However…

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

- Do the numbers have to be integers?
- Is zero a possible value?
- Are repeat numbers possible?

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

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

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

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

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

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

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

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

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

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

**Question 1:**

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

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

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

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(D) EACH statement ALONE is sufficient to answer the question asked

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

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

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

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

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

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

**Question 2:**

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

(A) $40,000

(B) $41,667

(C) $42,000

(D) $50,000

(E) $60,000

Here ask yourself the same questions:

1) The numbers do not have to be integers.

2) Zero is theoretically possible (but probably constrained by the 20% difference restriction)

3) Numbers absolutely can repeat (which will be very important)

4) What’s your strategy? If you want the LOWEST possible single salary, then use your answer to #3 (they can repeat) and give the other 20 salaries the maximum. That way your calculation looks like:

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

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

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

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

*By Brian Galvin*

Why?

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

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

a_______b________c

3_______4________5

5______12_______13

x_______x______x*(sqrt 2)___(in an isosceles right triangle)

x____x*(sqrt3)___2x________(in a 30-60-90 triangle)

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

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

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

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

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

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

What is the perimeter of triangle ABC?

(1) Side AB measures 5 meters.

(2) Side AC measures 12 meters.

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

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

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

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

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

(A) 100

(B) 120

(C) 140

(D) 150

(E) 165

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

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

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

*By Brian Galvin*

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

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

*By Brian Galvin*

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

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

(A) 3

(B) 6

(C) 7.2

(D) 7.8

(E) 9

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

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

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

So…the answer is E. Right?

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

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

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

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

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

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

*By Brian Galvin*

Wait for it.

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

How?

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

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

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

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

Correct:

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

Incorrect:

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

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

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

Signals of verb tense: since, from, until

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

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

*By Brian Galvin*

1) What is the VIN number on your car?

2) What is your health insurance policy number?

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

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

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

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

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

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

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

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

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

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

*By Brian Galvin*

Derek Jeter’s final game at Yankee Stadium?

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

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

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

Step One: Somewhat difficult statement that takes some work but “satisfies your intellect” as the 650-and-up crowd finally realizes why it’s sufficient. (i.e. Jeter’s double and reached-base-on-error to set up a Yankee win)

Step Two: A much easier statement that seems a mere formality to deal with, but that for the truly elite (i.e. Jeter) provides an opportunity to really shine (i.e. the blown save in the top of the 9th)

Step Three: The chance for the hero to deliver.

Consider this problem:

What is the value of integer z?

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

(2) x is not a prime number

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

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

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

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

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

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

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

The real takeaway here?

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

*By Brian Galvin*

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

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

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

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

Hit, Out, Out, Out

Out, Hit, Out, Out

Out, Out, Hit, Out

or episodes with multiple hits:

Out, Hit, Hit, Out, Out

Hit, Out, Hit, Out, Hit, Out

or even

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

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

Out, Out, Out

Which has a probability of:

3/4 * 3/4 * 3/4

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

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

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

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

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

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

4) Subtract that total from 1

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

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

*By Brian Galvin*

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

**1) Check your work and be thorough.**

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

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

**2) Know when to give up and guess.**

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

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

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

Quant Section

After question 10 you should have approximately 53 minutes left

After question 20, approximately 33 minutes left

After question 30, approximately 13 minutes left

Verbal Section

After question 10, approximately 56 minutes left

After question 20, approximately 37 minutes left

After question 30, approximately 18 minutes left

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

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

*By Brian Galvin*

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

**1) Why was the right answer right?**

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

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

**2) Why was my answer wrong?**

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

**3) Why was my wrong answer tempting?**

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

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

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

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

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

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

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

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

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

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

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

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

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

*By Brian Galvin*