved-diagram geometry? long-winded word problem? multiple roots that you just couldn’t eliminate?) so that you can try to get more familiar with the content in practice, and so that, failing that, you can know when you may just need to guess on test day. Or if you had too much time at the end, you now know that too – which types of problems would you get right if you only had 15-20 extra seconds to slow down or check your work? Now you have that time to spare.

2) Did any question or two get you down, waste your time, shake your confidence?

Many who experience a frustrating test can just about pinpoint “It all seemed like it was going well, but then I saw ______________ and it all went downhill from there.” If you have a similar experience, you can learn from that – why did that problem get you down? How can you identify a “time-suck” problem and know when to guess and live to fight another day? If your confidence was shaken, why? Knowing the types of problems that you need to face a little more confidently or time-effectively – or just guess since no one ANSWER will ruin your day but one QUESTION can certainly do so if you let it – can help you avoid that pitfall on your next attempt.

3) Did you see anything that you felt unprepared for? Any question types or content areas that you saw way too much of (and that you were kind of hoping you wouldn’t see much of)?

Many students go into the GMAT feeling prepared, but then see questions that seem like they’re completely out of nowhere. Why is this so frequent? Because often they’re studying from a limited pool of questions (maybe those in the Official Guide for GMAT Review) and after seeing the same questions a few times each they’ve mastered the *study* questions but not necessarily the thought processes required for new questions. Or perhaps they’ve focused on certain content areas and forgot/avoided others, or studied content in a way disproportionate to what the GMAT actually tests (this happens frequently with Sentence Correction – people study tons of idioms, which aren’t often if ever tested, and don’t do nearly enough work on logical meaning). Either way, if you see concepts tested on your official exam and know you weren’t as prepared as you needed to be, now you have a blueprint for what you need to emphasize before you take it again.

4) The night before your test as you struggled to relax and fall asleep, which 2-3 things were on your mind?

Similarly, it’s not uncommon to cut a few corners when studying, doing one more set of number properties problems, for example, when we know we really should be focusing on geometry. That night before the test tends to be quite truthful…what you knew you should have studied but justified to yourself that you’d get to later, or what you could talk yourself into thinking you’d do well but really didn’t understand as well as you should – those things probably came to light as you laid down with your thoughts the night before the test. And now you have a new chance to address those.

5) Given your test day experience, what do you wish you had studied more (or less)? What do you wish you had done differently?

This catchall question should speak for itself – now that you’ve faced the real test under real conditions, you should have a better understanding of what you need to do. Practice tests and study sessions are extremely helpful, but there’s nothing like the experience of knowing that “this time it counts” to really teach you how you’re going to perform under pressure with the full experience. Many examinees fail to live up to their expectations when they’re first in that situation; those who end up at the schools of their dreams, though, learn everything they can from that experience and then add that to their study regimen to make the second (or third) time the charm.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: LeBron James Says Don’t Be Cavalier About Your Initial Data Sufficiency Decision

GMAT Tip of the WeekIt’s all anyone can talk about today – LeBron James has decided to reverse “The Decision” and return home to play for Cleveland. In doing so he forced many people to change their minds.

Let’s take a look at some of those people:

-LeBron himself, who once decided to leave and now comes home as the prodigal son
-Cavaliers owner Dan Gilbert, who once wrote a scathing letter about James the week he left the Cavs for South Beach
-Cavaliers fans, who once burned LeBron’s jersey and rallied against him
-Dwayne Wade, who just last week opted out of a $40 million contract to restructure his deal to create space to attract more players to his and LeBron’s Heat team

-And hopefully you, in the way that you approach Data Sufficiency

What does that mean? Consider this question:

A Miami-based sporting goods store is selling LeBron James #6 jerseys at a deep “everything must go” discount. If each jersey sells for (not one, not two, not three, but…) four dollars, how much revenue did the store earn from the sale of discounted LeBron James jerseys on Friday?

(1) On Friday, the store sells 100 of the white jerseys LeBron wore for home games, and 80 of the black jerseys that LeBron wore for away games.

(2) On Friday, the store sold 50 of the red jerseys that LeBron wore for nationally-televised Sunday games.

After statement 1, you were probably thinking “sufficient” and taking your talents to A or D, right? “Home” and “Away” seem mutually exclusive, so shouldn’t that tell you that there were 180 jerseys sold total at $4/each? If you made The Decision to pick either A or D, you’re not alone…and you have a lot of reason to feel confident. But like LeBron has shown us, it’s never too late to change your mind. Statement 2 supplies information that *should* give you reason to change your mind about statement 1 – there’s a third type of jersey that the store sold, and so statement 1 didn’t tell the complete story. Statement 2 helps to prove that statement 1 actually wasn’t sufficient, allowing you to change your mind and reconsider your answer*.

(*This problem probably doesn’t have a valid solution since there’s no great way to tell mathematically if there might be a 4th type of jersey; this wouldn’t appear as a question on the actual test, but the logic of “statement 2 should prove to you that you didn’t know everything you thought you did on statement 1” is absolutely fair game)

The lesson, really, is this – although “the book” says that you should treat the statements as completely separate, wisdom will show you that often one statement will give you a clue about the other and allow you to change your mind. Typically this happens when:

-One statement is OBVIOUSLY not sufficient

or

-One statement is OBVIOUSLY sufficient

In either of these cases, that obvious piece of information will likely shed some light on what may be important for the other statement. For example:

Is a/b > c?

(1) a > bc

(2) b < 0

Here statement 1 may well look sufficient…but look how obviously unhelpful statement 2 is. Why is it there? To alert you to the fact that b could be negative – in which case you would have to flip the sign when dividing by b in statement 1:

Statement 1 when b is positive: a > bc becomes a/b > c (YES!)

Statement 2 when b is negative: a > bc becomes a/b < c (NO!)

So while you may have quickly made The Decision – in a youthful spirit of hubris – that statement 1 is sufficient, patience and maturity should lead you to reconsider after statement 2 offers useless-by-itself information that can only serve as a clue: maybe you should change your mind!

Such is the game of Data Sufficiency – much like in NBA Free Agency, hasty, youthful decisions can be reversed, and often on challenging questions the correct answer requires you to let “the other statement” convince you that you’ve made a mistake. So learn from LeBron – it’s okay to change your mind; maybe, in fact, that’s The Decision that’s correct.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Woulda, Shoulda, Coulda – How To Analyze Your Practice Test Results

GMAT Tip of the WeekSo you’ve taken a practice test and want to know how to use it to improve. You’re not alone, but actually you’re a step ahead of much of the competition! Read the various GMAT forums and you’ll see a lot of data dumps:

On my most recent CATs I scored 640, 610, 630, 580, and 620. What must I do to score 750+ for H/S/W???? Please Help!

Particularly if you’ve taken reputable tests (we recommend GMATPrep and, naturally, the Next-Generation Veritas Prep exams, both types being scored using Item Response Theory) the scores can be quite helpful in gauging whether you’re near the range you’d like to score in on test day. But think about other scored or timed pursuits: Michael Phelps didn’t become a great swimmer by simply looking at the clock at the end of each race, but rather by analyzing his stroke, his aerodynamics (or I guess hydrodynamics), his conditioning, etc. Similarly, the best use of your practice tests isn’t as a gauge of your score, but rather as evidence of why your score is approximately what it is. To capitalize on that information, it’s important that you analyze your results so that you can prioritize your study. Here’s how:

1) Never take a practice test without analyzing its results.

There’s flawed conventional “wisdom” that simply taking practice tests will improve your score. But real improvement comes between those tests, when you’re reviewing the results and considering what they tell you. Did you miss several questions of the same type? Did you mismanage your pacing? Did you fall into common traps and make silly mistakes? Doing the tests helps – it builds stamina and familiarity with the interface and exposes you to dozens of practice problems under real conditions – but analyzing the tests helps you to learn from your mistakes. Once you’ve seen your mistakes or determined your weaknesses, you can use the next few study sessions to address them – revieiwing skills you missed, drilling problems of those types under timed conditions, creating mental checklists to avoid the same mistakes, etc.

2) Prioritize your study sessions by categorizing mistakes.

This is critical – many people will simply look at their problems and say “I missed X geometry questions, Y sentence corrections, etc.” but remember that not all questions are created equally! Were the questions you missed easy or hard? Did you miss them because of silly mistakes or because you just didn’t know what to do? One way to prioritize your study is to divide your mistakes into categories:

Should Get Right – these are the questions that should hurt the most; you knew what you were doing but made a silly mistake or dove hard for the trap answer or completely blanked on something you’d ordinarily remember. These are your top priorities – don’t write them off as “silly mistakes,” but instead come up with a plan to avoid those mistakes. See if these come up in families (“answered the wrong question” vs. “calculation mistake” vs. “made an assumption” etc.) and if they do make it an even more critical plan to have a reminder on test day to slow down and double check. These problems are probably holding you back the most, since “shoulda” questions are in your CAT scoring wheelhouse and missing them lowers your score significantly.

Could Get Right – these problems aren’t silly mistakes, but you know that the concepts aren’t beyond you. You could invest a little more time in practice to make them strengths, so you should carve out some study time and consult a few study resources (like maybe our YouTube channel) to build those iffy concepts or question types into strengths.

Probably Wouldn’t Get Right Anytime Soon – These are the problems you save for later. Anything that you stare at and say “I don’t even…” – these are probably problems that would waste your study time and your test day time. And that’s okay, at least for now – until you can comfortably get problems around your ability level or a little higher correct, these problems well beyond you won’t impact your score much at all. Think about it – getting a monster question right in a CAT test means you get an even scarier question next, and that one will take even longer. You need to shore up your floor before you shoot for the ceiling. Which isn’t to say you’ll never get these, just that they’re not your top priority right now. Since much GMAT study is incremental – harder probability questions require you to be good with algebra and factors/multiples, for example – while you’re shoring up that floor you’re already building toward these, too.

3) Focus on Why – Not Just What

People love to give themselves surface information (think of those Buzzfeed “Which _________ Are You?” quizzes – they’re almost never all that detailed or thought out, but we can’t help but click on them), so you naturally gravitate to “I missed ____ geometry questions and only _____ algebra questions.” But those are big families of conceptual knowledge, and often the reason you missed a geometry question isn’t “geometry” but rather “I screwed up the algebra” or “I assumed something in a Data Sufficiency construct”. Hold yourself accountable for the “why” you got it wrong so that you can better address your specific needs.

4) Be Practical With Pacing

Look for problems on which you spent way too much time and be honest: were you going to get it right and just ran out of time, or were you spinning your wheels the whole time? Look at problems that you missed in a minute or less: could you have gotten it right with 10 seconds of double-check? It’s easy to see a test and say “if I get pacing under control I won’t make those mistakes” but that “if” is a really big hypothetical. Keep track of the types of problems that take you too long and know that as you get closer to test day you may need to triage them, guessing earlier to save time. And keep track of the types of problems that you miss when you’re rushing; that extra time you save by having a quick “guess” trigger finger may save the day on these. Far too many examinees take “I just ran out of time” lightly and assume that will get better on its own; those who know better know that pacing is almost always a struggle for even the 750+ crowd, and make plans to address pacing, not excuses for why pacing held them back on this particular test.

Remember – taking a practice test is only part of the battle; analyzing it and using it for improvement is the other half and arguably the most important half. When you’re done taking your test you’re not done with it overall – put in some analysis time and watch how it impacts your score on the next one.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: GMAT Scoring Is Like The World Cup

If you’re like…probably most human beings this week, you’re at least aware and likely excited for the 2014 World Cup, which began this week in Brazil. As this article is being written, in fact, the 2010 finalists, Spain and the Netherlands, are doing battle in the event’s third game (congratulations to Brazil and Mexico, winners of the first two). And if you’re streaming this game or others at work or if you’ve taken days off to enjoy, you can learn quite a bit from what’s going on in these early group-stage games – lessons that can help you better understand the GMAT scoring system and better plan your test-day and study strategies.

How? There are two major parallels:

It doesn’t matter how prepared you are for the finals; you have to get there
Take Spain and the Netherlands today – two of the world’s most elite sides. If the game doesn’t end in a draw, one of these sides will have “wasted” an entire match with no points to show for it, meaning that it will face must-win (or at least cannot-lose) situations in its remaining two contests against Australia and Chile. Each team has the potential to advance back to the final, but neither is immune from the “mundane” group stage. A team that loses in today’s game will have its work cut out for it well before the tournament rounds begin…much like you’ll see on the GMAT.

On the GMAT, many would-be-Spains – students shooting for the 700+ stratosphere – have spent months preparing, attacking challenge problem after challenge problem, learning obscure formulas and math shortcuts to help them save time for that monster word problem or geometry exercise. But the GMAT scoring algorithm can be fickle – much like World Cup group play, the “easier” questions may preempt you from ever seeing the bigger “games” that you’ve prepared for. When you miss easier questions, the system has substantial reason to doubt your ability – not just that “you aren’t as smart as we thought you were” but even “and maybe your ability is even lower than this question might have indicated”. So the system shows you a slightly easier question, assessing your “floor” and wasting one valuable question that might otherwise have been an opportunity for you to prove yourself worthy of an even higher challenge. Silly mistakes hurt you twice – they reduce your score in the moment *and* they prompt the system to check your ability on even-easier questions. So your top-end ability might not matter much at all if you don’t “survive pool play” and successfully navigate those problems that may seem beneath you.

So what does that mean? You simply MUST get questions right if you can get them right – you can survive a slip-up or two but if you rush through the “easier” questions and make careless mistakes you run the risk of staying mired in that band of difficulty toward the lower end of your ability range, never earning enough opportunities to really test yourself on those extremely-challenging problems you’ve practiced. So make sure that you don’t leave yourself a leaky floor as you push to raise your ceiling – if you make mistakes in practice, address them; if you make them more than once, make a mental note to double and triple check for them on test day. Don’t let silly mistakes – those careless errors that are so easy to write off as “well that was just dumb…I knew that” – hold you back from your true potential. In other words, make sure that you don’t focus so much on tournament play that you find yourself surprised in group play.

Sometimes a draw – or even a close loss – is a cause for celebration
In World Cup group play, your primary – if not only – goal is to advance to the tournament. Accordingly, going for the win but also exposing yourself to a loss – playing too aggressively on offense that your defense becomes vulnerable – can be wildly problematic. You’ll find some of the most elite teams in the Cup playing very conservative soccer in certain games, playing specifically for the draw and the “guaranteed” points to ensure that they survive the group stage. You’ll also find teams that weren’t predicted to advance becoming thrilled when they draw with a world power like Brazil or Germany, having saved a point when it seemed like none were possible and having slightly-but-significantly outpaced the other two teams in the group. And when there are ties in the standings during group play, the tiebreakers are based on goal differentials, meaning that a 1-nil loss to a world power might be a real triumph if your competitors have lost even worse.

Similarly, on the GMAT you may need to play for the “draw” on extremely challenging questions. When a question could easily cost you 3-4 (or more) minutes en route to a guess or mistake, recognizing that it’s safer to play defense – to guess relatively quickly and save your time for the problems that you could get right – is often a smart move. This saves time to ensure that you get the problems within your wheelhouse right, and although it may not seem satisfying in the moment it helps you to avoid those silly mistakes that often come from poor pacing and a need to rush in the end.

There are plenty of GMAT lessons to be learned from the World Cup – coaches even instruct players to “form triangles” on the field (ensuring that the ballcarrier has two options at all times) much like you should look to form triangles when geometry problems get difficult – so as you watch these upcoming matches pay attention to the strategy. American audiences are often confused by the happiness of opposing fans at a draw and by the international strategies that seem less than aggressive, but the elite soccer community knows that they produce results. The same is true of a slightly conservative strategy on the GMAT.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: 99 Problems But Probability Ain’t One

GMAT Tip of the WeekSome of the GMAT’s hardest Problem Solving problems can be made exponentially easier by keeping a famous Jay-Z lyric in the back of your mind. When you hear the phrase:

If you’re having girl problems, I feel bad for you son?

What immediately springs to mind?

I got 99 problems but a b**** ain’t one.

Now, what’s the GMAT genius in Hova’s lyric? He didn’t tell you what his problems WERE, he just told you what they WEREN’T. Explaining 99 problems would take way more than the two minutes you’d have for a quant problem or the ~3 minutes that Jay wants to spend on a track. And, like Jay-Z, you want to be Mr. One Take on GMAT problems, doing things the efficient way and getting to the answer much more quickly. So heed his advice when you see a problem like:

Solange takes four roundhouse swings at her brother-in-law. If she is just as likely to connect on any one punch as she is to not connect on that punch, what is the probability that she connects on at least one punch?

Now, there are plenty of sequences in which she can connect:

Hit, Miss, Hit, Miss
Miss, Miss, Miss, Hit
Hit, Hit, Hit, Hit (ouch!)
etc.

Trying to list out all the different ways in which she can land a punch is almost as time-consuming as listing all of one’s 99 problems. But think of it this way – which of the sequences available “ain’t one”; which ways does she NOT land a punch. There’s only one:

Miss, Miss, Miss, Miss

And so if we’re calculating the probability among the 16 total sequences (each of two things can happen at each of four points, so the total number of sequences is 2^4 = 16), then if one doesn’t work the other 15 must work. So the probability is 15/16. And the “formula” to use on this essentially derives straight from Jay-Z’s lyrics about what “ain’t one”:

For complementary events (when the probability of A + the probability of B = 100%), the probability of A = (1 – “not A”). And most strategically, this can be used as:

The probability of “At least one” = (1 – probability of “none”)

So if you’re calculating the probability of an outcome that has many different paths, see if it’s a cleaner calculation to determine the number of paths that “ain’t one” of your desired outcomes, and then just subtract those from one.

Note that this ideology doesn’t just extend to probability. In many problems, calculating all the outcomes that “are” desired is a whole lot harder than calculating the outcomes that “ain’t one” of the desired. Consider this problem from this week’s G-MATT Mondays session:

Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?

A) 66

B) 67

C) 68

D) 69

E) 70

Here look at the answer choices – they’re all very, very high numbers for the range (1-70) in question. So if your goal is to try to come up with all the possible coin combinations that work, you’ll be there a while. But what about the combinations that “ain’t one” of the possibilities? Since the maximum is 70, if you find the combinations that don’t work you’re doing this much more efficiently…and the answer choices tell you that at maximum only four won’t work so your job just became a lot easier.

With 2 and 5 cent coins as your options, you can’t get to 1 and you can’t get to 3, so those are two “ain’t one” possibilities. And then “100% minus… comes back into play” – Notice too that 70¢ is the maximum possible sum (that would use all the coins), so 70¢ – 1¢, or 69¢, and 70¢ – 3¢, or 67¢ are impossible too. So the answer is 66, but the takeaway is bigger: when calculating all the possibilities looks to be far too time-consuming, you often have the opportunity to calculate the possibilities that “ain’t one.” You’ve got a lot of problems to tackle on test day; hopefully this strategy allows you to make one question much less of one.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Free Points On Sentence Correction

GMAT Tip of the WeekWhile summer hasn’t officially started with the solstice coming in a few weeks, this post-Memorial-Day short week and a final farewell to winter weather has started the summer season in earnest for most Northern Hemispherians. And thus beginneth the season of sentences like:

It’s not only the heat but also the humidity.

and

Both the heat and the humidity have been awful this summer.

And while you lament the oppressive heat waves with such sentences this summer, you can not only wish you had air conditioning but also prepare for the GMAT. “Not only…but also;” “Both _____ and ______;” “Just as X, so Y;” and other similar phrases should be free points for you on the GMAT if you heed this advice (which is not only valid GMAT advice but also terrific summertime skin care advice):

Cover up.

As an example, consider this partial sentence correction question:

This weekend, Anna will either go surfing at Paradise Cove or sailing at Montego Marina.

(A) go surfing at Paradise Cove or sailing

(B) surf at Paradise Cove or she will sail

(C) go surfing at Paradise Cove or go sailing

The technique? Cover up everything from “either” through “or” (or from “not only” through “but also” or from “both” through “and” when you see those structures) and if the sentence doesn’t still make sense, it’s wrong. Try it:

(A) This weekend, Anna will…sailing at Montego Marina.

(B) This weekend, Anna will…she will sail at Montego Marina

(C) This weekend, Anna will…go sailing at Montego Marina

As you should see, C is the only one that makes sense, so it has to be right. The reason? These “structures that split in two” require parallel construction – if there’s a verb right after “either” there has to be a verb right after “or.” But if the subject comes right after “either,” there has to be a subject (like she) right after “or.” And the byproduct of that is that if that parallel structure is broken, the second half of the sentence won’t make sense – it will either be missing an important word or it will include a redundant word or phrase (like “it will”).

So when you see any of these constructions:

Both X and Y

Either X or Y

Neither X nor Y

Just as X, so Y

Not only X, but also Y

Seize the opportunity and cover up everything between (and including) those structural phrases. If the resulting sentence doesn’t make sense, that answer is wrong. And since people often struggle mightily with parallel structures, the “Cover Up” strategy should give you free points on that question. So while you may not be a fan of either the heat or the humidity this summer, paying attention to parallel structure when you issue those complaints can help you get into both Harvard and into Stanford in the fall.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: The Most Important Word on the GMAT

GMAT Tip of the WeekOver the course of your GMAT exam, you’ll read thousands of words. Each Reading Comp passage, for example, will have ~300 of them; each Sentence Correction prompt will have ~40. And while you won’t spend much time reading the words in the Data Sufficiency answer choices, having long since internalized what each letter means, you’ll spend plenty of time poring over keywords in the question stem. You’ll need to process tons of words as you take the GMAT, but on most questions one word will make all the difference:

The word they didn’t have to say.

Consider this new Data Sufficiency question from the Veritas Prep Question Bank:

What is the value of n?

(1) 36n > n^2 + 324

(2) 325 > n^2 > 323

Many will see statement 1 with its quadratic mixed with inequality and think “well, n could be anything”. But look a little closer – what word (or in this case symbol) did the question not have to use? What rare qualifier is in there?

That’s right – it’s not “greater than,” it’s “greater than OR equal to”. That little underline should stand out to you – almost any time we use an inequality we use > or >.

And here that should be your clue that it’s worth it to do the math. When you’re asked for a specific value and given a one-sided inequality (as opposed to a bracketed inequality like you see in statement 2) that usually isn’t going to help you. But that underline should indicate to you that something’s up…that you need to do some work. And if you do:

36n > n^2 + 324

becomes a quadratic:

0 > n^2 – 36n + 324

which factors:

0 > (n – 18)^2

meaning that:

0 is greater than OR equal to (n – 18)

And here’s where that sixth sense really kicks in…you know something’s up, so you investigate a little further. 0 can’t be greater than a square, as anything squared, no matter how negative, is either 0 or positive. So (n – 18) MUST BE 0, the “or equal to” portion. (and since statement 2 allows for noninteger values of n, too, the answer is A).

And the real lesson? Pay attention to the word (or symbol, or phrase) that the question doesn’t have to say. If there’s a word that seems out of the ordinary, it’s usually there for a reason and that’s your clue as to what will make the question interesting or challenging.

In a Critical Reasoning context this happens frequently, too. Consider:

Raisins are made by drying grapes in the sun. Although some of the sugar in the grapes is caramelized in the process, nothing is added. Moreover, the only thing removed from the grapes is the water that evaporates during the drying, and water contains no calories or nutrients. The fact that raisins contain more iron per food calorie than grapes do is thus puzzling.

Which one of the following, if true, most helps to explain why raisins contain more iron per calorie than do grapes?

(A) Since grapes are bigger than raisins, it takes several bunches of grapes to provide the same amount of iron as a handful of raisins does.
(B) Caramelized sugar cannot be digested, so its calories do not count toward the food calorie content of raisins.
(C) The body can absorb iron and other nutrients more quickly from grapes than from raisins because of the relatively high water content of grapes.
(D) Raisins, but not grapes, are available year-round, so many people get a greater share of their yearly iron intake from raisins than from grapes.
(E) Raisins are often eaten in combination with other iron-containing foods, while grapes are usually eaten by themselves.

Look at that question stem – what doesn’t it have to say? It could say:

Which one of the following, if true, most helps to explain why raisins contain more iron per calorie than do grapes?

And very few would notice or care that “per calorie” is missing. So that phrase “per calorie” becomes supremely important – it’s not about raising having more iron…it’s about a change to the iron-per-calorie ratio. That little phrase that didn’t really need to be said is what makes this question interesting, and what determines the correct answer B (which changes the iron/calorie ratio by reducing the number of calories in that ratio).

So train yourself to look for that word, symbol, or phrase that doesn’t really need to be there but that should now stick out like a sore thumb to you. If a question says that:

x and y are distinct integers —> that word “distinct” doesn’t need to be there, so it’s going to be important that x can’t equal y

Therefore, Company B will need to reduce its shipping costs in order to remain profitable –> that word “shipping” doesn’t need to be there, so it’s going to be important

What is the value of nonnegative integer y? –> “nonnegative” is just so slightly different from “positive” – it’s going to be important that y could also be 0

There are lots of words on the GMAT, but in many questions one word reigns supreme in importance over all the others. Train yourself to notice that word that doesn’t need to be said, and “your GMAT score” will require that extra word in there to read “your high GMAT score.”

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Maximizing Your Efficiency on Min-Max Problems

GMAT Tip of the WeekOn nearly every GMAT, you’ll see at least one of the “Min/Max” variety of word problems, a category that’s difficult for even the brightest quant minds largely for one major reason: these aren’t your typical word problems, and they don’t lend themselves very well to algebra. They tend to be every bit as “situational” as “mathematical” and in fact are labeled “scenario-driven Min/Max problems” in the Veritas Prep Word Problems lesson. Why? Because they’re almost entirely driven by the situation, including:

The figures almost always have to be integers. The problems use situations like “the number of people” or “the number of trees,” a subtle clue that algebra won’t quite work because you’re not using all real numbers, but instead nonnegative integers. But be careful (as you’ll see below).

The questions ask for a very specific value in a very specific way. You’ll often see them ask “did at least three” (3 or more means “yes”) or “was the number sold greater than 50” (50 itself means “no” – to get “yes” it has to be 51 or more, provided you’re dealing with integers).

The rules of the game often dictate whether repeat numbers are allowed. Quite often you’ll find a stipulation that “no two could be the same” (but make sure you see that stipulation before you act on it!).

Some of the information in a Data Sufficiency version of a Min/Max is much more sufficient than it usually appears. This is largely because of the scenario, numbers, and question stem they’ve carefully crafted to sneak sufficiency past you.

Let’s consider an example so that you can see how one of these works:

Five friends recently visited a famous chocolatier, and collectively purchased a total of 16 pounds of fudge. Did any one friend purchase more than 5 pounds of fudge?

(1) No two friends purchased the same amount of fudge.

(2) The minimum increment in which the chocolatier sells fudge is one pound.

Look at the familiar symptoms of a min/max problem:

*The question stem asks a yes/no question about a very specific value (5 pounds)

*Statement 1 provides the caveat “no two can be the same”

*While the problem itself doesn’t dictate “integers” via the scenario – “pounds of fudge” can certainly come in fractions – Statement 2 comes in to limit the values to integers

Now, if you’re looking at the information from the question stem and statement 1, you could try to set up some algebra:

The given information: a + b + c + d + e = 16

Statement 1: a > b > c > d > e

The question, then: Is a > 5?

You should immediately see that this isn’t sufficient; with nonintegers in play, a could be 15.9 and the other four could add up to 0.1 (“yes”) or they could each be right around the average of 3.2, just a hair off to satisfy the inequality (“no”). But you should also see what makes problems like this tricky with algebra – there are a lot of variables and there’s a lot of inequality. Min/Max problems tend to require a lot more trial and error, and live up to their name because the technique that works best on them is to minimize and maximize particular values to figure out the possible range of the value in question. Eschewing algebra, let’s look at statement 2:

Given Information: 16 total pounds were purchased.

Statement 2: The purchases had to be in integer increments.

The question: Was one of those integers 5 or higher?

Here, to find the maximum value you can minimize the other values. What if four friends didn’t buy anything (0, 0, 0, 0) and the fifth bought all 16 pounds? That’s a resounding “yes”. But they could have split things much more easily – you’d do this by maximizing the smallest value(s). 3, 3, 3, 3, 3 would give you 15, allowing that one final pound to go to the highest making the highest value 4. So there’s your “no” and statement 2 is not sufficient.

When you take the statements together, however, you should see what really makes these problems tick. With algebra it’s still awful:

a + b + c + d + e = 16
a > b > c > d > e
a, b, c, d, and e are integers
Is a > 5?

But with an intent to minimize the highest value (by maximizing the others, sucking as much value away as possible) and maximize the highest value (by minimizing the others to drive all value toward the highest), you have a blueprint for trial and error.

Maximize the highest value / Minimize the others. To make sure you can get a “yes”, minimize the smallest values to see how high the highest can go. That means 0, 1, 2, and 3 – a total of 6 pounds leaving 10 for the highest. It’s easy to get a “yes”.

Minimize the highest value / Maximize the others. Since highest = 5 gives you “no”, see if you can then minimize that highest (5) and maximize the others (4, 3, 2, and 1). But notice that that only gives you a total of 15, and you need to account for 16. And here you cannot give that extra pound to any of the lower values without matching a higher one (add it to 1 and you match 2; add it to 2 and you match 3; etc.). So this guarantees that the highest value is 6 or more, and the answer is sufficient, C.

More importantly, look at the technique – many great mathematical minds hate these problems because the “pure math” algebra is so ugly…but the GMAT loves these because they force you to think logically through a few situations. Since so many of these are Yes/No Data Sufficiency problems, keep in mind that your goals are to “prove insufficiency” looking for both a Yes and a No answer, by:

Minimizing the highest value by maximizing the others

Maximizing the highest value by minimizing the others

Minimizing the lowest value by maximizing the others

Maximizing the lowest value by minimizing the others

Essentially to ______ize one value, do the opposite to the others, and doing so will help you test the possible range. As you do so, make sure you consider:

-Can the values be nonintegers, negative numbers, or 0? (often the scenario dictates that the answer to a few of these is “no”)

-Can values repeat?

Min/Max Scenario problems can be a pain, as they maximize the amount of time you have to spend on them while minimizing your score. But if you know the game, you have an advantage – these problems are all about trial-and-error of Min/Max situations and about taking acute inventory of what is allowable for the values you do try. Play the game correctly, and you’ll be set up for maximal success with minimal (comparative) effort.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Mother Knows Best on Sentence Correction

GMAT Tip of the WeekSo it’s Mother’s Day weekend, and all of us should be thanking our moms this weekend. For all kinds of things, of course, but for one that you may not have realized all these years growing up:

Your mom taught you one of the greatest Sentence Correction lessons you’ll ever learn.

How? She told you to clean your room. Now, remember – when your mom told you to clean your room you were rarely doing it with disinfectant or using a deep-cleaner on the carpet. Your job wasn’t so much to deep clean your room chemically, but more to just “declutter” it, putting things away and tidying up for a cleaner, more livable space. She taught you the virtue of “everything in its place and a place for everything,” and in doing so gave you the tools you need to make Sentence Correction significantly easier.

Let’s demonstrate with a problem:

Visitors to the zoo have often looked up in to the leafy aviary and saw macaws resting on the branches, whose tails trail like brightly colored splatters of paint on a green canvas.

(A) saw macaws resting on the branches, whose tails trail
(B) saw macaws resting on the branches, whose tails were trailing
(C) saw macaws resting on the branches, with tails trailing
(D) seen macaws resting on the branches, with tails trailing
(E) seen macaws resting on the branches, whose tails have trailed

Much of this sentence is simply clutter. So many of the phrases add extra description, but are the kinds of things your mother would tell you to put away and “declutter” – namely, the prepositional phrases. So let’s get rid of the clutter with “to the zoo”; “often”; “in to the leafy aviary”; “on the branches”; and “whose tails trail like brightly colored splatters of paint on a green canvas”. On the GMAT, description often serves as clutter, so if you can envision the sentence without the descriptive clutter (similar to how your mom wanted to envision your bedroom), you’d be left with;

Visitors have looked up and saw macaws resting.

Without all of the clutter, your ear should tell you that this is just wrong – the expression should be parallel in timeline: “Visitors have looked up and seen macaws.” And that only leaves D and E.

Now, to make this next decision you’ll need to bring back some of the description, as you can see that the only remaining decision is between “with tails trailing” and “whose tails have trailed”. And here, yet again, is where your mother’s life lessons can help you. What did you often do to make sure your room passed your mom’s test? You took anything that *might* be considered clutter, buried it in a closet or under a bed, and then dug back in to pull out the things that you really wanted. And that’s the case on GMAT Sentence Correction – when you “eliminate” clutter you don’t get rid of it forever, you just ignore it temporarily. Here if you bring back the description in question, you have:

(D) seen macaws resting on the branches, with tails trailing
(E) seen macaws resting on the branches, whose tails have trailed

Here the description/modifiers are important, and astute test-takers should see that branches don’t have tails, but birds do (your mom probably took you to the zoo, too – one more lesson to thank her for). So E cannot be right, and the answer is D.

Most importantly here, remember what your mother taught you – a clean room is a happy room, and a clean, clutter-free sentence makes for much happier and more effective Sentence Correction. This weekend you have millions of reasons to thank your mom, but as you study for the GMAT you know that she’d be thrilled with even 700…

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: The Data Sufficiency Reward System

GMAT Tip of the WeekIf you’ve studied for the GMAT for a while, you likely have a decent understanding of the answer choices:

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
(D) EACH statement ALONE is sufficient to answer the question asked;
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

And you probably have a device to help you both remember these answer choices and use process of elimination. Some like “AD/BCE” (make your decision on statement 1 and cross out one side), others like “1-2-TEN” (1 alone, 2 alone, together, either, neither). But, ultimately, remembering the answer choices (which are always attached to the question on test day anyway) and understanding how to use process of elimination is just the “price of entry” for actually solving these problems correctly. For true Data Sufficiency mastery and a competitive advantage, you should think of the answer choices this way:

___D___
A_____B
___C___
___E___

Why?

As an added bonus it’s helpful for process of elimination (like the other tools) but as a strategic thought process it can be instrumental in using your time wisely and avoiding trap answers. Because what these answers really mean is:

___D___ — Each statement alone is sufficient
A_____B — One statement alone is sufficient; the other is not
___C___ — Both together are sufficient, but neither alone is sufficient
___E___ — The statements are not sufficient, even together

And since most Data Sufficiency questions are created with one of these constructs:

*One answer seems fairly obvious but it’s a trap
*One statement is clearly sufficient; the other is a little tricky
*One statement is clearly insufficient, but gives you a clue as to something you need to consider on the other

The above chart tells you how to better assess the answer given the answer that looks most promising. Consider a question like:

Set J consists of terms {2, 7, 12, 17, a}. Is a > 7?

(1) a is the median of set J
(2) Set J does not have a mode

For most, statement 1 looks very sufficient, as if a is the “middle number” then it would go between 7 and 12 on the list {2, 7, a, 12, 17}. That would mean that on this chart, you’re at A, as statement 2 is pretty worthless on its own:

___D___
A_____B
___C___
___E___

You can very confidently eliminate B and probably E, too, but if you’re sitting on a “probable A,” you’ll want to consider one level above and one level below your answer on the chart. Why? Because if the answer is, indeed, trickier than your first-30-seconds-assessment, the options are that either:

*The statement you thought was sufficient was close, but there’s a little hiccup (you thought A, but it’s C)
*The statement you thought was not sufficient was actually really cleverly sufficient had you just worked a little harder to reveal it (you thought A, but it’s D)

This is what Veritas Prep’s Data Sufficiency book calls “The Reward System” – many questions are created to reward those examinees who dig deeper on an “obvious” answer via critical thinking, and to “punish” those who leap to judgement and fall for the sucker choice. If A is the sucker choice, the answer is almost always D or C, so you know what you have to do…check to make sure that statement 2 is not sufficient, and then check (often using statement 2) to make sure that you haven’t overlooked a unique situation that would show that statement 1 is actually not sufficient. And here, further review shows this:

If a = 7, a is still the median of the set, but 7 is NOT greater than 7, so that answer would be “no” – there’s a way that a is not greater than 7, so we actually need statement 2. If there is no mode, then a can’t be 7 (that would be a duplicate number, making 7 the mode). So the answer is C, and the Reward System thinking can help make sure you streamline your thought process to help you identify that. If you picked A you’re not alone – many do. But if you picked A and then considered the chart:

___D___
A_____B
___C___
___E___

You should have spent that extra 30 seconds making sure that the answer wasn’t C or D, and that may have given you the opportunity to reap the rewards of thinking critically via the Data Sufficiency question structure.

So remember – merely knowing what the answer choices are is an elementary step in Data Sufficiency mastery; learning to use those to your advantage via the Reward System will help you avoid trap answers and stake your place among those being rewarded.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Your 3 Step Pacing Plan

GMAT Tip of the WeekWhat makes the GMAT difficult? For most examinees, the time pressure is arguably the biggest factor; given unlimited time, most 700-level aspirants could get most problems right, but with that clock ticking and time of the essence we’re all vulnerable to silly mistakes, mental blocks, and the need to give up on hard questions.

So how can you overcome the pressures of pacing? Try this three-step method:


1) Take Your Time

This may seem a bit counter-intuitive if you’re pressed for time, but the GMAT scoring algorithm so heavily punishes you for missing “easy” questions that you can’t afford to fall victim to silly or careless mistakes. Most test-takers could finish between 32-34 quant questions and 36-38 verbal questions in the 75 allotted minutes, but it’s that 37 quant / 41 verbal question allocation that forces examinees to budget time. If, for example, on quant you’d be great if you could average 2:20 per question instead of the allotted 2:05, that extra 15 seconds you’d like per question may well be your Achilles’ heel if, in your haste to get down closer to 2 minutes per question, you fall victim to:

-Silly calculation mistakes
-Setting up an equation incorrectly
-Leaving a problem one step short and picking the trap answer
-Answering “the wrong question” (e.g. they asked for y, you solved for x)

These mistakes, as you’ve likely seen in your practice tests and homework sets, are quite common, so make sure that you’re aware of them and know to slow down to avoid them. Double check your work, which can largely go wrong in the first 20-30 seconds of a problem (setting up a problem incorrectly) or the last 20-30 seconds (answering the wrong question, skipping a calculation step because it looks like you’ll get right to one answer choice). Know your common mistakes and spend that extra 10-15 seconds double-checking for them. Too many examinees, knowing that they’d need 10% more time than they have, do a “90% job on 100% of questions” (a lot of wrong answers) instead of a “100% job on 90% of questions” (making sure that when they can get a question right, they do. As we say often on the GMAT, your floor is more important than your ceiling – missing easy questions hurts you much more significantly than correctly answering hard question helps you. So step 1 on pacing – make sure that you take the time you need to successfully finish problems on which you’ve done most of the work right.

2) Plan to Guess

Here’s where you get the time back. If you still know that the above strategy – take the time that you need – will leave you 5-6 minutes short of where you’d need to be to finish the section, then save that time by knowing that up to 3-4 times per section you’ll just guess early on a problem to bank that time for when you really need it. Why does this work? If you’re doing well on a section by successfully answering most of those questions within your ability level, you’re going to see some extremely difficult questions as your “reward” based on the adaptive algorithm. You WILL get questions wrong, and the key is to not invest too much time in questions that you were probably going to get wrong anyway. The problem with guessing is much more psychological than real – when you get stuck on a problem and “have to” guess, you get that panic feeling in your mind and it shakes your confidence for future questions. Plus you’ve probably spent up to your average pace-per-question (if not more) by that point, so you’re doubly worried…time is ticking away *and* you just had to blow a guess.

The remedy? Give yourself up to 4 “free passes,” questions on which you’ll just guess in the first 20-25 seconds if you realize that it’s probably beyond you and/or it will probably sap a lot of time. (For example, plenty of 750+ scorers have admitted that “hard to start” geometry problems fall into this category for them…geometry with detailed figures can be very time-consuming, so if they don’t see the path early on they know to just save that time for something more concrete) By consciously using a “free pass” instead of nervously venturing a guess, you own the guess as a strategy and not a cop-out, and you’ll save that time for when you need it and can best use it for correct answers.

3) Have a Pacing Plan

How do you know when you need to guess? Segment each section into approximate quarters and have benchmarks for where you’ll want to be. Since the clock ticks down from 75 minutes, have those benchmarks in mind the way you’ll see them:

Quant

After 10 questions —- 53 minutes remaining*
After 20 questions —- 33 minutes remaining
After 30 questions —- 14 minutes remaining
(which leaves about 2 minutes per question)

Verbal

After 10 questions —- 55 minutes remaining*
After 20 questions —- 36 minutes remaining
After 30 questions —- 18 minutes remaining
(which leaves about 1:40 per question)

(*You can adjust these benchmarks to your liking; here we’re using a little more time in the initial 10 questions, not because “they’re more important” as the myth goes, but more because you can’t use any additional time at the end of the section, so if you’re going to err on pacing it’s better to get the early questions right and hustle a little later than it is to make silly mistakes early, banking time that won’t help you later.)

Whenever you’re more than a minute or so behind your desired pace, that’s when you’ll want to look at using a “free pass” within the next 4-5 questions to get back on track. By having a plan to check every 10 questions, you’ll avoid that pressure (and wasted time) that comes from calculating your pace-per-question frequently throughout the test (seriously, people do this – they’re so worried about not having enough time that they waste valuable time doing extra, irrelevant math problems!!) and you’ll have a contingency plan in place so that you’re not panicked if you are a little behind. If you’re behind, you have a “free pass” in your back pocket to help get back to where you want to be.

Pacing on the GMAT is tricky for everyone – that’s a major factor of what makes it “the GMAT.” But if you follow this process, you can make the best out of that limited time and maximize your chance of success. Remember, 75 minutes per section is hard for just about everyone, so even if you’re not comfortable with the pacing but you have a better plan for how to use that scarce resource, pacing can be your competitive advantage.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Change the Way You Think About Change-Related Graphics Interpretation

GMAT Tip of the WeekOne of the great benefits of the Veritas Prep Question Bank is that with its 4 million user responses to GMAT practice questions it does an excellent job of highlighting test-taker trends. These statistics can point out trap answers that examinees too readily fall for, conceptual areas that students need to address, and other valuable insights into the way the world takes the GMAT. And this week, one particular trend caught our eye in a major way:

Test-takers struggle mightily with the concept of “Rate of Change” vs. “Actual Number”.

Consider this quick data table, which displays the average monthly temperature in Chicago, Illinois:

Month…….Average High Temperature
February……..34.7
March………46.1
April………58
May………69.9
June………79.2
July………83.5
August……..81.2

Now, from a quick glance you should see that the temperature increases every month from February through July. But there’s another angle to this data, too, and challenging Integrated Reasoning questions can hinge on that exact point. The temperature INCREASES every month, but the GROWTH RATE declines – from February to March the temperature increases by 11.4 degrees, but from June to July it only goes up 4.3 degrees as summer temperatures level off. So while the data table above might clearly demonstrate that the temperature is rising (we promise, Chicago – although we know it hasn’t been too noticeable just yet!), an Integrated Reasoning question might show you this graph:

Based on this graph, most students would incorrectly answer the question: “From March through August, how many months did the average temperature decrease?”, as most would look at the graph and see several months of decline. But the important thing to keep in mind is “WHAT declined?”. And in this case it’s “the growth rate in the temperature” not “the temperature itself”. In this graph, any time the data point is above 0, that means the temperature increased. Only one month (August) was colder than the month prior.

This next graph will plot both “average temperature” and temperature growth” together to highlight this concept.

So what is the lesson? Make sure that you’re aware of the difference between the “actual number” and the “rate of change” and that you look for that concept to be tested on Graphics Interpretation questions. When newscasters say that “Apple’s earnings growth dropped 5% this quarter” that doesn’t necessarily mean that Apple lost money or didn’t improve upon the last quarter; it just means that it grew slower. Think back to physics classes and the difference between acceleration and velocity – “percent change” is the acceleration component, but people often mistake it for the velocity. And based on Question Bank data, every time this concept has been tested more than half of users missed this concept!

So remember – the rate of change can decline while the actual number still increases…just not as quickly. Understanding and recognizing this concept can keep both metrics positive for your Integrated Reasoning score.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: ASAP Test Taking Can Be Rocky (That’s Your Freaking Problem)

As Hip Hop Month draws to a close in the GMAT Tip of the Week space, it’s time to pass the torch to the new school; while Eminem, Tupac, the Wu Tang Clan, and other classic acts have taught you some important lessons about the GMAT, it’s time for the young bucks to impart some wisdom. So today we bring you an important message from A$AP Rocky, Drake, and Kendrick Lamar, who will show you one of the most common (f****g) problems that test-takers encounter while taking the GMAT.

In their incredibly-vulgar but even-catchier track “F*****g Problems,” they refrain “I love bad b******s that’s my f*****g problem; and yeah I like to f***, I’ve got a f*****g problem”. And in doing so, they (we promise) tell the familiar tale of GMAT pacing gone awry:

GMAT test-takers far too often go through easy-to-moderate level problems “A$AP”, which leads to a Rocky performance. Why? Because we love hard problems, that’s our effing problem. We’re in such a hurry to save time for the hardest problems out there that we make silly mistakes on the problems we should get right, then dump far too much time into the problems – those bad b*****s – that we probably wouldn’t have gotten right anyway.

Try this – look at your next practice test and see how you allocated your time. Your quant performance, for example, might look like:

Time taken….Correct/Incorrect
1:47….Correct
1:58….Incorrect
1:22….Incorrect
1:45….Correct
3:05….Incorrect
1:12….Incorrect
1:58….Correct
1:50….Correct
2:58….Correct

Because of the way the GMAT scoring algorithm works, missing “easy” questions – perhaps by going through them ASAP and not spending that extra few seconds double-checking your work – hurts you substantially more than getting really hard questions correct helps you. After all, the system has to assume that it’s possible for you to guess correctly on 20% of the questions way above your head, so it can chalk that up to “probability”, whereas when you miss easy questions that’s just on you. And if you look at this sample section breakdown, that’s likely what the user did – spending 1:22 and 1:12 on “easier” problems (those that came after another incorrect answer) and getting those wrong, while spending ~3 minutes on “harder” questions and not really helping the cause. Even that correct answer at the end came at the expense of some valuable time and may well have been a guess (or could have been guessed correctly, anyway.

The problem that many GMAT students have – and it’s human nature, so you just need to be aware of it – is that they disproportionately spend their time on those “bad b******s” hard problems and go through the easier problems a little too ASAP. In doing so, they often make just enough careless mistakes on the easier questions that their score suffers mightily. So how can you fix that? Let’s borrow a line from A$AP Rocky as he opens the song in question:

“Hold up, b*****s simmer down…”

What he means, obviously, is to spend that extra 5-10 seconds on early problems to “hold up / simmer down” and double-check your work to make sure that you didn’t make a careless mistake or dive right into a trap answer. Those seconds are more valuable to you in rescuing yourself from a silly error than they are in attacking a problem that you probably wouldn’t have gotten right, anyway. ASAP answers can be rocky.

Now, you may be asking “okay, I’ll spend an extra 5 seconds per question double-checking my work, but what if I’m already short on time – where does that time come from?”. And the answer is this – most students struggle to comfortably complete the full section in 75 minutes, but most could complete most of that section – maybe 33-34 quant or 38-39 verbal questions – comfortably in that time. So rather than rush through all 37 / 41 questions ASAP leading to a rocky performance, learn from A$AP’s next lyric:

“Taking hella-long, b***, give it to me now”

Meaning, of course, on problems that would take you a hella-long time to answer, rather than spend 2-4 minutes en route to what might end up being a blind guess, anyway, make your guess now (and make that thing pop like a semi or a nine…). If you know you can’t comfortably answer all the questions in 75 minutes, give yourself 2-3 time-saving “I pass” questions per section, and when you see something that seems labor-intensive and outside your comfort zone, blow in your 20% shot at a guess and bank that 2 minutes to make sure you do your best work on the problems that you should get right. It’s better to do your best work on 34 quant questions and completely blow off 3 than it is to do 90% effective work on all 37, as silly little mistakes on the easier questions will significantly hold back your score. If you can get a question right, get it right.

Naturally, this takes practice to implement, and so it’s important to get a feel for your own pacing (ideally you never need to guess, but realistically most students do at some point). Which is why the Veritas Prep practice tests include pacing statistics per question (your pace vs. the average pace for all users) *and* a feature entitled “The Three Easiest Question You Got Wrong” to help you determine which types of questions require that extra 5-10 seconds to make sure you’re not leaving those easy points on the table. With any pacing or “triage” strategy, you’ll need to practice to see how it works for you, and if ‘finding a test that’s real is your f**** problem, bring your practice to our Item Response Theory tests and maybe we can solve it’.

Most importantly, recognize that one of the biggest f**** problems test takers have on the GMAT is going through problems ASAP and leaving themselves vulnerable to silly mistakes and a rocky performance. Don’t bank the time for those “bad b*****s”, the hardest problems out there; instead, hold up/simmer down, double-check for silly mistakes, and maximize your score. We hope this pep talk turns into a pep rally as you celebrate GMAT success.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Tupac Slow Jams the GMAT

Where the Venn Diagram of “Hip Hop Month in the Veritas Prep GMAT Tip space” and “Guy who Photoshops all the preview images for these posts does so for the last time before leaving for an amazing new opportunity” intersects, you’ll find a lot of Boyz II Men, rap ballads, and other assorted slow jams playing bittersweetly in the background. And as it so happens, arguably the best of those slow jams – Tupac’s “Life Goes On” – is a perfect metaphor for GMAT test-day strategy:

“How many brothers fell victim to the streets, rest in peace young brother there’s a heaven for a G. I’d be a liar if I told you that I’ve never thought of death. My brother, we’re the last ones left.”

While Pac isn’t necessarily talking about the GMAT, he might as well be, as arguably the single most important test-day strategy you need to have in mind is, essentially, Life Goes On. The computer-adaptive algorithm ensures that just about everyone will “lose” questions like Tupac loses homeboys. How many questions will fall victim to the pressures of time and difficulty? More than you’d think. The CAT algorithm is designed to keep testing your upper threshold of ability, so you will miss questions even if – and actually especially if – you’re doing really well. The key is to recognize that life goes on, that struggling through a problem or even guessing on a few problems isn’t a terrible thing. Like Tupac says in the line “my brother, we’re the last ones left” the GMAT is a test of survival and not as much of pure mastery. You need to roll with the punches and keep looking forward.

To better exemplify the Life Goes On approach to test-day strategy, take this lesson from GMAC’s OG, Dr. Rudner. The brain behind the GMAT’s scoring algorithm was once taking the exam (for both “fun” and “quality control”) in pursuit of a perfect 51 on the quant section. At one point he encountered a question that he couldn’t quite solve – even with a PhD in statistics and a day job that *is* the GMAT – but couldn’t let go of, either. As the minutes ticked by and his multiple approaches to the problem continued to fall short, he says he laughed to himself that “I wrote the algorithm – I know this is stupid to waste time on one question when one single question probably won’t affect my score” but still he soldiered on. And when he checked the internal report the next day to see his question-by-question performance and the statistics on that particular item, he had to laugh again – that question was an unscored, experimental item that absolutely did not count toward his score. Life goes on; you’ll fall victim to a few questions now and then, and you have to know that it’s okay to let them go.

So as you take the GMAT, remember:

-You will miss questions and you can miss quite a few questions and still get a great score. Don’t let any one question affect your confidence or your pace.

-You can guess to save time. The 37 questions in 75 minutes quant pace and 41 in 75 verbal pace is aggressive for most students, who would perform significantly better if the section were just 3-4 questions shorter. Don’t rush through and make silly mistakes on several questions because you’re intent on doing your best on absolutely every question; if you need to guess on couple awful-looking questions to bank a few minutes to perform comfortably on the others, that’s not a bad strategy.

-Not all questions will look difficult, and that’s okay too – don’t let the “hard questions mean you’re doing well” logic convince you of the inverse, that an easy question means you’ve blown it. You may see an easy experimental, or you may find that a question looks easy but has a subtle twist that you didn’t see that makes it hard. Don’t try to read into your performance as you go – that mental energy and time are better spent solving the problem you’re on. Easy or hard, life goes on.

On the GMAT, as in life, hardships will hit you but life goes on. You’ll miss questions like we’ll miss Jeremy; in either case, Tupac can slow jam you back to success.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Started From the Bottom, Now We Here

As Hip Hop Month rolls along in the GMAT Tip space, we’ll pass the torch from classic artists to the future, today letting Drake take the mic.

In MBA-speak, Drake is a natural Kellogg candidate, a collaborative type who loves group projects, always appearing on tracks with other artists and bragging not just about his own success, but “now my whole team here.” So in that teamwork spirit, let’s work with Drake to help him solve his most famous math problem with some lyrics of his own:


The problem:
“The square root of 69 is 8 something; I’ve been trying to work it out”

The solution: “Started from the bottom, now we here.”

On the GMAT, a problem that asks you for the square root of a not-that-common square (you have to have the squares memorized up to about 15 and you should know that 25^2 is 625, too) is almost always going to be an exercise in “starting from the bottom,” using the answer choices to help guide your work. The GMAT doesn’t care if you can calculate the square root of 69, but it does care about whether you can leverage assets like answer choices to help you solve the problem. So on a problem like Drake’s, answer choices might look like:

(A) Between 6 and 7
(B) Between 7 and 8
(C) Between 8 and 9
(D) Between 9 and 10
(E) Between 10 and 11

And in that case, starting from the bottom – looking at the answer choices before you begin your work – can tell you two things:

1) You don’t need an exact number; an estimate will suffice.
2) They’re giving you the numbers to use as an estimate; if you start in the middle of the range (using 8 and 9), you can determine whether you need bigger or smaller numbers.

So if you try 8^2 to give yourself a range of numbers, you’ll see that the square root of 69 is going to be bigger than 8, since 8^2 is 64. So then try the next highest integer, 9, and when you see that 9^2 is 81, bigger than 69, you’ve bracketed in the range at between 8 and 9 and you don’t need to do any more work. When math looks like it could be labor-intensive, the answer choices often show you that you don’t have to do it all!

Even if the problem were a bit tougher, and gave exact numbers like:

(D) 8.31
(E) 8.66

You could again lighten the load by picking an easier-to-calculate number in between, like 8.5. That’s not the easiest math in the world, but multiplying by 5s is typically fairly quick and you’d see that the number has to be less than 8.5 (since 8.5-squared is 72.25).

So the lesson is this – on most Problem Solving and Sentence Correction questions, it pays to “start at the bottom” so to speak, at least taking a quick glance at the answer choices to see if anything jumps out to help you guide your work on the problem. For Problem Solving, some of the prime candidates are:

  • If the units digits of the answers are all different, you can shortcut the multiplication
  • If one variable from the problem (say the problem has x, y, and z) is missing in the answers (say they only have x and z), you’ll want to start working to eliminate that missing variable
  • If the answer choices contain telltale signs of a certain shape or relationship (the square root of 3 usually comes from a 30-60-90 or equilateral triangle; pi usually comes from circles), your job is to find and leverage that shape
  • If the answer choices include fractions, you can use the factors in the numerator and denominator to guide your math (for example, if three of the choices have a denominator of 3 and two have a denominator of 6, part of your work will include the question “will the denominator be even?”)

On Sentence Correction, pay attention to the first and last words (or phrases) of the answer choices for obvious differences. You may see:

  • Two use a singular pronoun (its) and three use a plural (their) – this means that as you read the sentence you’re looking to find the noun that the pronoun refers to
  • The answer choices use different tenses of the same verb (are vs. were vs. have been) – this means that your job is to pay attention to the timeline in the sentence to see which verb tenses are consistent with the logical sequence of events
  • Two use “that of (noun)” and three just use the noun – this means that there’s a comparison going on, and you need to determine whether you’re comparing the possessions (the GDP of Canada vs. that of the UK) or the nouns themselves

Naturally, there are many, many more examples of clues that the answer choices can leave for you, so the true lesson is as simple as Drake’s lyrics. On Problem Solving and Sentence Correction problems, start (briefly) from the bottom to see if there’s anything you can glean from a quick peek at the answers that will help you more quickly get “here”, to the right answer.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Learning Math from Mathers

March has traditionally been “Hip Hop Month” in the GMAT Tip of the Week space, so with March only hours away and winter weather gripping the world, let’s round up to springtime and start Hip Hop March a few hours early, this time borrowing a page from USC-Marshall Mathers. There are plenty of GMAT lessons to learn from Eminem. He’s a master, as are the authors of GMAT Critical Reasoning, of “precision in language“. He flips sentence structures around to create more interesting wordplay, a hallmark of Sentence Correction authors. But what can one of the world’s greatest vocal wordsmiths teach you about quant?

On his latest album, Eminem talks about feeling like a “Rap God”. And while that track – 6,077 words in 6 minutes, or about 18 Reading Comprehension passages’ worth of words – is more dense than anything you’ll have to read for the GMAT, it supplies a few nuggets of wisdom that can dramatically increase your score, most notably this lyric in which he mocks other MCs who have accused him of being too mainstream, too pop:

“I don’t know how to make songs like that
I don’t know what words to use”
Let me know when it occurs to you
While I’m ripping any one of these verses that versus you

Now, while Em is mocking other emcees, he could very well be mimicking the way that the GMAT would mock *you* on certain problems. The GMAT is designed in large part to be a “quantitative reasoning” test as opposed to a “math” test, and leads a lot of students to stare at problems nervously saying, essentially, “I don’t know how to solve problems like that; I don’t know what tools to use”. All the while, the 75-minute section clock ticks down and the GMAT sits back, smirking, thinking “let me know when it occurs to you how to solve this problem that versus you”.

In other words, difficult GMAT problems are often difficult because people waste a lot of time sitting scared not knowing how to get started. And in many of those cases, the way to get started is to go much more “mainstream” than you’d think. Consider this example:

With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
-##
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9

Now, many would look at this problem and think “I don’t know how to solve problems like that…”, as it’s not a classic “Algebra” problem, but it’s not a straight-up “Subtraction” problem, either. It uses the common GMAT themes of Abstraction and Reverse-Engineering to test you conceptually to see how you think critically to solve problems. And in true Eminem-mocking form, the key to a complicated-looking problem like this is a lot more mainstream than it is advanced. You have to just get started playing with the numbers, testing possibilities for # and & and seeing what you learn from it.

When GMAT students lament that “I don’t know what tools to use” to start on a tough problem, they’re often missing this piece of GMAT wisdom – *that’s* the point. You’re supposed to look at this with some trial-and-error like you would in a business meeting, throwing some ideas out and eliminating those that definitely won’t work so that you can spend some more time on the ones that have a good chance. In this case, throw out a couple ideas for #. Could # be 5? If it were, then you’d have a number in the 500s and you’d subtract something from it. There’s no way to get to 667 if you start smaller than that and only subtract, so even with pretty limited information you can guarantee that # has to be 6 or bigger.

And by the same logic, try a value like 9 for #. That would give you 900-and-something, and the most that ## could be is 99 (the largest two-digit number), which would mean that your answer would still be greater than 800. You need a number for # that allows you to stay in the 667 range, meaning that # has to be 6 or 7. That means that you’re working with:

6&& – 66 = 667

or

7&& – 77 = 667

And just by playing with numbers, you’ve been able to take a very abstract problem and make it quite a bit more concrete. If you examine the first of those options, keep in mind that the biggest that & can be is 9, and that would leave you with:

699 – 66 = 633, demonstrating that even at the biggest possible value of &, if # = 6 you can’t get a big enough result to equal 667. So, again, by playing with numbers to find minimums and maximums, we’ve proven that the problem has to be:

7&& – 77 = 667, and now you can treat it just like an algebra problem, since the only unknown is now 7&&. Adding 77 to both sides, you get 7&& = 744, so the answer is 4.

More important than this problem, however, is the takeaway – GMAT problems are often designed to look abstract and to test math in a different “order” (here you had two unknowns to “start” the problem and were given the “answer”), and the exam does a masterful job of taking common concepts (this was a subtraction problem) and presenting them to look like something you’ve never seen. The most dangerous mindset you can have on the GMAT quant section is “I don’t know how to solve problems like this” or “I’ve never seen this before”, whereas the successful strategy is to take a look at what you’re given and at least try a few possibilities. With symbol problems (like this), sequence problems, numbers-too-large-to-calculate problems, etc., often the biggest key is to go a lot more mainstream than “advanced math” – try a few small numbers to test the relationship in the problem, and use that to narrow the range of possibilities, find a pattern, or learn a little more about the concept in the problem.

If your standard mindset on abstract-looking problems is “I don’t know how to solve problems like that”, both Em and the G-Em-A-T are right to chide you a bit mockingly, as that’s often the entire point of the problem, to reward those who are willing to try (the entrepreneurial, self-starter types) and “punish” those who won’t think beyond the process they’ve memorized. Even if you don’t become a GMAT God, if you follow some of Eminem’s lessons you can at least find yourself saying “Hi, my name is…” over and over again at b-school orientation.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Synchronizing Twizzles in Critical Reasoning

GMAT Tip of the WeekAs the Sochi Olympics enter their final weekend, we all have our lists of things we’ll miss and not miss from this sixteen-day celebration of snow and ice. We’ll almost all miss the hashtag #sochiproblems, the cutaway shots of a scowling Vladimir Putin, the bro show of American snowboarders and TJ Oshie, and the debate over whether the skating judges conspired to give Russia the team gold and the US the ice dancing gold.

And almost none of us will miss Bob Costas’s pinkeye, aggressive interviews designed to make Bode Miller cry, prime time events that lasted well past bedtime for a school night, and the way that announcers for figure skating so critically point out potential deductions and problems even while these athletes do unconscionably amazing things on thin blades on ice.

But we can learn from those skating announcers. They’re critical because the job demands it, because the untrained eye doesn’t recognize those ever-important subtleties that take otherwise amazing performances and separate the gold from the bronze. Much like a good Critical Reasoning test-taker has to notice those subtle-but-significant flaws that make otherwise-valid arguments fail, skating judges and announcers make their money by noting those tiny flaws. That’s the way the game is played.

So your job on Critical Reasoning questions is essentially to be a figure skating announcer – you need to notice those subtle flaws. In skating, sometimes the twizzles aren’t perfectly synchronized; in Critical Reasoning, too, sometimes the premises and conclusion aren’t perfectly synchronized. As an example, try this problem:

The team of Schleicher and Sun should win the gold medal in ice dancing. After all, they were leading after the short program and they skated the long program with fewer mistakes than any other pair. Therefore, they should end up with the highest overall score.

The argument above relies on which of the following assumptions?

(A) None of the judges will allow bias to affect their scoring decisions.

(B) Schleicher and Sun also skated the short program with fewer mistakes than any other pair.

(C) Schleicher and Sun did not make any noticeable mistakes in either the short or the long program.

(D) Factors other than their number of mistakes do not affect a pair’s overall score.

(E) Schleicher and Sun’s twizzles were perfectly synchronized.

On the surface, the argument above may make a lot of sense. But look at the way that the major premise (“they skated the long program with fewer mistakes”) and the conclusion (“they should end up with the highest overall score”) are not synchronized. “Fewest mistakes” isn’t the same thing as “highest score”. If you’ve been watching the Olympics, you might bring in that knowledge that degree of difficulty plays a factor, as often does the difficulty toward the latter half of the long program. But even if you didn’t have that outside knowledge – which you won’t have on most GMAT CR questions – you should see that the premise and conclusion are not synchronized. They don’t talk about the same thing, even though it’s close. And *that* is the blueprint for most Strengthen/Weaken CR questions – when the premise and conclusion aren’t quite synchronized, when they leave a little room in between them because they’re not talking about the exact same thing, that’s where you know you can be critical. That’s where the deductions lie.

In this question, that leaves D open as a correct answer. Since “Number of mistakes” is part of – but not necessarily all of – the scoring of a pair’s routine, choice D exploits that little lack of synchronization. More important is the lesson – just as the television announcers are quick to point out unsynchronized twizzles, you should train yourself to notice those little lacks of synchronization between premise and conclusion. Often this can happen when:

  • the premise is a subset of the conclusion (like “number of mistakes” and “overall score”, or “arrests” and “crimes committed”)
  • the premise and conclusion are very similar but not quite the same thing (like “revenue” and “profit”)
  • the premise or conclusion adds a limiting word that makes it narrower than the other (for example, if the conclusion is about “manufacturing costs” but the premise is only about “overall cost”)

Remember, the question type “Critical Reasoning” has “critical” right there in the name – like figure skating announcers, then, you need to be critical as the job demands it. So steal a page from their book – if the premise and conclusion aren’t synchronized, you have to acknowledge that flaw.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin