-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*

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*

*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*

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.

*By Brian Galvin*

*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.

*By Brian Galvin*

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.

*By Brian Galvin*

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.”

*By Brian Galvin*

**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.

*By Brian Galvin*

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…

*By Brian Galvin*

(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.

*By Brian Galvin*