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!)

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.


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:



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:


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:


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:


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)


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

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

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 &?


(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


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

GMAT Tip of the Week: What Do the Olympics and Sentence Correction Have in Common?

GMAT TipThe Winter Olympics start tonight in Sochi, and while journalists tweet about the less-than-ideal living conditions in the Russian resort town the athletes themselves have a job to do.  Whether they’re skiing or luging or bobsledding, the vast majority of athletes will share one goal:

Get downhill quickly.

On GMAT Sentence Correction problems, that should be your goal, too.  Olympians will get downhill quickly by focusing all their momentum and vision to the bottom of the mountain, and on Sentence Correction you’ll want to focus most of your attention “downhill” on the answer choices.

What does that mean?

While the “top of the mountain” – the original sentence itself – is certainly important, keeping your eyes downhill toward the answer choices is the best way to notice the decisions that the GMAT is asking you to make.  Paying attention to differences in the answer choices will help you to determine which portions of the prompt are most important.

For example, consider these fragments of answer choices:

(A) …..have been

(B) …..has been

(C) …..had been

(D) …..have been

(E) …..has been

If you’re reading a 40-word sentence, it’s helpful to know beforehand that the two most important things here are:

has been vs. have been – Subject/Verb Agreement.  Make sure you find the subject of the verb!

had been vs. has/have been – Verb Tense / Logical Timeline.  Make sure that you assess the timeline of events with an eye for “is this event still happening” (if so, eliminate “had been”) or “is this event over (if so, the answer is C)

Or consider this example:

(A) which….

(B) and which….

(C) which…..

(D) and which…

(E) which….

Here there’s one primary decision you need to make – is there a previous “which” phrase in the non-underlined portion that you need to link to the answer choice with “and which”, or not?

The answer choices in Sentence Correction problems quite often give away at least one of the primary decisions that you’ll need to make, so if you glance at the answer choices for an obvious decision you can save quite a bit of time and energy by hunting specifically for the word or phrase that controls that decision and not by reading the original sentence hoping to stumble on it.

In short, keep your eyes downhill when attempting Sentence Correction problems, looking at the answer choices for obvious differences like:

  • Verb differences
  • Pronoun differences
  • Singular/plural noun differences
  • The presence vs. absence or difference between connector words (like “and”, “or”, “but”, etc.)
  • Notable differences between the first and last words of each answer choice

When you see obvious differences, go back to the prompt with that decision point in mind.  Looking downhill is the most efficient way to win the race, whether you’re Julia Mancuso in the Olympic downhill or a GMAT student on an SC question.  Go to the answer choices; go for the gold.

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: Peyton Manning & Omaha!

The crisis has largely been averted. As we approach Sunday’s Super Bowl, our collective eyes are no longer intently watching the thermometer in East Rutherford wondering how a polar vortex might affect the most American of all holidays, Super Bowl Sunday. We can now get back to the number we all REALLY care about:


How many times will Peyton Manning yell “Omaha” during the game?

The current estimate from Las Vegas sportsbooks is 27.5.

While we all poke fun at Peyton’s repetitive cadence and while Peyton himself cashes in on endorsement deals from all the biggest firms in Nebraska, let us not forget that there are two major GMAT lessons you can learn from Peyton’s “Omaha” calls at the line:

1) Do the same thing every time.

Peyton Manning says Omaha a lot. He’s incredibly deliberate and repetitive in everything he does. And it’s taken him to the summit of his industry. GMAT test takers would be wise to heed his example – note that Peyton deals with time pressure (the play clock, the 2-minute drill) all the time but his deliberation makes him comfortable. And by doing the same thing over and over again his routine is incredibly effective at getting him through the first few seconds of any important play.

You should do the same. In a word problem, you should always read actively, assign variables, and check for anything unique in the answer choices, all in the first 30 seconds of seeing the problem. In a Critical Reasoning problem, you should read the question stem first, identify your goal, and usually check the conclusion, all within the first 30 seconds. When exponents are present you should look for relationships between the bases (and try to get them all the same) and look for opportunities to factor addition/subtraction into multiplication, all in the first 30 seconds. Good GMAT test-takers are boring – they have a system for each type of problem and their first 30 seconds are typically somewhat scripted. They don’t see “unique snowflakes” in each question, but instead they see standardized components and go to work on them.

Peyton yells “Omaha”, never “Des Moines” or “Topeka”. Learn from the man. Form good habits and stick to them. Be predictable, be boring, be successful.

2) But be flexible.

The reason Peyton yells “Omaha” is to allow for flexible play calls at the line of scrimmage. Reportedly, the Broncos go to the line with two different play calls in mind, and “Omaha” signals that they’re going to the B play. In football, like on the GMAT, you have to be flexible. Sometimes the defense surprises you and you need to go a different direction.

This comes up often on the GMAT – you start to set up the algebra but realize that your second step gets messier than what you started with. You have to call an Omaha and go back to testing answer choices. You identify clearly that statement 1 is sufficient but then statement 2 points out that you haven’t even considered the possibility of a non-integer. You have to call an Omaha and reassess statement 1. You’ve eliminated answers A, B, and C but D and E are awful, too. You need to call an Omaha and reconsider which decision points you’re using to dictate your choices. Maybe that clumsy-looking sentence structure is valid, after all.

You can’t yell out “Omaha” in the test center without repercussions, but you can heed the advice from what “Omaha” stands for. On the GMAT you’ll find that most questions are best answered with a regimented-to-the-point-of-boredom approach, but that sometimes you have to be ready to adapt. Omaha covers all of that. So as you watch the Super Bowl this Sunday, pay attention to Peyton Manning, a master of both rigidity and flexibility. The road to New York City, Palo Alto, and Cambridge goes right through Omaha.

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: Richard Sherman, the Sorry GMAT, and the Result You’re Going To Get

By now you’ve seen the interview heard round the world – Richard Sherman’s immediate post-game interview with Erin Andrews – and all the fallout from it: Twitter hysteria, discussions about what that Twitter hysteria says about culture, little kid parodies, and everything else. And regardless of what you think about Richard Sherman, if you’re reading a blog post about MBA admissions you want to be Richard Sherman:

-Richard Sherman is one of the best in the world at his profession
-Richard Sherman went to Stanford
-Richard Sherman is going to New York to compete at the highest level anyone in his profession can reach

So whatever words you’d use to describe Sherman’s interview – confident, cocky, arrogant, calculated – you’ll want to bring some of that into the GMAT with you, because in the world of the GMAT you’ll face a lot of sorry questions like Crabtree and if you strategically use Sherman’s bravado you know what result you’re going to get (and it’s a good one).

Here’s why – the GMAT is, really, a lot like Michael Crabtree. Crabtree is a very good wide receiver – he’s big, fast, etc. – just like the GMAT is a very difficult test (it’s clever, labor-intensive, etc.). But both Crabtree and the GMAT are predictable, and if you know what they’re going to do you can approach them with the same level of confidence. And like a defensive back can approach Crabtree, there are two ways that you can approach the GMAT and its traps:

1) Woe is me. When you see a Data Sufficiency question like:

The product of consecutive integers a and b is 156. What is the value of b?

(1) b is prime

(2) b > a

You might fall for the trap answer, D. You’ll break down 156 into 13 times 12 (and realize that you can’t break 13 down any further so there’s no other way to recombine the prime factors to find consecutive integers with a prime), and note that b has to be 13 and a has to be 12. So choice A is, indeed, sufficient. And then when you get to statement 2 you’ll think – yeah, freebie. 13 is bigger than 12, so it has to be 13. But wait – why can’t it be -12 while a is -13? You’ve fallen into the trap – you assumed negative! Woe is you…why do you keep falling for these traps?!

2) The GMAT is mediocre. And when you test a great test-taker like me with a mediocre question like that, that’s the result you’re going to get.

If you go Richard Sherman on a question like this, you’re angry at it. They’re not going to beat you with a mediocre and commonplace trap like “bet you forgot it could be negative”. You’re above that…they may beat you with a crazy challenge that’s way over your head, but they’re not going to beat you with a sorry trap like “could be negative” or “doesn’t have to be an integer”. Now, like Richard Sherman you have to prepare – Sherman KNEW that when Crabtree took off for the corner of the end zone it was going to be a corner fade / jump ball, and you should KNOW that when the GMAT includes an inequality in Data Sufficiency there’s a big change that negative/positive comes into play. So you do have to prepare like a champion to be a champion.

But there’s also a huge question of attitude. When the GMAT traps you, don’t get sad, get mad. Take it upon yourself to not let them beat you with a trap they’ve beaten you with before. Some people fall into a trap and get nervous that they’ll fall into it again. The Stanford-bound like Richard Sherman make it a point to never make that same mistake again, and they see that as a fun challenge. “Oh no GMAT – not today…I know your game and you’d better step it up to beat me”

Remember, attitude and confidence count for a lot whether it’s the NFC championship or the GMAT, and how you approach common GMAT traps can have a lot to do with your performance. Don’t fear those mistakes you’ve made a couple times – realize that they’re so commonplace and predictable as to be mediocre.


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: Tonya Harding Teaches Data Sufficiency

Twenty years later, the figure skater you’d never have called “trendy” was trending last night. As ESPN aired its 30 For 30 special on Tonya Harding and Nancy Kerrigan, the biggest pre-OJ story of 1994 became the hottest topic of early 2014. Heading into the 1994 Olympics, both Nancy and Tonya were Olympic veterans, having placed 3rd and 4th, respectively, at the 1992 Games. With 1992 gold medalist Kristi Yamaguchi out of the way, the table was set for a Nancy vs. Tonya showdown and both were up to the task, Tonya having been 1991 U.S. Champion and Nancy having won that title in 1993.

Tonya Harding was poised to recapture that glory of 1991-92, having shaken off some personal issues to refocus on skating. And with two Americans guaranteed to make the Olympic team, it seemed overwhelmingly likely that Nancy and Tonya would represent the U.S. together and that Tonya would have her best-ever chance at an Olympic medal. And then it all came crumbling down because Jeff Gillooly doesn’t understand Data Sufficiency.

Here’s the question, and here are the facts. Will Tonya Harding make the Olympic team? The top two finishers make the team, and Tonya is as good as Nancy but maybe a little better or maybe a little worse, and both of them are better than the rest of the field. So if we assess this as a Data Sufficiency prompt, we’d have:

Is Tonya one of the two highest values in Set USA?

(1) Nancy > Tonya > all other values in Set USA

Statement 1 here is sufficient – if we can prove that Tonya is at the very worst the second-best competitor, she’s guaranteed to make the team. But then along came Jeff Gillooly, not the sharpest tool in the shed, making one of the most common GMAT mistakes anyone can make.

Jeff Gillooly picked C.

Jeff Gillooly took a look at a Statement 2 that only existed in his own mind and went for it, hiring a goon to club Nancy Kerrigan in the knee and introduce this statement to the problem: “Set USA does not contain Nancy”. The problem then looked like:

Is Tonya one of the two highest values in Set USA?

(1) Nancy > Tonya > all other values in Set USA

(2) Set USA does not contain Nancy

Jeff Gillooly looked at that problem and made the same mistake that so many GMAT test-takers make. He thought “If together Nancy and Tonya are the two highest values, and then if Nancy isn’t in the set, then Tonya is guaranteed to be one of the two highest values in the set (and therefore make the Olympic team and win me and my creepball moustache a free trip to Norway!).” So Jeff Gillooly picked C, forgetting that there are two clauses to that answer choice:

(C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Read past the comma, Gillooly. Tonya Harding was sufficient ALONE. With Nancy Kerrigan out of the picture, Tonya won the US Nationals meaning that even had Nancy been absolutely amazing on the ice in that competition Tonya at worst would have gotten second and gone to the Olympics. In GMAT-speak, even though we all love having two pieces of information, if we only need one of them we’re punished for using both. If one statement alone is sufficient, you can’t pick C. Don’t be a Gillooly!

Since not many (if any) actual GMAT problems will be about Tonya Harding, let’s see this same concept in action with a real GMAT problem:

Is 0 < x < 1? (1) x^2 < x (2) x > 0

As you unpack statement 1, you’ll probably recognize that a fraction like 1/2 satisfies that inequality. If you square 1/2 you get 1/4, a number less than the original. So most people will look at statement 1 and say “x has to be a fraction, so that’s probably sufficient”. But then statement 2 hits a lot of people’s minds like a club to the knee – “Oh, but I need to know that it’s positive, too! I’ll pick C.”

Go back, though – if you try a negative fraction like -1/2, when you square it it becomes positive, and x^2 is greater than x. Statement 2 already tells us that x is positive – statement 1 is sufficient ALONE. All statement 2 really does is reinforce something that was already sufficient alone. Statement 2 is the Gillooly trap. Before you pick C, you’d better make sure that neither statement is sufficient ALONE. And like in the Nancy/Tonya situation, a statement (or skater) is often sufficient ALONE only through some hard work – beware the “easy way out” statement that makes C seem “obvious” when you could have taken a few extra steps (a little extra algebra, some extra work on your triple salchow) to make a statement sufficient ALONE.

There are plenty of lessons that a GMAT test-taker can take from the Nancy/Tonya saga – cheaters always get caught, make sure your shoelaces are tied before you enter the test center – but one reigns supreme above them:

Don’t use both statements if one alone will do the trick. Don’t be a Gillooly.

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: Keep the Bridge Clear and Your Score High

The GMAT, it seems, is a lot like politics:

-You can’t win them all – in fact, with Item Response Theory scoring much like with democracy you can achieve a resounding “victory” with even 55-60% success in many cases.

-You’ll have gaffes and blunders along the way and you’ll have no choice but to recover from them as best you can.

-You’ll have to think quickly on your feet and make sound, logical decisions with incomplete information and in less-than-ideal circumstances.

-You’ll need to make compromises – you might be able to get a question right in 4-5 minutes but you’ll need to make the conscious decision to let that one go in favor of having more “capital” (time) to spend on future questions.

-And when you do succeed, the rewards last for a long term (2-6 years in politics; 5 years is how long your GMAT score stays valid).

So when thinking about the GMAT and how to approach it, it’s only reasonable that you might consider the example of Chris Christie and the George Washington Bridge.

Allegedly, Chris Christie became so fixated on a setback (the mayor of Fort Lee, NJ did not publicly endorse Christie for NJ Governor) that in the end didn’t matter (Christie still won in a landslide) that he allowed it not just to clog his mind but also cloud his judgment, clogging the heavily-trafficked George Washington Bridge into New York City as “punishment” for the citizens of Fort Lee. And in so doing, Christie followed the not-so-successful example of GMAT test takers everywhere:

When the GMAT deals you a setback, don’t let it shut down the whole system – keep the bridge clear!

Just across the bridge from Fort Lee in Manhattan, a Veritas Prep student (to preserve her anonymity, let’s call her “Christie”) Chris Christied her way out of a 700+ score a few years ago. Here’s the transcript (well, re-enactment) of her call to VP headquarters after her test:

CHRISTIE:Can someone please help me? I just finished the GMAT and I don’t know what to do or where to go from here.

INSTRUCTOR: Sure, yeah – tell me how the test went for you and we’ll see if we can figure out what went wrong.

CHRISTIE:I was getting above 700 on all my practice tests and I got a 590 today. I don’t know what to do. What happened?

INSTRUCTOR: Well let’s start breaking it down. Tell me about the quant section – did you run out of time? Can you pinpoint a question or two that you think may be responsible for getting you down?

CHRISTIE:It honestly felt great for the first 25 questions or so. My pacing was good – I actually had a little more time than I thought so I could double-check some answers and spend some extra time drawing out geometry figures. But then around question 30 I noticed a couple easy questions in a row since the test is adaptive I knew that meant I was doing poorly. I tried to stay focused but after all that hard work, to know that I blew it, I just couldn’t. I finished the section – I guessed on the last two because I just couldn’t focus now – and that’s when I knew that it was over.

INSTRUCTOR: Wow, ok – that’s frustrating because it sounded like everything had been going really well. I understand how that must have felt.

CHRISTIE:It was terrible. I ran to the bathroom during the break and just started crying. All that hard work, all those practice tests… I know the break is for 8 minutes but I couldn’t tell how long I was in there. I didn’t want to go back into the test room still crying, but every time I thought I could stop and go back to finish the test – to at least see my verbal score – I’d start crying again. By the time I got back to my seat the verbal clock had already been running and I lost probably 4-5 minutes.

INSTRUCTOR: Wow, so it sounds like things really went downhill. I’m so sorry for you. Do you remember much from the verbal section?

CHRISTIE: I tried to read but I was still shaking a little from crying and my eyes were blurry, plus I was so far behind on time. I guessed on a few because I just couldn’t focus, and then by the time I could compose myself again the questions were really, really easy and that got me teared up again. I couldn’t even try on Reading Comp – I couldn’t focus long enough on a passage to really get through it, so I guessed on just about all of those and probably most of the Critical Reasoning. It was bad – I was just so upset for having blown it like that.

INSTRUCTOR: So wait – you basically didn’t even do the verbal section, but your score was still a 590 right?


INSTRUCTOR: That’s almost a full standard deviation above average. What was your split between quant and verbal?

CHRISTIE: Um, I think it was about 88th percentile quant and maybe 5th percentile verbal. That part was really bad.

INSTRUCTOR: So think about that, though – your verbal was terrible because you were so upset for having bombed the quant, but you didn’t bomb the quant at all. You had a great quant section!

CHRISTIE: Oh…I hadn’t thought about it like that.

INSTRUCTOR: My advice for next time, Christie – you have to let it go even if you know you made a mistake or feel like you’re struggling. The only thing you have to fear is fear itself!


What can we learn from Christie in Manhattan? Don’t let setbacks hold you back. Don’t stop thinking about tomorrow (or the next question). Don’t let a setback clog your mind or clog the bridge – we have to keep moving forward. Whether your goal is an 800 or a 1600 (Pennsylvania Avenue), you won’t get that by dwelling on the past or focusing on the little bumps in the road on your way there. You have to keep the bridge – and your mind – clear.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Goodbye to “No, But…” and Hello to “Yes, And…”

GMAT Tip of the WeekIt’s a new year, which is often a good time for a new mindset. And if you’ve already decided that 2014 is the year for you to get serious about graduate school, the “hard work pays off” mindset is one you’ve already adopted. So before the year gets too old and habits get too hard to change, try adding one more new outlook to your study regimen (and your life) this year:

“Yes, and…”

A common mantra for improv acting and comedy, “Yes, and…” is immensely helpful when studying, too, mostly because it replaces the single most counterproductive mindset in all of GMAT Preparation, “No, but…”

Here’s the difference: in improv shows, a “no, but” response shuts the scene down and makes it an argument between the actors. When an improv actor makes a decision she has to go with it; if she wants to play the NYPD cop with a British accent, her costar can’t try to counteract it “No, but my character needs you to have a Brooklyn accent!”. The scene would die and the audience would either be confused or just plain ticked off. “Yes, and…” allows the costar to accept that choice – the British accent – and create an interesting scene (“Yes, and I have a Boston accent…what do Brits and Bostonians have in common? They both hate the Yankees…”).

“No, but” similarly shuts down your learning capacity. “No, but” is defensive and combative – when students get a wrong answer they often try to debate it, either with their teacher or the solution in the book: “No but I thought you always had to…” or “No but I divided by x and got…”. In those cases you’re forgetting that your goal in GMAT preparation isn’t to be right on every practice question, but instead to learn from every question so that you’re right more often on test day. “Yes, and…” is the philosophy of saying “yes, I see that the answer is D and here is how the test is twisting my logic against me” or “Yes this seems to violate the rule I was applying and here’s the reason that the rule doesn’t apply here.”

“Yes, and…” accepts that the test is hard but learnable, that you know you’ll make mistakes but you’re ready to learn from them and work to improve. And “Yes, and…” fits the GMAT perfectly well – the “no, but” mentality usually stems from either adherence to “rules” that are either tendencies more so than rules (“being” is usually wrong on Sentence Correction, but it’s definitely not a rule) or limited-use rules that the GMAT will tempt you with when they don’t apply (you can always divide both sides of an equation by a variable UNLESS that variable could be 0).

The “no, but” response is one that tries to disprove the test, to know more than the test/teacher/book – and *sometimes* you’ll be right, but way, way more often you’ll be missing an important point that is much easier absorbed with a “yes, and” mentality. Because the GMAT isn’t a cram-and-regurgitate test, but rather a test of reasoning and critical thinking, “no but”ing your way through practice problems can leave you mired in a memorization state when you could be learning to think more critically and pick up on tendencies of the test.

So adopt a new mindset for the new year – “yes, and” is a powerful way to get the most out of your studies and other facets of your life.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: No Resolution!

GMAT Tip of the WeekSo you have a few more days to commit to your New Year’s Resolution, and if you’re like most people you have something like 35 days until you break it. Resolutions don’t often stick, but if your New Year’s Resolution is to apply to business school in 2014, and if as part of that resolution you’re planning to get a high GMAT score, you’re in luck:

Data Sufficiency problems don’t need resolutions.

Or perhaps better put, they’re problems that don’t always need to be resolved. As long as you know that you could finish the problem, you don’t need to finish it (kind of like once you’ve proven to yourself by January 16 that you *could* make it to the gym by 6am every day this year, you’ll decide that that’s enough and start sleeping in). That’s because Data Sufficiency questions are about whether you could get an answer, not about what the answer actually is. Consider this question:

What is the value of x?

(1) x^2 – 5x – 5 = 0

(2) x > 0

While you *could* do all the work to solve for x, you could also pretty lazily answer C without resolving the problem by factoring statement 1 and incorporating statement 2. How? Since the quadratic in statement 1 has a negative for the non-x term, then the parentheses when you factor it will look like:

(x + ___)(x – ____)

Meaning that there is one positive and one negative value of x. So there are two solutions – a positive and a negative – for statement 1, and clearly statement 2 is no good on its own. But taken together, you know that of the two solutions that statement 1 gives you, it has to be the positive solution based on the definition given in statement 2. So even if you didn’t resolve the quadratic in statement 1, you can get to the answer (C) quickly, saving valuable time and energy for later questions in the quant section – or for fun and relaxation after your study session since you did make that resolution to do 20 problems a day in 2014.


Now a caveat – use this advice carefully, because although you may not need to resolve some Data Sufficiency problems, hard problems will reward those who are resolute. Consider this problem, which should look similar:

What is the value of x?

(1) x^2 – 4x + 4 = 0

(2) x > 0

In statement 1, you can actually factor that into: (x – 2)(x – 2) = 0, which means that x MUST equal 2, making statement 1 sufficient alone (and the answer A). So don’t go crazy not doing any work. If you don’t know for certain that you can avoid the work, do the work. But as you practice with Data Sufficiency, resolve to avoid at least some resolution. Make 2014 the year of efficiency (then the year of admission-cy).

Happy New Year from the GMAT Tip of the Week team! We resolve to be back next week with even more useful GMAT strategies to help make your 2014 successful.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Become a Reading Comprehension Has Been (that’s a good thing)

GMAT Tip of the WeekOne of the things that makes Reading Comprehension difficult is the inclusion of so many words that you either don’t know or don’t spend much time thinking about. Triglyceride, germination, privatization, immunological.

But by the same token, certain words – those that you should think about regularly if you don’t already – can make your job exponentially easier. Consider, for example, these sentence fragments from the beginnings of official GMAT passages:


The antigen-antibody immunological reaction used to be regarded as typical…

Anthropologists studying the Hopi people of the southwestern United States often characterize…

The modern multinational corporation is described as having originated…

Many scholars have theorized that economic development, particularly…

In all of these cases, the first sentence of a passage describes something that “has been” considered to be the case or that “used to be regarded as typical.” And in all of these cases, the author’s main point in the passage (you can find most of these in the GMATPrep software available for download at to see for yourself) is to reject the “conventional wisdom” and either offer his own theory or show how things have changed since then. So what does that mean for you strategically?

When the first sentence of a passage talks about “the conventional wisdom,” there is a massive likelihood that the author’s main point is to buck convention.

Which means that if you start reading something about what “has been” or “is usually,” be ready for things to change. Look for the author’s transition to come – be it the word “however” or “but” or another paragraph that begins with “Alternatively…”, you’re very likely to find a transition coming up soon, after which will be the author’s purpose for writing the passage. And most comforting of all – it almost doesn’t matter what the subject matter is. Once you’ve determined that the other shoe is going to drop, you don’t have to worry much about the conventional wisdom unless they ask you for it. The author’s real mission is what comes after the transition so you can focus your attention there.

Now, this might fall under the category of “somewhat helpful” when you’re reading one practice passage, but consider how these will appear on test day – you’ll have been racing through Sentence Correction and Critical Reasoning prompts after having grinded out the quant section. Every advantage is a big help, and if you have insider information as to what the author is probably trying to do, you can read much more efficiently and confidently. Instead of reading and waiting for the author to prove the point, you can “attack”, looking proactively for what you’ll likely find.

So become a Reading Comprehension “Has Been” – if you see that the passage starts by talking about what has been or used to be the case, get ready for a change in direction to what the author thinks is now true. Thinking like a “has been” can be your ticket to achieving a score that “never was” possible before.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Mental Agility

GMAT Tip of the WeekThe axiom has been tweaked and twisted so often that perhaps no one knows the exact term, but we all know the definition.

The definition of insanity is…
The definition of stupidity is…
(WAIT! Google confirms that it’s insanity, but you’ve probably heard it as any number of terms)

…doing the same thing over and over again and expecting different results.

Well, on the GMAT the definition changes from time to time, so we’ll add this caveat that applies to problems above the 600 level:

GMAT stubbornness is doing the same thing over and over again and being surprised when it doesn’t always work.

Here’s why – it would be wrong to categorically say that the GMAT is not testing your ability to learn, remember, and apply a process. To a fair extent the GMAT does test exactly that. But that’s not ALL it’s testing. Once you get to above-average level problems (and remember that’s above average in a pool that contains just about exclusively college graduates, so it’s an elite academic group to begin with) the GMAT is testing more than just “can you follow directions” – it’s testing things like “can you think on your feet when the situation changes,” “can you manage uncertainty,” and “can you find innovative ways to solve problems when the tried-and-true process doesn’t work.” And that’s where Mental Agility comes in – the GMAT, at the top end, will punish “one trick ponies” and reward those who can adapt on the fly. Consider an example (and please excuse the ugly in-line math formatting):

If a + 2b = (16 – b^2)/a, what is (a + b)^4?

It’s very easy to become seduced by the (16 – b^2) term, recognizing that as a classic “Difference of Squares” setup to be factored into (4 + b)(4 – b). And with good reason – the Difference of Squares rule is a very important concept and extremely helpful on plenty of GMAT problems. But here it makes the expression even messier – you can’t use it to eliminate or combine anything on the left hand side of the equation (a + 2b). So as much as you may beat your head against the wall trying, you need to find a new outlet. And that you can get by multiplying both sides by a to get rid of the denominator on the right:

a^2 + 2ab = 16 – b^2

Here’s where another common “squares” equation comes in: x^2 + 2xy + y^2 = (x + y)^2. If you can see that as your goal, then you have another outlet; you can add b^2 to both sides and you’ll have a squares equation ready to go:

a^2 + 2ab + b^2 = 16, which then becomes (a + b)^2 = 16. And if (a + b)^2 is 16 and we need (a + b)^4, we can square 16 to get 256.

The bigger lesson here is that it pays to have mental agility – many “hard” GMAT problems look easy in retrospect, as they’re not about grinding out long calculations or employing obscure rules. The range of math concepts tested on the GMAT is finite and (relatively, compared to what you learned in high school) small, but the GMAT makes it difficult by punishing those who don’t see the opportunity to change paths. IF your goal is to “grind” – to find a formula for each question, put your head down, and apply it – you may find some trouble. A few key takeaways from this problem include:

  • If the “obvious” process or rule isn’t working after a few steps, take a step back and see if there’s another way
  • If an algebra problem asks for a combination of variables (here it’s (a + b)^4) try to find a way to get that combination alone and not necessarily solve for that variable. Most “processes” you know are geared toward solving for individual variables; the GMAT knows that and loves to ask for combinations (like xy or (a + b)).
  • As you study, pay attention to which “surprise” techniques you didn’t see at first but ended up being the key to solving a problem. Having that quick reference list to scan through in your mind will pay off. For example, this “squares” rule can be extremely helpful any time you’re asked to solve for a combination of variables squared (like (a + b)^2) *or* for a combination of variables multiplied (like 2ab…that comes from that middle term in a^2 + 2ab + b^2).

Most importantly, recognize that while in life doing the same thing over and over again usually gives you the same results, on the GMAT questions are written specifically to reward those who aren’t afraid to change gears when “what’s always worked before” doesn’t work in this case. On 700+ level problems, insanity just might be doing the same thing over and over again and wondering why you didn’t get the same result; the GMAT rewards mental agility.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Avoiding Writer’s Block On AWA

GMAT Tip of the WeekWhile it’s certainly not the score you care about most, the Analytical Writing Assessment can bring with it some stress and even despair. Why? For one, it comes first on the test, and for two it’s the only section that isn’t multiple choice. The answer isn’t already in front of you, but rather you have to create it yourself. And like this blog post (author’s note – I’m attending a conference with the folks from the Graduate Management Admissions Council and have a dinner in an hour with some of our partners in the industry before the conference, so I have 30 minutes to write something intelligible here), the AWA can lead directly to that panic you’ve likely felt on blue book exams and the night before book reports: writer’s block.

How can you combat that on the AWA?

1) Remember that there’s no (well, some but not a ton) shame in leaving an AWA essay “incomplete”.

The graders and schools know that the AWA is a bit artificial; it’s a writing sample but in the real world you’ll have plenty of time to edit your work, research topics, pass it along to a colleague for a review, and use the Microsoft Word thesaurus feature to make it sound smarter. But on the AWA you have exactly 30 minutes in a higher-stress environment. Your grade will reflect that – a few typos here and there won’t hurt you, and if you have to hastily write a conclusion to wrap it up it’s not going to be devastating to your score. In fact, the worst thing you can do is let the AWA cause you undue stress for the rest of the exam. Relax and know that your essay is going to be shorter than you’d probably want it if you were presenting to the board at your company and you’ll realize later that you could have used a better phrase or example. The AWA is, by design, a short examination, so don’t worry.

2) Plan ahead.

Writer’s block comes when you don’t know what to say next, so make sure you *do* know what to say next. Before you begin writing, jot down 3-4 problems with the argument in question (all AWA essays ask you to “analyze an argument”) so that your body paragraphs are already brainstormed before you get there. Then write based on those notes. Much like a blue book exam, as long as you know the general topic (e.g. “one assumption the author makes is that current trends will continue”) you can write circles around it to come up with what looks to be a decent paragraph (e.g. “but suppose, for a second, that the growth rate were to dramatically slow down, bucking the conventional wisdom. That would force the organization to dramatically change its strategy…”). Even if it’s not ideal, it will give the reader a glimpse of your writing ability and a chance to show that you can craft/organize an argument on the fly. Sure, you should be able to do better, but in terms of disaster management at least you won’t hit a point 15 minutes into the essay at which you don’t know what to type next.

3) Use a template in your practice tests and then replicate it on test day.

In many ways, more than half your AWA essay should be mentally written before you even get to the test center. The instructions are always the same, and the format should therefore always be the same. Your first paragraph should be an introduction, the last a conclusion, and between should be three body paragraphs each exposing a problem with the argument. And since most of your job is to show clear organization, you can have the transitions between paragraphs (e.g. “Another assumption the author makes is that ______________________. This may not be the case, however, as _______________________. Therefore, the author should take care to _____________________________.”) pre-selected so that all you have to do is fill in some content items from the prompt and you’re all set.

4) Don’t let “perfect” get in the way of “good enough”.

The AWA is the gateway to the rest of the test. If you stay relaxed, confident, and efficient you’ll turn over into the Integrated Reasoning section and then the rest of the test with your mind sharp, your demeanor calm, and your potential high. A 5 (or even a 4.5) on the AWA won’t keep you out of any schools that a 6 would have gotten you into, so don’t try to be perfect. Your job is to get it done adequately and save the stress for the sections that matter more (or, really, to just not stress at all, but obviously that’s tough to avoid).

Rest assured that a pretty well-written essay can easily be written in less time than it takes Domino’s to make and deliver your pizza. This blog post is (we hope) living proof. Good luck out there!

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Subconsciously Speaking

GMAT Tip of the WeekDo some of your best ideas come while you’re driving, running, taking a shower or just about to fall asleep? Have you ever spent what felt like an eternity reading a solution over and over again to no avail, only to revisit that problem a few days later and know how to do it almost so intuitively that just feels easy?

There are reasons for that – that happens to everyone, and while it can’t really help you on test day (there are no known Pearson/VUE test centers that will let you take the GMAT on a treadmill or under running water), it can absolutely give your study routine a much needed lift. The simple advice?

Put the book down.

Not immediately, and not forever, but from time to time you need to take breaks in your study routine to give your subconscious a chance to process all the work you’re doing. Some of the most effective GMAT study comes after you’ve “studied” when you’re not officially studying at all. You *get* factors, multiples, and divisibility when you’re noticing that the number on your dinner bill is divisible by 3 or that the prime factors of that 65 on the speed limit sign are 5 and 13. You’ve begun to really master Sentence Correction when you see both that this sentence is using the common “both X and Y” structure and see that it’s written incorrectly because the verb “see” came before the word “both” and therefore is redundant after the word “and” (it’s either “see both that X and that Y” or “both see that X and see that Y”). You have the GMAT right where you want it when your study extends to those places you want to be outside the library.

So how can you use this advice productively?

1) When you’re studying exhausted, let yourself rest. This doesn’t mean that you can always claim “Exhausted! Not studying!”, but if you’ve been at it for two hours and you feel like you’re beating your head against a wall and not getting anywhere, it’s just good strategy to let it rest and let your mind process it on its own time and in its own way.

2) Take entire days off. With muscle training, rest days are essential to allow the muscles to build up after you’ve broken them down. And the brain is just that, a muscle. Your subconscious is your brain’s way of regenerating and reorganizing itself – that’s an important process, so give your brain time to do it.

3) Challenge yourself to use GMAT concepts and thought processes outside of GMAT books. GMAT practice problems are designed to be challenging, and most solutions and content review units can be dryer and denser than you’d ever find entertaining. But you can let yourself “win” when you’re the one to calculate the tip or divide up the bill at dinner, or when you convert kilometers to miles while driving (a 10k is 6.2 miles, so every kilometer is approximately 3/5 of a mile). In that way, you’re proving to yourself that you know the concept and you’re challenging yourself to apply the concept…and the GMAT is more an application test than just a knowledge test, so practical application practice is some of the best practice you can get.

Most importantly, trust in the power of your subconscious mind to strengthen and organize the fruits of your conscious study labor. There’s value in rest, so give your brain that chance to rest up before your next monster study session.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Beware the Coincidence

GMAT Tip of the WeekToday marks the 50th anniversary of the assassination of US President John F. Kennedy, and amidst all of the memorial articles and TV specials and conspiracy theories, you’ll undoubtedly see that email forward that details the eerie similarities between the two presidents assassinated almost 100 years apart, Kennedy and Abraham Lincoln:

– Kennedy had a secretary named Lincoln, and Lincoln had a secretary named Kennedy
– Both men were assassinated by men with three names (Lee Harvey Oswald and John Wilkes Booth), each containing 15 letters
– Both were elected in ’60, and then succeeded by vice presidents named Johnson, etc.

And while it’s fascinating every time you read it, it’s just a bunch of coincidences. Even the flaxseediest protester in front of the White House can’t put together an argument for why any of those coincidences could possibly scream “conspiracy” or anything other than “sometimes there are coincidences.” No matter how much significance we want to ascribe (but Kennedy was killed in a LINCOLN town car, and Lincoln is owned by Ford, and Lincoln was shot at Ford’s Theater!) to events that happen concurrently, often those things are just coincidences. And realizing that “coincidences happen” can help you master Critical Reasoning problems.

Much like the Lincoln-Kennedy coincidences, other coincidences happen frequently on the GMAT and bait us into trying to see them as related. Consider these facts:

Beginning in the early 1990s, New York City instituted a program called “broken window policing,” in which even small acts of vandalism or petty crime were actively pursued, prosecuted, and corrected. The prevailing wisdom was that such policing would both send a message to would-be criminals and encourage all citizens to take more pride in their city and each other. Between 1994 and 2001 the violent crime rate steadily decreased by over 50%, from a rate of 1,861 violent crimes per 100,000 people in 1994 down to 851 violent crimes per 100,000 people in 2001.

What can you conclude? Your mind wants to see the “broken window policing” policy as the cause of that dramatic decrease in crime. But based simply on the above can you prove it? What if the two are just coincidences; what if a massive decrease in the unemployment rate or (as predicted in the bestseller Freakonomics) a dramatic decrease in the birth rate of potential criminals were the drivers? When you’re presented with those facts above, your mind naturally tries to link them together, but in GMAT Critical Reasoning you have to consider the idea that two concurrent facts – no matter how much they might seem related – could just be coincidences. Consider this problem:

About two million years ago, lava dammed up a river in western Asia and caused a small lake to form. The lake existed for about half a million years. Bones of an early human ancestor were recently found in the ancient lakebottom sediments on top of the layer of lava. Therefore, ancestors of modern humans lived in Western Asia between 2 million and 1.5 million years ago.

Which one of the following is an assumption required by the argument?

(A) There were not other lakes in the immediate area before the lava dammed up the river.
(B) The lake contained fish that the human ancestors could have used for food.
(C) The lava under the lake-bottom sediments did not contain any human fossil remains.
(D) The lake was deep enough that a person could drown in it.
(E) The bones were already in the sediments by the time the lake disappeared.

When you read the stimulus here, you’re likely to accept it as pretty airtight truth. The bones in that part of the fossil record are proof that people lived during that time period, right?

But what if the bones are just coincidentally in those sediments? The ONLY evidence we have is those bones, so before we take this conclusion at face value we should consider whether they’re really the smoking gun that they’re set out to be. And there’s the possibility that they just coincidentally happened to be in that part of the sediments during whatever archaeological dig found them. Perhaps they were much more recent but an earthquake shook them down a few hundred thousand years deeper into the sediments; perhaps Lee Harvey Oswald III and his punk teenage friends decided to play a trick on the archaeologists and deposited the bones (of a man named Lincoln?) in that sedimentary zone as a prank. If you can see that “bones in the sediment now” doesn’t necessarily “bones in the sediment during that timeframe” – if you can see that it might be a coincidence – you’ll realize that answer choice E is necessary to take away the coincidence factor.

Notice, too, about this problem that it’s of the “Assumption” variety. Quite often Assumption questions are hard mainly because it’s so easy to buy the argument at face value – to see two concurrent items as causal or related because they just seem so likely to fit. That’s why it’s important to make sure you emphasize the “Critical” part of Critical Reasoning. Do not buy the argument – keep in mind that two events could always be coincidental or correlated if you don’t have definite proof that one caused the other.

Heed this wisdom, and your 700+ score will be no strange coincidence.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Beware of (Richie) Incognito Information

If you’ve been following the strangest story to hit the NFL since Manti Te’o did, you’ve probably noticed that Richie Incognito is nowhere near incognito. There’s nothing subtle or understated about the guy. He’s Rob Ford in a different jersey. But there’s something about that name…

While you don’t have to fear Richie Incognito on the GMAT, there is a little bit to fear about the bullying you could receive from a different kind of “Incognito”. The GMAT – and in particular Data Sufficiency – loves to bully you with incognito information. Consider these two questions:

The swimming pool at Jonathan’s house can contain up to x gallons of water. How many gallons does the pool hold when completely full of water?

(1) x^2 = 160000

(2) 399 < x < 401


The aquarium at Stephen Ross’s house can contain up to y dolphins. How many dolphins does the aquarium hold when completely filled with dolphins?

(1) y^2 = 160000

(2) 399 < y < 401

Those questions look the same, right? It’s just that the second has a slightly goofier backstory, but other than that what’s the difference?

Much to Jonathan’s and Mr. Ross’s fears, Incognito appears in both of them, twice in the second one.

For statement 1 in each case, taking the square root of both sides gets you to either 400 or -400, which even to a rookie GMAT student being hazed by tough practice questions screams “beware the negative! Insufficient!” But wait – where’s Incognito? Neither question tells you specifically that the variable has to be positive, but incognito information guarantees it. You can’t have a negative amount of water in a pool, and you can’t have a negative number of dolphins in a pool (although as Mr. Ross knows, you can have negative Dolphins on your team so you need to police that locker room). So in each statement 1 the information is sufficient. Only 400 is a plausible answer.

In Question 2, Statement 2, Incognito strikes again. In the first question, it’s certainly possible to have 399.5 gallons of water. But you can’t have 399.5 dolphins. In subtle, incognito fashion the backstory in the second questions guarantees both “positive” and “integer”, making the answer to the second question D while the first is A. And in either case, what looked like just a plain backstory behind the algebra was actually quite important to the answer – it was important definitions (positive, integer) masquerading as window dressing. It was the GMAT gone Incognito.

What can you learn from this? Make sure to be on the lookout for incognito information, which can include:

-In Geometry questions where exponents are present, you can’t have negative lengths or volumes. Geometry in its incognito way rules out negative.
-When the units they choose can’t be divided smaller than integers, you have incognito positive and integer information.
-Ratio problems are famous for incognito information. If the ratio is 2:3, the total number will be a multiple of 5; you can derive an extra multiple just from the individual components. (but wait – if there’s possibly a third component to the ratio, then that hidden possibility ruins the total/multiple trick)
-In Venn Diagram problems, the “Neither” component also often travels incognito. If you get the information “10 people are in group A, 12 are in group B, and 20 are out there total”, you’re tempted to say that 2 people are in both…but “Neither” is lurking there all unsuspecting and incognito on you.

There are other examples, but the main lesson is this – the GMAT thrives on Incognito bullying. It will punish you by hiding important information in disguise, so be on the lookout for Incognito.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Patience Pays Off

GMAT Tip of the WeekOn a timed test like the GMAT, test-takers often fall victim to a simple fact about the way the English language works: we read from left to right.

Why is that? We’re often in such a hurry to make a decision on each answer choice that we make our decisions within the first 5-10 words of a choice without being patient and hearing the whole thing out. A savvy question creator – and rest assured that the GMAT is written by several of those – will use this against you, embedding something early in an answer choice and baiting you into a bad decision.

At Veritas Prep, we refer to this as one of two elements of the testmaker toolkit:

*”Hide the Right Answer”


*”Sell the Wrong Answer”

Consider this in a Sentence Correction question:

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 interested in 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

This is a classic example of a hybrid “Hide the Right Answer” / “Sell the Wrong Answer” technique that preys on people’s desire to make a quick decision early in the answer choice. People do not like the (correct, but lesser-used) structure “so X that Y”, so they often eliminate A (the “hidden right answer”) for C (the “sold wrong answer”) because they prefer “so X that Y”. But the real decision to be made here isn’t one of sentence structure (both structures in A and C are correct) but rather one of verb tense (this is all ongoing, so “posed” in B, C, and D must be wrong”. Amazingly, very few students even get to the point at which they’ll notice the verb tense difference in pose/posed, having been so effectively drawn to the “false decision point” to the left. Those who are patient will be rewarded with a verb tense difference – one you should study quite a bit in practice – but many simply cannot help themselves and make their decision too early, too hastily, too far to the left-hand side of the screen.

Consider another example, this time from Critical Reasoning:

Citizen: Each year since 1970, a new record has been set for the number of murders committed in this city. This fact points to the decreasing ability of our law enforcement system to prevent violent crime.
City Official: You overlook the fact that the city’s population has risen steadily since 1970. In fact, the number of murder victims per 100 people has actually fallen slightly in the city since 1970.

Which one of the following, if true, would most strongly counter the city official’s response?

A. The incidence of fraud has greatly increased in the city since 1970.
B. The rate of murders in the city since 1970 decreased according to the age group of the victim, decreasing more for younger victims.
C. Murders and other violent crimes are more likely to be reported now than they were in 1970.
D. The number of law enforcement officials in the city has increased at a rate judged by city law enforcement experts to be sufficient to serve the city’s increased population.
E. If the health care received by assault victims last year had been of the same quality as it was in 1970, the murder rate in the city last year would have turned out to be several times what it actually was.

In this problem, the official’s conclusion is basically a direct contradiction of the previous claim that “you are not adequately preventing violent crime”, and he bases his contradiction on the fact that, hey look, the murder rate has gone down. His argument effectively reads:

Premise: The murder rate has gone down
Conclusion: Therefore we have done a good job preventing violent crime

In an effort to weaken his conclusion, you want to find a choice that exploits the gap “murder isn’t the only type of violent crime” – you want an answer that shows that another type of violent crime, or violent crime overall, is up.

And here’s where patience pays off (and haste hurts you):

Answer choice E does exactly what we want, showing that people are being violently assaulted at a high rate, they’re just not dying. The murder rate is down, but not because violent crime is down but instead because healthcare is preventing the victims from dying. But hasty test-takers only see “If the health care…” and think that this answer choice is way out of scope. Why would health care be important in a discussion of crime?!

Again, patience is the key here – the testmaker knows that it can “Hide the Right Answer” by taking 10-12 words to get to the main point, and those of us racing to make our decisions quickly won’t have enough presence of mind to let it develop.

So take these lessons from the testmaker’s toolkit – the authors of hard questions will bet that you’ll work too quickly, make your decisions too far to the left-hand side of the screen, and miss the crucial part of the effective decision. Be patient, and more often you’ll be correct.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: The Day Before The GMAT

GMAT Tip of the WeekSome stories are best told in the first person, so forgive me for the break from journalistic standards. As a longtime GMAT instructor – 10th anniversary coming up next month actually – I most empathize with my students when I’m preparing for any big event of my own, usually running and triathlon races. The months of grinding preparation, the sleepless night before the event, that helpless “if I’m not ready by now I guess I’ll never be ready, so here goes nothing” last week before the big day… I get to feel what my students feel leading up to their GMAT, and symbiotically I can both learn more about that experience and benefit from the advice I’ve always given about the GMAT.

So it was this past weekend, my last “long” run before tomorrow’s triathlon, that I had to heed my own advice about the last day or two before the test:

Don’t try to do new problems – and definitely don’t try to do a practice test – within 24 hours of your GMAT.

Why? Well here’s my story – I run along “The Strand” in Southern California, a long winding bike path along the beach. And my goal is to never get passed from behind – which sometimes is unavoidable (it’s busy out there, and some truly elite athletes train there) but if I’m working hard I can usually pull it off. Saturday was a “taper workout” – in the 10-14 days before a big race you tend to gradually back off the intensity to rest muscles, but then again running 15 miles is still running 15 miles. And for some reason – that extra half cup of coffee that took 10 minutes, or the time I woke up, or whatever it was – I happened out on that long-but-supposed-to-be-easy run right around the same time that at least a few pretty fast track clubs were in the middle of their workouts. And while I was going for distance, they must have been going for speed – on my first loop I got passed at least 15-20 times, but not without my pride turning an easy run into a “don’t get passed!” sprint pace at times.

And if I weren’t a longtime GMAT instructor, and had I not coached so many students against such a similar phenomenon over the past ten years, it might have been the most stressful and counterproductive workout you could have before a big race. How, after all this long training, was I getting beaten so badly by so many? And why, knowing that this wasn’t a race, was I sprinting to race random strangers when I was supposed to be casually stretching my legs?

I had to rely on the same speech I give my GMAT students – within a certain time period of your test, you won’t be able to improve by “learning more things” or putting in more effort. At a certain point – be it 48 hours prior if you’ve been studying a while, or just the day prior if you’ve condensed your studies to within a month or so – the best thing you can do is “keep the muscles fresh”. Because here’s what can happen if you try new problem sets or (heaven forbid) take a practice test:

  • You can catch a run of bad luck or tough problems (like my parade of sprinters on the Strand) and ruin your confidence with wrong answers and tough concepts. And while learning-by-doing is huge with weeks to go until your test, the day before confidence is much more important.
  • You can wear yourself out mentally, stressing through a test or monster problem set when your mind needs to be fresh and relaxed very soon.
  • You can wear yourself out physically, sitting in one spot too long and not letting your body burn off anxious energy by exercising or just walking around. Or you can lose sleep by trying to fit in that extra study session before or after work.
  • You can study the wrong thing and lose your focus on what’s important. The above for most are dangers you’re aware of, but this one is a little more subtle – people tend to chase “obscure” topics when they grind out new problem sets or attack the last practice test they haven’t taken yet, but the GMAT is much more a test of core skills and thought processes. If you spend a few hours the day before the test trying to master “Permutations With Restrictions”, when the odds are you may see 2 problems at maximum on that topic, you’re taking time away from reviewing the main thought processes for Data Sufficiency and Sentence Correction questions, those core processes that you’ll use around 15 times each on test day. The last 24-48 hours is not the time to try to chase new information that’s been baffling or challenging you; it is the time to remind yourself what you want to do (and avoid) on the exam.

There’s a strong link between athletic performance and the GMAT performance, so take a lesson from how athletes spend the day before a competition. It’s rarely if ever a hard workout or installing a new gameplan. It usually has two components:

1) A “walkthough”, reviewing the gameplan
2) A light workout, keeping the muscles fresh

How does this apply to your last day before the GMAT?

That day, you should spend time reviewing your approach for each question type, and reminding yourself of what to do (“Note all transition words in the passage, then make quick notes on the direction of the passage”) and what not to do (“don’t assume any variables are integers or positive numbers – always double check that”). And you shouldn’t do “nothing” – it would feel too strange to completely ignore the test, so carve out an hour to review a handful of problems of each type – problems you’ve seen before so that you don’t happen to pick a challenge set and shake your confidence, but so that you can remind yourself how to perform at your peak.

A successful GMAT tends to follow a successful day before the GMAT, so put some thought in to how you spend that last day. Stay fresh, stay confident, and stay off the Strand…man, those runners are fast sometimes!

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Get Clued In

GMAT Tip of the WeekHave you ever finished a GMAT problem, read the explanation (or listened to your instructor give it), and thought “well how was I supposed to know ___________?!”?

If so, you’re not alone. Many test-takers become frustrated when the key to a tricky question falls outside the normal realm of math. How was I supposed to know to estimate? How was I supposed to know to flip the diagram over to notice that side AB could also be the base of this triangle? How was I supposed to know that the word “production” next to “costs” was going to be so important?

The real answer to that question, like it or not, is “you’re not”.

You’re not supposed to know those things just as a matter of course, because the GMAT is not a test of what you’re supposed to know. Geometry won’t help your financial career. Sentence Correction probably won’t help you launch a tech startup. Much of the content on the GMAT is tangential at best to the cause of becoming a captain of industry. What the GMAT is doing, in large part, is assessing whether you can recognize opportunities where others don’t, whether you can play devil’s advocate when others rush to a probable-but-not-definite conclusion, whether you can determine which details are most likely to impact the success or failure of your mission.

So while you’re not “supposed to” know the key to unlocking many of these problems, you can train yourself to spot clues on the test and then leverage those to get to the bottom of the question. Consider the example:

A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1585 boxes for a combined value of $1588.75. How many boxes of plain cookies did she sell?

(A) 0

(B) 285

(C) 500

(D) 695

(E) 785

Now, you might first look at this one and see that it has a natural algebraic setup. First, the number of plain (p) boxes plus the number of chocolate chip (c) boxes has to add to 1585, so:

p + c = 1585

Second, the price per box times the number of each boxes has to add to the total revenue:

.75p + 1.25c =1588.75

But given the size of the numbers and the decimal nature of the coefficients in the second equation, that’s not really algebra that you want to do if you can avoid it. So what clues exist to bail you out?

1) The answer choices are far apart

If the answer choices seem widely spread, as they are here (at least 90 between each choice here), there’s a good chance that you can get away with an estimate rather than an exact calculation.

2) 1585 and $1588.75 are eerily similar and close together

Because the main numbers in the problem – total revenue and total unit volume – are almost the exact same, you should see that something may be up. That means that you’re looking at almost exactly a $1.00 per box average price (a little over that), and since the average price of one of each is $1.00 (75 cents for plain, 1.25 for chocolate chip), then you’re only going to sell a hair more chocolate chip than plain but the total amounts will be just about exactly the same.

With that in mind, if you scan the answer choices, only E has a chance. An even number of each type would mean you’d sell 1585/2 of each (792.5 boxes of each), so you’re bound to sell just a little under 792 boxes of plain. And only E is anywhere near that.

Now, back to the major function of this post – you may not have immediately seen that there was a conceptual alternative to the algebra. And that may be frustrating if you spent several minutes grinding out the math (and/or giving up). The algebra is a direct blueprint for how to solve this problem, but in this case it was inefficient for many and impossible or wrought with error potential for others. So how are you supposed to know to avoid it?

It comes down to clues. The GMAT embeds clues in its problems and rewards those who finds them (more so than punishing those who don’t, actually). So part of your goal is to train yourself to recognize clues like:

-Far apart answer choices mean you may want to estimate in Problem Solving questions
-An “easy” answer of C or E on Data Sufficiency means you’re probably missing something
-The presence of a word like “all” or “only” in a CR answer choice means you need to hold that universal statement up to extra scrutiny
-A word like “its” or “and which” well outside the underlined portion of an SC question may signify that you need a singular subject or an initial “which” clause in the underline

There are plenty of clues hiding in plain sight on the GMAT, and often those clues will supersede the “tried and true mechanical” approach. Your best strategy? Keep your eyes open and be on the alert for those clues in practice, and pay attention when you recognize one so that you can find something similar in the future. And see those clues for what they are – rewards. You’ll be rewarded for seeing those clues where others don’t, so see the process of learning and searching for them as a challenge. You’re not necessarily supposed to know how to do every problem, but if you pay attention to clues you may well be able to solve them anyway.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. 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 – Best of 7

GMAT Tip of the WeekWith the Major League Baseball playoffs on many minds, and the beginning of the NBA and NHL seasons on others, you’ll hear a lot in the news these days about trends in a “best of 7” series, in which a team needs to win four games to advance to the next round.

“Only x% (a very small percentage) of teams have ever come back from a 3-1 deficit to win”
“Only one team has ever come back from a 3-0 deficit to win”
“If a team takes a 2-0 lead there’s a (very high) chance that they win the series”

These adages go much like the trends you see thrown around in the GMAT space:

“The first 10 questions have a disproportional bearing on your score” (note, this is an overplayed rumor)
“If you get the first 10 right you’re guaranteed a…”
“If you get the first 10 wrong you’re guaranteed…”
“We’ve researched it, and if you get the first 10 right vs. the middle 10 right vs. the last 10 right…”

And in either case, people buy the hype without questioning it – or “critical reasoning” it. Think about a 162-game baseball season for a team like the LA Dodgers, who went down in the NLCS by a 3-1 margin. The Dodgers from that point had to win 3 games to advance (they’ve won the first of those and play again tonight), a herculean feat if you believe the SportsCenter anchors and newspaper pundits, but wait – the Dodgers won 3 straight games dozens of times this season. They won well more than 3 in a row several times. Is winning 3 in a row really as big a deal as they say?

The major reasons that it’s so hard to come back from 3-0 or 3-1 are about the same as the reasons that the first 10 questions of the GMAT are so predictive of your score:

1) Losing the first 3 – or answering several of the first 10 questions incorrectly – are a sign of being overmatched.

People forget in sports that it’s not at all uncommon to win 3 or 4 straight. It’s not the daunting nature of *that* feat that makes coming back so hard – it’s doing it against a team that has demonstrated that it’s better than you. You have to beat a team that’s been repeatedly beating you – they’re probably better. Similarly on the GMAT, it’s not that the first 10 questions “matter more” toward your score, it’s more that if you get 8 of them right, you’re probably really good at this GMAT thing, and if you get 7 of them wrong you’re probably not, at least not today. So yes, if you analyze practice tests those who do better in the first 10 almost always score better than those who do worse, but it’s not the order of the questions that does it, it’s what the results are starting to prove – if you don’t have it, you don’t have it.

2) Losing the first 3 – or answering several of the first 10 incorrectly – lower your margin for error.

Another major reason that going down so early in a series, or starting so slowly on the GMAT, tends to correlate with poor results is that in order to recover you have to be a lot closer the rest of the way – you can’t afford mistakes. If you’re down 3-1 in a “4 wins and it’s over” series, you can only afford one more loss until it’s over. You just can’t make mistakes at that point – one ill-timed throwing error, one meatball pitch taken for a home run and even if you’re building momentum you’ve lost it.

It’s similar on the GMAT – you *can* recover from a poor performance on the first 10 questions, but very few do. It’s rare for any student to get 10+ questions right in a row at any point, partially because the adaptive system continues to challenge your upper threshold the more you get right, but also because you’re human…you make mistakes. If your estimated score is lower than you’d like after the 10th question, you may just fall victim to the old sports adage “they didn’t lose, they just ran out of time” – a phrase that applies to teams that try to mount a ferocious comeback and fall just short. If on the quant section you’re behind your goal after 10 questions, you only have 27 more to build that up, and like an itsy-bitsy spider climbing up a water spout, if you slip down a notch or two because of an ill-timed mistake (a slippery spout?) you have that much farther to climb.

Now, all of this serves to show that the myths about GMAT scoring tend to – in classic GMAT Critical Reasoning style – mistake correlation and causation. But there is another actionable lesson here:

You should:

Avoid mistakes in the first 10 questions, even if that means spending a couple extra seconds to double-check your work. Like in best-of-sevens, early struggles dig you a very deep hole that’s tough to climb out of, so it’s important to avoid early “losses” if at all possible. The first 10 questions are worth an extra 90-120 seconds of your time (in total) to make sure you don’t set yourself up for failure.

You should not:

Go “all-in” on the first 10. This is where students succumb to the myth. Say that the Detroit Tigers, having won game 1 of their best-of-seven with Boston, looked at the stats and said “if we win the first 2 on the road we’re all but guaranteed to win the series”. They might, then, have replaced starter Max Scherzer (who gave them 7 great innings before turning it over to the bullpen) with aces Justin Verlander and Doug Fister – the Tigers could have won Game 2 by burning out their superstar arms in relief…but then they’d have had no one left for Games 3, 4, and even 5.

This is what many GMAT students do – they spend 50% more time than they should, or more, on the first 10 questions, because “if you get the first 10 right you almost always end up with a 700+”. That’s mainly true because of point 1 above – those who get 8 to 10 of those first 10 right are usually great test-takers. If you game the system and set yourself up for failure in the last 30 questions, you’re using false correlation and mythology, and you’ll almost always get burned.

So as you watch these best-of-sevens unfold and hear the pundits talk about statistical trends, heed a lesson about GMAT scoring – what you do early does matter a lot, but much more as an indicator of how you’ll perform throughout and less as a direct causation of success. Or as Yogi Berra said best – and we’re not sure if he meant “baseball” or “GMAT” – it ain’t over ’til it’s over.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Breaking Down Factors With Breaking Bad

America has been buzzing for weeks about the last season of Breaking Bad, and the echo effect has taken hold even after this past Sunday’s finale as thousands rush to catch up on Netflix or DVD to get into the hype.

But regardless of where you are in the series, it’s important that you hear this one Breaking Bad spoiler:

Walter White would absolutely kill the GMAT.

For those of us still a season behind (but catching up rapidly) we don’t know yet whether Walter can outsmart the DEA, the Mexican cartel, or the New Mexican cartel (or even Jesse or Skyler for that matter) but we do know that he’d perform extremely well on the GMAT.


In large part because the GMAT has a strong conceptual emphasis on factors, multiples, and prime numbers, and because one of the best ways to understand the concept of prime factors is to see them like a chemist would.

Take the number 12 and the substance ‘water’ for example. Water is H20 = two hydrogen atoms and one oxygen atom. We identify water by H20 because hydrogen and oxygen are as far as you can really break water down without splitting atoms (which isn’t required on the GMAT). Once you’ve taken water all the way down to the atomic level, you know exactly what it takes to make water – two hydrogen atoms and one oxygen atom.

So, for example, if you had 75 hydrogen atoms and 20 oxygen atoms, how many molecules of water – H2O – could you make? You’re limited by the 20 oxygens, so 20 water molecules. Take those 20 oxygens, pair each one with two hydrogens (for a total of 40 hydrogens), and you’ll have enough for 20 water molecules with 35 “free” hydrogen molecules left over.

And in a more complicated example, say you had 5 molecules of propane (C3H8 – 3 carbons and 8 hydrogens per molecule) and 6 molecules of carbon dioxide (C02 – one carbon, two oxygens), how many molecules of water could you make from that mixture (obviously assuming you could break those bonds, etc.). You’ll want to first determine how many molecules of each you have: 5*8 of hydrogen, so 40 hydrogens, and 6*2 of oxygen, so 12 oxygen. So here we have plenty of hydrogen – enough for 20 molecules of water – but only 12 oxygen molecules, so we can only make 12 molecules of water with a bunch of carbon and hydrogen left over.

If you get that about chemistry, you can use that analogy to think about the number 12 differently. We can break a number like 12 down into its “atomic” components, too, via division. 12 is 6 * 2 or it’s 3 * 4, but either way if you keep dividing until you only have prime numbers, you get it down to 2 * 2 * 3, or 2^2 * 3. When you’re talking about factors, multiples, and divisibility, prime numbers play the role of atoms, and instead of H20 you use 2^2 * 3. But the concepts work quite similarly.

Take this question, for example – how many times can you divide the number 12! by 12 and still have an integer remaining?

Much like our water question above, this one can be solved by using an atomic/prime breakdown. To divide by 12, as we know, we need two 2s and a 3. So if we break out 12! into:

12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Our goal, like we did with hydrogen and oxygen above, is to get our 2s and 3s out where we can combine them into 12s. That number line above then becomes:

(2 * 2 * 3) * 11 * (2 * 5) * (3 * 3) * (2 * 2 * 2) * 7 * (2 * 3) * 5 * (2 * 2) * 3 * 2 * 1

That’s ten 2s and five 3s, and we need two 2s and a 3 for each 12, so we can make five 12s.

The GMAT loves questions that deal with factors and multiples in this way – they’re conceptual, they don’t lend themselves well to brute-force calculations – and so being able to think in terms of prime factors is a very important skill. And for the chemistry-inclined, thinking of prime numbers as atoms is a helpful analogy. Factors and multiples work a lot like atoms and molecules – you can combine prime factors in many ways, but astute GMAT “chemists” see the ability to break apart those factors to see what they’re *really* looking at at the prime factor level. So if you’re chasing Harvard crimson or Stanford cardinal the way that Hank and the DEA were chasing blue crystal, borrow a tactic from Walter White and think about the chemistry of factors and multiples.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: No News Is Good News

GMAT Tip of the WeekWe all have a laundry list of answers to the question “what makes Data Sufficiency difficult?” — it’s a unique question type; the math skills involved can be quite tricky; subtle phrasing and precision-in-wording can make huge differences; the situations are often abstract and difficult to conceptualize. But what about a better question – “what makes Data Sufficiency easier?” There are actually quite a few examples of this, and many relate to the Veritas Prep mindset “Think Like the Testmaker”. We can even break it down to one word:


In all actuality, business schools don’t much care whether you can list all the factors of 224 or whether you know that the diameter and tangent of a circle are perpendicular at that point of tangency. What they do care about, though, is your ability to see opportunity – or danger – where others do not; your ability to recognize trends and use them to make decisions; your ability to read your opponent, whether a competitor or a negotiator, and come out on top. And so a great many “difficult” Data Sufficiency questions are written so that they embed clues to help astute test-takers – those with the abilities prized by business schools and employers – avoid trap answers and make good decisions.

One such clue comes in the form of what we’ll call “No News is Good News”, meaning that if the two statements in a Data Sufficiency question provide the exact same information:

-The answer can only be D or E (one can’t be sufficient without the other, and if they say the same thing then there’s no benefit to using both together)
-You now have twice as much time to invest in “the work” on one statement, since that work will cover both statements
-You have an opportunity to save yourself from a bad decision

Let’s investigate all three of those points, but particularly the last one, with an example:

All attendees at a university gathering are faculty or alumni of the university. Are any of the attendees both faculty and alumni?

(1) 3/5 of the attendees are members of the university faculty

(2) 40% of the attendees are not members of the university faculty

Now, many test takers (about half in the Veritas Prep Question Bank, as well as a couple of admittedly-distracted VP staffers seeing this question for the first time) will go through the following progression:

1) 3/5 = 60%, so I see what’s going on here…statement 1 says 60% and statement 2 says 40%

2) (and this is incorrect…more on that in a second) Well if 60% are faculty and 40% are “something else”, and there are only faculty and alumni and no one at this event is “neither”, then it looks like it’s 60% faculty and 40% alumni with no overlap, so the answer must be C, both statements together.

Which isn’t horrible logic, even though it’s incorrect. It’s a relatively understandable progression – but here’s where “No News is Good News” can help. If you really think about it, statements 1 and 2 basically say the same thing. If someone were to ask “what percent of people are not faculty” after statement 1, you’d have to say “well if 60% are, then 40% are not”. So if you think about it, statement 2 doesn’t tell you anything new. So how could the answer be C?

This is your clue to go back and re-investigate and save yourself. Statement 2 doesn’t mean “exactly 40% are alumni”, it only means “40% are not faculty”. So those 40% have to be alumni, but alumni isn’t limited to 40%. That 40% is just “alumni who are not faculty”. Consider the hypothetical that, out of 100 attendees, 60 are faculty, 50 are alumni, and 10 are therefore “both”. That’s perfectly consistent with the statements but doesn’t give you the same number for “both” that you would have had had you picked C.

So the answer is E, but the lesson is probably more important – the fact that the two statements gave you the exact same information was your clue that had you initially thought “C” you had to go back and do some work. When the two statements each tell you the same thing, the answer has to be D or E, and usually that means you have to put in a little due diligence to make sure you choose wisely.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Thinking Like the Testmaker

GMAT Tip of the WeekEarlier this week, in creating a blog post for our friends at Poets & Quants, we wanted to punctuate the Data Sufficiency lesson in the post with a fairly-basic sample problem that would have these four characteristics:

– More than half of users would get it wrong

– Of those users, the vast majority would pick the trap answer that corresponded with one particular mistake, the subject of the post

– After reading the rest of the post, they’d easily understand the mistake they made

– Naturally, the question had to be perfectly valid and the trap answer couldn’t be a “dirty trick” but rather had to be a valuable lesson

Now, you’d think it might be hard to get more than half of users – those who are taking additional time to study for the GMAT, so they’re clearly taking things seriously and putting in the work…this isn’t a late night Leno or Kimmel sketch in which we find the least-educated, least-worldly tourists on Hollywood Blvd. to answer a current events question! – to get a fairly basic question wrong. But in all actuality? It took less than 5 minutes to come up with a question that would end up hitting all those metrics. Upon creating the question we posted it in the Veritas Prep Question Bank and 60% of users to date have gotten it wrong, with just over 50% of users picking the prescribed trap answer. The lesson?

Writing GMAT questions that smart people get wrong is easy, because GMAT test-takers are extremely predictable.

That’s the point of the Veritas Prep “Think Like the Testmaker” theme that reappears through our lessons. The GMAT can bait you into trap answers over and over again, because your mind is predictable. A standardized test lends itself quite well to a standardized set of mistakes. The questions themselves will very often seem unique to you, but the same blueprints come up over and over again for the testmaker. “How do I trap 60% of users? Well, let me dig into my playbook, which includes:

  • Hide a valuable piece of information in the question stem of a Data Sufficiency question. For added effect, make one of the statements just algebra-intensive enough that people have to spend 45 seconds on it and it steals their attention away from that juicy nugget in the question…they’ll have totally forgotten about it.
  • Use a strange – but correct – grammatical structure as the first 5-7 words of the correct Sentence Correction answer, and people will eliminate it quickly and end up choosing between two incorrect answers that both passed the “I prefer this phrasing” test up front.
  • Set up a calculation for a word problem that leads people to solve for an intermediate step first, then make that number – the number they get right before they should take one more step – an answer choice, and prey on those who aren’t keeping track of which question was actually asked.
  • Create a problem that seems like it’s just testing a concept that everyone memorizes via flashcards, but make that memorized concept only one of two correct options.
  • Use a modifier or qualifier to eat up the first 7-10 words of the correct Critical Reasoning answer, knowing that impatient test-takers will quickly make their decision that it’s “out of scope” before reading the whole thing.

These testmaker traps – and more – come up very frequently on the GMAT, but test taker who are paying attention can learn to sniff them out before they fall into them. That’s the payoff to Thinking Like the Testmaker – if you get a geometry question wrong, it’s not necessarily that you don’t know the geometry (although most people will jot down “study more triangles” as their takeaway), as it could very well be that the testmaker beat you by knowing how you think instead.

For example, the lesson in the aforementioned blog post was “make sure you note important information in the question stem of a Data Sufficiency question”. Why? We see it all the time – students are in such a hurry to start “doing math” that they quickly skim through the question stem, then hustle to the statements. And this blueprint will get around half of test-takers just about every time even if the math isn’t that hard:

1) Embed a piece of information in the question stem; make it something that isn’t obvious…that the student will have to think about just a little to make it “actionable”

2) Make one of the statements require multiple steps and “satisfy the intellect” of the test-taker once they’ve finished those steps

3) Make it so that the question stem piece of information is critical

So our question:

If the product xy is not equal to 0, what is the value of x?

(1) y(x^2) + 4xy + 4y = 0

(2) y = 6

How does this fit the blueprint?

1) That “xy is not equal to 0” line requires just a bit of unpacking. For xy to not be 0, neither x nor y can equal 0.

2) In order to unravel the quadratic in statement 1, you have to do a few steps of factoring:

Factor the common ys: y(x^2 + 4x + 4) = 0
Notice that the x terms form a common quadratic – it’s (x + 2)^2 —> y(x + 2)(x + 2) = 0

By this point, many have forgotten about the fact that y can’t be 0. They may still look at this and say “either x = -2 or y = 0”, and the stats show that more than half of users don’t think this is sufficient. The main reason? They haven’t unpacked that question stem – had they, they could eliminate y = 0 as a possibility (meaning x must be -2) or they’d have just divided both sides by y in the original (you can’t do that if y might equal 0, but since we know it can’t you can divide it out) and been done with y forever. Most people (52% or so) pick C, and several pick E (perhaps not seeing that there’s only one solution for x).

The bigger lesson? It pays to not just see your mistakes in terms of content – those who picked C on this problem do not have a major problem with quadratics! In order to pick C, you have to be able to factor out statement 1 and realize that there’s only one value of x. If you picked C – as most do – you didn’t get beaten on content, you got beaten because the GMAT knew it could sneak xy isn’t 0 past you in the question stem. So as you study, pay attention to your mistakes and Think Like the Testmaker. The more you recognize these blueprints for trap answers, the bigger you’ll smile when you see the GMAT setting you up for them.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Why Johnny Manziel Would Beat the GMAT (but maybe not Bama)

GMAT Tip of the WeekHeading into this weekend’s giant Alabama vs. Texas A&M game, college football fans are probably as sick of hearing about Johnny Manziel as aspiring MBAs are of studying for the GMAT. But both, at least to some degree, are necessary evils – Manziel represents the best chance that football fans have of seeing someone other than Alabama playing for the national championship, and the GMAT is essential to a well-rounded MBA application. And there’s an overlap between the two – Manziel’s playing style can help you learn to beat the daunting GMAT the same way that he’s the only recent QB to beat that daunting Alabama defense. Here’s how summoning your inner Johnny Football can help you become Johnny (or Jenny) GMAT:

1) He can improvise

Manziel is most dangerous when the play breaks down and he has to create on his own outside of “the system”. He can check out of the assigned play call, scramble backward, decide to run and change his mind at the last minute when a receiver is open, or decide to pass and then at the last minute see that cornerback closing and tuck the ball to run like crazy for the pylon. Like any good GMAT test-taker, Manziel knows how to stick to the playbook when the first option is there, but he’s able to change gears when it becomes clear that the defense – or the question – has shifted into something entirely different.

The GMAT requires you to improvise, to realize on the fly that your first inclination might not work but that there’s another angle you can try. The GMAT rewards flexibility and the ability to almost make a mistake but learn from it in the moment. On quant questions, the algebra may lead you down a path that actually gets messier, and you might realize that it’s time to plug in some answer choices. Or your first sentence correction decision point may leave you with two flawed answers, and you’ll need to go reinvestigate answers you’ve eliminated. Hard GMAT questions will often force you to use a second strategy – those who have practiced with flexibility will have the advantage.

2) He’s not afraid to push the limits when it comes to rules

Manziel spent most of the summer testing authority and pushing the limits of the rules. And by doing so he was able to see just how far he could push the limits and get away with it, whether it was signing autographs for money (allegedly) or doing a little underage drinking / drug-experimentation on his rivals’ campus in Austin (also allegedly). He’s no worse for the wear – the NCAA helped keep him healthy by resting him during the Rice game – and showed you an important strategy for the GMAT…you have to push the limits when it comes to the rules. Like Manziel, the GMAT loves to play to the edges.

When a GMAT question gives the stipulation that “x is positive”, it’s up to you to push the limits – how small can you go? 0.00001? How high can you go? Infinity? Pushing boundaries is the key on many Data Sufficiency questions, like:

Is y > x?

(1) y = x^3

(2) x > 0

In your investigation of statement 1, you might quickly recognize “sure, if x = 2, then y’s bigger…but what about a negative? If x = -2, then y = -8, so negatives are the gamechangers.” And then with statement 2 (which should clearly be insufficient on its own), a lesser Man might say “oh, well together they’re sufficient because I can’t use negatives anymore”. But a full-fledged Manziel would push the limits a little: x can’t be negative, but what if it’s only hair over 0, like 1/4. 1/4 to the third power is 1/64, which is smaller. So y could still be smaller than x if we push the limits and go as small as the statements will let us go – the answer is E, but you have to get there by challenging the statements as far as they’ll let you.

3) He’s cocky

Manziel wasn’t intimidated running out the tunnel in Tuscaloosa last year, playing the defending national champions with a massive NFL-bound defensive line in front of a rabid fanbase. And he wouldn’t be intimidated by having his palm scanned and his digital photograph taken at the Pearson/VUE GMAT test center, either. Manziel is confident – to a fault, many college football enthusiasts would argue, but confident nonetheless. He trusts his instincts and like all good quarterbacks he’s able to leave a bad play behind him to focus on the next play.

To succeed on the GMAT, you need to be able to do that, too – to not be intimidated by convoluted-looking questions (start with what you know) and to not let one bad question unravel your confidence for the next question. Confidence is important, but you don’t have to be an impossibly cocky quarterback to summon the practical things that Manziel does well:

  • Know that everyone misses several questions. A mistake or two won’t kill your score, so stay upbeat and trust yourself.
  • Remember that if you’re nervous, that’s just your body’s adrenalin preparing you for peak performance. Nerves and anxiety are a biological response to the expectation of success – no one gets nervous buying a lottery ticket or Tweeting their celebrity crush, but you do get nervous when you’re asking for a promotion you think you deserve or when you’re asking out that girl from the coffee shop who has been flirting with you.
  • Don’t let what looks like an “easy” question seem like an indicator that you’re not doing well. Maybe it’s just easy for you, maybe it’s experimental, or maybe it’s harder than it looks. There are plenty of explanations for why that question might look easy even though you’re doing extremely well.
  • Don’t let hard questions get you down. You’ve earned them by doing well!
  • Don’t be afraid to guess. Like Manziel, sometimes you have to throw it out of bounds on second down to avoid the sack and make for a manageable third down. On the GMAT, spending 4-5 minutes on an impossible problem can leave you rushing later on, making silly mistakes that hurt your score a lot more. Guessing is ok – in many cases it’s strategically the right move.

Whether you’re an avid member of Texas A&M’s 12th Man, you greet people every morning with “Roll Tide”, or you’re somewhere in between, you can use the hype for this weekend’s Alabamanziel-apalooza to your advantage, studying how Johnny Manziel’s demeanor and ability can help you conquer the GMAT.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Get Exxxtreeeme!!!! on Logic-Based Math Questions

GMAT Tip of the WeekWhat do Mountain Dew, Tough Mudder, and Data Sufficiency have in common? Maybe they’re your plans for this weekend, but more universally they all lend themselves to the mentality, lifestyle, and even spelling of the eXXtreme!! And while we could fill this space with extreme-to-the-max tips about Mountain Dew (please don’t drink it for breakfast, high school students) and Tough Mudder (bring your wallet…their marketing is as extreme as the event itself), it’s more helpful to show you how taking it to the extreme can help you succeed on logic-based quant questions.

The name if the game with Data Sufficiency is “must be true”, as in “you have sufficient information to answer the question if the same answer must be true in all allowable cases”. So if you get a question like:

Is x^2 greater than 16?

With a statement like:

(1) x < 4

While the “obvious” values of x might be 3 (which squared is 9, so “no”) and 2 (which squared is 4, so also “no”), you’ll be rewarded for thinking of more-extreme answers allowed by the facts (what about a really, really negative number like -100: its square root will be very big and very positive, so that can give you your “yes”, making this statement not sufficient).

The GMAT likes to play to the extremes when it gives you limits on Data Sufficiency and “must be true” Problem Solving problems. When they give you the stipulation that x > 0, a wise test taker won’t start thinking only at 1 (what about a tiny fraction like 1/10?) and won’t stop thinking at 9 or 10 (what about a million?). The GMAT will reward you for pushing the limits of the possible range of values, and by that same token punish you if you stay within the typical comfort zone.

Consider this example:

If a, b, and c are consecutive odd positive integers and a < b < c, which of the following must be true?

I. at least one of the three numbers is prime
II. ab > c
III. a + b + c = 3b

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

For this question, most test-takers realize quickly that statement III must be true, as for consecutive odd integers, c will equal b + 2 and a will equal b – 2, so they’ll net out to 3b.

Statement II can be eliminated by going to the lower extreme: 1(3) is not greater than 5, but for all other versions (3*5 is greater than 7; 5*7 is greater than 9, etc.) the answer is “yes”. You have to go to the low extreme to eliminate statement II.

Statement I is the crux of this problem – about 70% of all respondents to this question in the Veritas Prep Question Bank see statement I as definitely true, when in fact it’s not. Their mistake? They don’t go to extremes. With two-digit numbers, at least one of every three odds in a row is prime. But that’s just because there aren’t enough numbers to be divisible by. There are only 14 multiples of 7 and 9 multiples of 11 within that set, meaning that you’re leaning extremely heavily on factors of 3 and 5 to find odd numbers that aren’t prime. But by the time you hit triple digits, there are plenty of potential factors, and prime numbers become much more rare. Consider 121, 123, and 125 – none are prime. If you go high enough in your search – with some logic behind it – you can fairly easily prove statement 1 not to be true. And the technique for doing so is to recognize that it’s easy to find multiples of 5 (if a number ends in 5, it’s an odd multiple of 5) and multiples of 3 (if the sum of the digits of a number is a multiple of 3, that number is divisible by 3). So you want to find multiples of 7 or 11 that don’t end in 5 and make those your starting point. 11-squared works perfectly – it’s only divisible by 11 – and then you can check two odds in either direction to see if they pass the 3s and 5s tests. 217 is another great one – you know that 210 and 7 are both divisible by 7, and then next to that you can find 215 (divisible by 5) and 213 (divisible by 3).

The problem with this problem is that people don’t look to the extremes. They’re relatively happy to check 3-4 sets of one and two digit numbers and feel that they’ve proven a trend, whereas on Must Be True questions it pays to get extreme.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Spend Your Labor Day Making Quant Problems Less Labor-Intensive

GMAT Tip of the WeekSo it’s Labor Day weekend, and hopefully you’ll celebrate by relaxing. But wait – Harvard’s admissions deadline is only about two weeks away, and Stanford’s is soon to follow, and within the next six weeks most top 20 programs will begin reviewing Round One applications.

So maybe you can’t afford to put your feet up just yet – maybe you do have to use your day off on Labor Day to start working toward your next career. But if you do decide to do some GMAT labor on Labor Day, keep in mind that you can still honor the spirit of the holiday, a day for the working man to celebrate the fruits of his labor by resting. You can practice GMAT math in the least labor-intensive way possible.

Two of the most common ways to reduce your workload on GMAT quant problems are:

  • Recognize “number properties”. If you can note that the correct answer must be negative (vs. positive) or odd (vs. even) or end in a certain digit, often you can avoid doing all the math and just follow the pattern to the correct answer.
  • Use the answer choices. If you can get away with an estimate, or eliminate certain answer choices for not having the right characteristics, or plug answer choices back into the problem (“backsolve”) to avoid doing the algebra, you can let the answer choices guide you away from hard labor.

So let’s look at an example of a problem for which the two above strategies can help us avoid some excess workload:

What is the square root of (x^2 * y^2) if x < 0 and y > 0?

(A) -xy
(B) xy
(C) -(absolute value of (xy))
(D) (absolute value of y)(x)
(E) Cannot be determined

Now, this problem can be solved using algebra but it may look a little intimidating that way, too. And algebra can lead to labor if you’re not careful. But you have clues:

*The presence of “x < 0”, “y > 0”, and two absolute value signs in the answer choices should indicate that this is a positive/negative number properties problem. The actual values of x and y don’t matter much (there are no actual values given anywhere in the problem) as long as you can figure out whether the right answer needs to be negative or positive, and whether each answer choice gives you that correctly. So in a case like this, you can avoid strange, conceptual algebra by picking numbers consistent with the stipulations in the problem:

x must be negative, so let’s call it -2
y must be positive, so let’s call it 3
Note: by avoiding 1 and -1 we avoid numbers with really unique problems, and since we’re squaring/rooting numbers by using a different base (2 vs. 3) for each we can more easily track the importance of each variable.

With x = -2 and y = 3, then inside the radical we have (-2)^2 * (3)^2 = 4 * 9 = 36. And the square root of 36 is 6, so we know that in our situation the result of that operation is 6. Now we can plug those numbers into the answer choices to see if we get 6:

(A) -(-2)(3) = 6, so A could work

(B) -2(3) = -6, so B is wrong

(C) The absolute value of -2(3) is 6, so -(6) = -6 and C is wrong

(D) The absolute value of 3 is 3, so it’s (3)(-2) = -6, so D is wrong

So of those answer choices, only A works, so A is correct.

More important is the takeaway – on this problem, if you can see that actual numbers aren’t as important as the number property, positive vs. negative, you can avoid having to do all the algebraic work in search of a solution and instead you can test numbers to see what type of positive/negative you need. Heeding these kinds of clues and using the answer choices to your advantage can help you avoid plenty of undue labor. So if you’re working on the GMAT this Labor Day, keep these strategies in mind and you’ll be able to avoid too much hard work on Test Day, a holiday that at least this year might matter all the more.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

Tales From the Question Bank: Pros Before Idio-es

GMAT Tip of the WeekThe Veritas Prep Question Bank offers unique insights in to the habits of GMAT test-takers; while students from around the world answer free GMAT practice questions, the Question Bank tracks patterns in the answers that the world selects, and in this series we’ll highlight valuable lessons that you can learn from the statistical analysis of how people choose their answers.

For this post, we’ll tackle the Sentence Correction question below. Try your hand at this question, and below we’ll reveal the user statistics and break down what we can learn from them.

The data being collected in the current geological survey are providing a strong warning for engineers as they consider the new dam project, but their greatest importance might lie in how they influence the upcoming decision by those same engineers on whether to retrofit 75 bridges in the survey zone.

(A) The data being collected in the current geological survey are providing a strong warning for engineers as they consider the new dam project, but their greatest importance

(B) The data being collected in the current geological survey provide a strong warning for engineers as they consider the new dam project, but its greatest importance

(C) The data collected in the current geological survey is providing a strong warning for engineers as they consider the new dam project, but their greatest importance

(D) The data collected in the current geological survey provides a strong warning for engineers in consideration of the new dam project, but its greatest importance

(E) The data collected in the current geological survey provide a strong warning for engineers in consideration for the new dam project, but the greatest importance

Savvy test-takers will note a couple major differences between the answer choices:

-Two answer choices use the word “being” in “being collected”, and three do not (they simply omit that)
-Two answer choices use the pronoun “its” toward the end, and two use “their” (one omits the pronoun completely)

How did people tackle these decision points? Let’s take a look at the data:

A few noteworthy stats:

-Over 75% of users avoided the word “being”, which is *usually* incorrect on the GMAT (but then again it is an actual word, so it has to be used correctly in some function of speech, right?)
-About half of users went for “its” and a little more than a quarter for “their”

And the correct answer? It uses “being” and “their”, the two most unpopular decisions. So what can you learn from this?

It appears that most users made their first decision to eliminate “being”, which has a reputation in the GMATsphere for *being* (intentional) wrong. But here’s the thing – “being” can be correctly used as a present-tense verb, a noun (as in “human being”), and other contexts. Ain’t ain’t a word, but being is. There are a handful of these pieces of GMAT wisdom (that often start with the phrase “the GMAT prefers” or “the GMAT doesn’t like”) that actually aren’t terrible advice, they’re just awful first decisions. If you’re down between two answers and the only striking difference you see is that one of them uses “being”, odds are you should eliminate that one. But as a primary decision you can do better.

For the next decision, it appears that people attempt the “data…its” vs. “data…their” distinction by trying to determine whether data is singular or plural. Which isn’t a bad strategy – but when singular/plural decisions are to be made and appear tricky (words like “data”, “deer”, “fish”, etc. can be both), the GMAT very often cleverly hides a controlling word away from the underline. And here they do that – look at “…how they influence” a few words after the underline. That “they” can only apply to “data” (“engineers” are referred to separately in that same thought). So there is a binary decision point here – data is set by that outside-the-underline pronoun to be “their”, which eliminates B and D (the most popular answer). Then with choice C mixing singular/plural (“their” but “is providing”), you’re left with a tougher decision between A and E.

Here’s where “being” is perfectly okay and consistent – if the data are “being collected” and “are providing” valuable information about an “upcoming decision”, that present-tense “being” completely works. And it’s actually more specific and clear than the wording in choice E – in E “the greatest importance” is ambiguous…what’s important? In A, we know the data have one primary significance, and we also get a clear sense of the timeline – they are currently being collected and continuing to provide value.

So A is correct, but more important is what you can learn from the stats taken from your peers:

1) Pronoun decisions are much more binary and concrete than “idiomatic” decisions like “being” and others. In this question, many users missed it because they made that “being” decision first and eliminated the right answer immediately.

2) When making singular/plural decisions that seem more difficult than they should be, look past the underlined portion to see if there’s a smoking gun elsewhere – a fixed pronoun or verb that removes all doubt.

Remember, also, that the official GMAT complies this type of data and much, much more, so the authors of GMAT questions know that test-takers have certain exploitable tendencies. You can be certain that the GMAT is paying attention to data like this; make sure that you learn from your mistakes (and those of others) to gameplan for the test.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: What Does the Median Mean?

GMAT Tip of the WeekStatistics-based GMAT questions can be tricky, particularly for those who haven’t been formally trained in stats or for those whose knowledge of statistics is more incomplete than they realize. One concept for which many students have blind spots is that of the median, so let’s take a moment to identify and explain a few of these common knowledge gaps.

For starters, everyone taking the GMAT likely knows that the median is the “middle number” in a set of data, and that to find that middle number you have to first sort the values in order. So for a set:

{2, 5, 1, 3, 4}

The median isn’t 1, the middle number as it’s displayed above, but rather 3, the middle number once the data set has been sorted in order as: {1, 2, 3, 4, 5}.

Further, everyone likely knows that if there are an even number of terms, the median is the average of the two middle terms. So in the set {2, 4, 6, 8, 10, 12}, the median is the average of 6 and 8, which is 7.

But here are a few things that people who flip through that section of their prep book and think “median, yeah that’s easy” often tend to overlook and miss:

1) The median doesn’t have to be BETWEEN two other numbers

Take the set {7, 10, 12, x, 17, 19, 22}, in which x is defined as the median. You might look at that and think “oh, x has to be between 12 and 17”. But that’s not necessarily true. If x were 12, the set would list as: {7, 10, 12, (x =) 12, 17, 19, 22} and 12 would still be the 4th out of 7 numbers. x could match either 12 or 17.

This can be extremely important on Data Sufficiency questions. If the question were “Is x > 12?” and you were told that x is the median of that set, you’d be very much tempted to say that it has to be greater than 12. But remember – the median of a 7 term set doesn’t have to be between the 3rd and 5th terms; it could match one of those.

2) The median also means “an equal number of terms above and below”

This definition works with “the middle number” but it adds another level of conceptual understanding that can help you on challenging problems. Consider the problem:

Sets A, B, and C are combined together to create set J. What is the median of set J?

1. The medians of sets A, B, and C are all 25
2. Sets A, B, and C each have the same number of terms

You might very well be tempted to think that you need statement 2, but as it turns out statement 1 is sufficient alone based on that extra definition above. If sets A, B, and C each equally divide their terms above and below 25, then 25 will remain the median of the new combined set. You can see it with numbers:

Set A: {21, 23, 25, 27, 29} — two terms below 25, two terms above 25, one term is exactly 25
Set B: {24, 26} — one term below 25, one term above 25

Just seeing this, you should note that the new set will now have three terms below 25, three terms above 25, and the middle term is 25. Or if all the sets had an even number of values:

Set B: {24, 26}
Set C: {10, 20, 30, 40}

Note that when you combine them, the “innermost” pair of numbers that will form the middle two both come from Set B, keeping the median at 25. Any way you do this, the average will stay at 25.

So remember – in addition to “the middle term”, median also means “an equal number of values above and below”.

3) In an evenly spaced set, the median equals the mean

When a set is evenly spaced (such as “consecutive even numbers” or “consecutive multiples of 7”, the median and the mean will be the same. So in a set like:

{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}

if you want to find the average, you don’t actually have to add up all 15 values and divide by 15, you can instead just find the 8th value and that will be the average. The average will be 16.

Where this can be extremely helpful is when you’re asked to determine the sum of a set of evenly spaced values, such as in the question:

What is the sum of all the even numbers between 0 and 100, inclusive?

You can here use the average calculation that Average = Sum of values / Number of values, solving for the sum. You know that the average will be the middle number, 50, so then you just have to find the number of values (which is 51, calculated as the range (100) divided by 2 (since you only want every other number), plus one for “inclusive”). The answer is then 51*50, or 2550.

Knowing that you can use the median to your advantage this way can save you valuable time.

In summary, don’t let your knowledge of Median stop at just “the middle number”. It’s more than that, and savvy test takers can raise their score well above the GMAT’s median value by taking advantage of a more thorough understanding.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Trial, Error, and Success

GMAT Tip of the WeekOne of the most fascinating parts of being a GMAT instructor is getting to watch successful adults relive the math they did as kids. In many cases, an instructor can actually see that concept or point in time when the student stopped trying to really understand the math and just started relying on that combination of memorization and partial credit to get their Bs in math and search for a career path that would include no more of it. How many students decided at some point in junior high or high school that they just weren’t a “math person”?

While that’s sad on so many levels, it’s a particular challenge for many GMAT students in that somewhere down the line the binary nature of math – there’s always exactly one right answer, as opposed to an essay that you can write and back up your opinion of “To Kill A Mockingbird” in English – taught them that there wasn’t much value in trial and error. You either had the right answer or you didn’t, but for many math was never a discussion or a process. And so directly related to the GMAT the lesson that many students never embraced is this:

On the GMAT quant section, it’s okay to try and fail. And actually it’s more than okay – it’s absolutely necessary on some questions.

GMAT math is often not about “how DO I do this problem?” but much more about “how MIGHT I do this problem?”. There’s no one blueprint for most questions, but rather you need to be able to try out a concept and see if your reasoning holds up. Consider an example:

If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

(A) 51
(B) 54
(C) 72
(D) 162
(E) 50! + 2

Now, this is a unique problem structure – were you to see this problem on the test, you wouldn’t likely have seen a problem written all that closely to it before, so you probably don’t have a direct method to be able to solve it. For most of us, the thought process will have to include some trial and error. You may just have to have a conversation with yourself, thinking of numbers and trying to determine whether or not they’ll work:

-How about 51…I know that all the numbers 1 through 50 are factors of 50!. But wait – 51 is 3*17, and so both of those are factors of 50! so 51 doesn’t wok.
-How about 52 – well, no, that’s even and can quickly be broken down into 2*26, both factors of 50!.
-53 is prime and it’s bigger than all the individual components of 1*2*3*4*…49*50, so it would work. But wait – the question specifically says that it can’t be prime.
-If you keep going with other numbers like 54 (27*2) and 55 (5*11), if they’re not prime they’ll have smaller factors that fit within 50!, and if they are prime, well, the definition of the problem says they don’t work. So how do I lean on that smallest prime number of 53?
-Oh, I can make it “not prime” by multiplying it by the smallest possible number, 2, and then I have 106. It’s not a factor of 50! and that’s as small as you can get. So factor it out: 1, 106, 2, 53, and the sum is 162, answer choice D.

Now the takeaway from this – very few people will have a system to pick up that 106 is that number in question, but by thinking through several “wrong” numbers and finding out why they don’t work, you can incrementally develop a better understanding of the framework and lead yourself to the right number. Math is a conversation in many cases. So if a problem looks complicated and you don’t have a formula or system ready to go, start trying things and holding them up to logic until you realize that you’ve stumbled on the method. GMAT math requires a lot of trial and error. Often you need to fail in order to succeed on that very same question.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin