# GMAT Tip of the Week: Percents Are Easy, Words Are Hard

Pop quiz: 1) Your restaurant bill came to exactly \$64.00 and you want to leave a 20% tip. How much do you leave? 2) You’re running a charity half-marathon and your fundraising goal is \$6000. You’ve raised \$3300. What percent of your goal have you reached? 3) Your \$20,000 investment is now worth \$35,000. By what percent has your investment increased in value?

If that was easy for you, good. It better have been. After all, you’re applying to graduate school and that’s maybe 6th grade math in three real-life contexts. Percents are not hard! But percent problems can be. And that’s what savvy GMAT test-takers need to learn:

On the GMAT, percent problems aren’t hard because of the numbers. They’re hard because of the words.

Consider two situations:

1) A band sells concert t-shirts online for \$20 each, and in California, web-based sales are subject to a 10% sales tax. How much does a California-based purchaser pay in sales tax after buying a t-shirt?

2) At a concert in California, a band wants to sell t-shirts for \$20. For simplicity’s sake at a cash-only kiosk, the band wants patrons to be able to pay \$20 even – hopefully paying with a single \$20 bill – rather than having to pay sales tax on top. If t-shirts are subject to a 10% tax on the sale price, and the shirts are priced so that the after-tax price comes to \$20, how much will a patron pay in sales tax after buying a t-shirt?

The first, quite clearly, should be \$2. Take 10% of the \$20 price and there’s your answer. And taking 10% is easy – just divide by 10, which functionally means moving the decimal point one place to the left and keeping the digits the same.

The second is not \$2, however, and the reason is critical to your preparation for percent questions above the 600 level on the GMAT: the percent has to be taken OF the proper value. Patrons will pay 10% OF the before-tax price, not 10% of the after-tax price. \$20 is the after-tax price (just as \$22 is the after-tax price in the first example…note that there you definitely did not take the 10% of the \$22 after-tax price!). So the proper calculation is:

Price + 10% of the Price = \$20

1.1(P) = 20

P = 20/1.1 = 18.18

So the price comes out to \$18.18, meaning that \$1.82 is the amount paid in tax.

While the calculation of 20/1.1 may have been annoying, it’s not “clever” or “hard” – the reason that many people will just say \$2.00 to both isn’t that they screwed up dividing \$20 by 1.1, but instead because they saw a percent problem with two numbers (10% and \$20) and just “calculated a percent.” That’s what makes the majority of GMAT percent problems tricky – they require an attention to detail, to precision in wording, for examinees to ensure that the (generally pretty darned easy) percent calculations are taking the percent of the proper value.

They’re logic puzzles that require a bit of of arithmetic, not simple arithmetic problems that just test your ability to divide by 10 absent critical thought. So as you approach GMAT percent problems, remember that the math should be the easy part. GMAT percent problems are often more about reading comprehension and logic than they are about multiplication and division.

By Brian Galvin.

# GMAT Tip of the Week: Your GMAT Verbal (Donald) Trump Card

The general consensus coming out of this week’s Democratic debate for the 2016 U.S. Presidency was this: the Democrats were quick to defend and agree with each other, particularly in contrast to the recent Republican debates in which the candidates were much more apt to attack each other.

The Democrats discussed, but the Republicans DEBATED, fiercely and critically. And – putting politics aside – one of the main issues on which those Republican candidates have attacked each other is “who is the more successful CEO/entrepreneur?” (And the answer to that? Likely Wharton’s finest: Donald “You’re Fired” Trump.)

So as you watch the political debates in between GMAT study sessions, keep this in mind: on the GMAT verbal section, you want to think more like a Republican candidate, and if possible you want to think like The Donald. Trump thinking is your Trump card: on GMAT verbal, you should attack, not defend.

Why?

Because incorrect answers are very easy to defend if that’s your mindset. They’re wrong because of a small (but significant) technicality, but to the “I see the good in all answer choices” eye, they’ll often look correct. You want to be in attack mode, critically eliminating answer choices and enjoying the process of doing so. Consider an example:

From 1998 to 2008, the amount of oil exported from the nation of Livonia increased by nearly 20% as the world’s demand soared. Yet over the same period, Livonia lost over 8,000 jobs in oil drilling and refinement, representing a 25% increase in the nation’s unemployment rate.

Which of the following, if true, would best explain the discrepancy outlined above?

A) Because of a slumping local economy, Livonia also lost 5,000 service jobs and 7,500 manufacturing jobs.

B) Several other countries in the region reported similar percentages of jobs lost in the oil industry over the same period.

C) Because of Livonia’s overvalued currency, most of the nation’s crude oil is now being refined after it has been exported.

D) Technological advancements in oil drilling techniques have allowed for a greater percentage of the world’s oil to be obtained from underneath the ocean floor.

E) Many former oil employees have found more lucrative work in the Livonia’s burgeoning precious metals mining industry.

The paradox/discrepancy here is that oil exports are up, but that jobs in oil drilling and refinement are down. What’s a Wharton-bound Trump to do here? Donald certainly wouldn’t overlook the word “Critical” in “Critical Reasoning.” Almost immediately, he’d be attacking the two-part job loss – it’s not that “oil jobs” are down, it’s that oil jobs in “drilling AND refinement” are down. Divide and conquer, he’d think, one of those items (either drilling or refinement) is bound to be a “lightweight” ready to be attacked.

Choice A is something that you could talk yourself into. “Hey, the economy overall is down, so it only makes sense that oil jobs would be down, too.” But think critically – you ALREADY know that the oil sector is not down. Oil exports are up 20% and global demand is soaring, so these oil jobs should be different. Critical thinking shows you that the general economy and this particular segment are on different tracks. Choice A does not explain the discrepancy.

Choice B is similar: if you’re looking for a reason to make it right, you might think, “See, it’s just part of what’s going on in the world.” But again, be critical. This is a bad answer, because it overlooks information you already have. Livonia’s oil exports are up, so absent a major reason that those exports are occurring without human labor, we don’t have a sound explanation.

Choice C hits on Trump’s “divide and conquer” attack strategy outlined above: if a conclusion to a Critical Reasoning problem includes the word “AND” there’s a very high likelihood that one of the two portions is the weak link. So fixate on that “and” and try to find which is the lightweight. Here you see that the oil is being exported from Livonia, but no longer being REFINED there. Those are the jobs that are leaving the country, and that explains why exports could be up with employment going down.

Choice D is tempting (statistically the most popular incorrect answer choice to this problem, with Trump-like polling numbers in the ~25% range). Why? Because you’re conditioned to think, “Oh, they’re losing jobs to technology.” So if you’re looking to find a correct answer without much critical thought and effort, this one shines like a beacon. But get more critical on the second half of the sentence: it’s not that technology makes it easier to obtain oil without human labor, it’s that technology is allowing for more drilling from the ocean. But that’s irrelevant, because, again, Livonia’s exports are up! So whether it’s Livonia getting that seafloor oil or other countries doing so, the fact remains that with oil exports up, you’d think that Livonia would have more jobs in oil, and this answer doesn’t explain why that’s not the case.

Here it pays to be critical all the way through the sentence: just because the first few words match what you think you might want to hear, that doesn’t mean that the entire statement is true. Think of this in Trump terms: Megyn Kelly might start a sentence with, “Mr. Trump, you’re arguably the most successful businessman of your generation,” (and you know Trump will love that) but if she follows that with, “But many would argue that your success was largely a result of your father’s money and that your manipulation of bankruptcy laws is unbefitting of an American president,” you know he’d be in attack mode immediately thereafter. Don’t fall in love with the first few words of an answer choice – stay ready to attack at a moment’s notice!

And choice E is similarly vulnerable to attack: yes some oil employees may have taken other jobs, but someone has to be doing the oil work. And if unemployment is up overall (as you know from the stimulus) then people are waiting to take those jobs, so the fact that some employees have left doesn’t explain why no one has filled those spots. When Donald Trump had to surrender his post as the star of The Apprentice, Arnold Schwarzenegger was ready to take his place; so, too, should unemployed members of the labor pool in Livonia be ready to take those oil jobs, absent a major reason why they wouldn’t, and choice E fails to present one.

Overall, your job on GMAT Verbal is to be as critical as possible. You’re there to debate the answer choices, not to defend or discuss them. As you read the conclusion of a Critical Reasoning problem, you want to be scanning for a “lightweight” word or phrase that makes it all the more vulnerable to attack. And as you read each answer choice, you shouldn’t be quick to see the good in the sentence, but instead you should be probing it to see where it’s weak and vulnerable to attack.

Let the answer choices view you as a bully – you’re not at the GMAT test center to make friends. Always be attacking, always be looking for words, phrases, or ideas that are an answer choice’s undoing. Trump logic is your Trump card, take joy from telling four of five answer choices “You’re Fired.”

By Brian Galvin.

# GMAT Tip of the Week: What To Do When The GMAT Gets All Netflix On You

Picture this: a friend texts you and asks, “Do you want to get a pizza and watch a movie after work?”. Do you find that odd at all?

But now picture this: that same friend asks, instead, “Do you want to get a pepperoni, mushroom and olive pizza with white sauce on thin crust from Domino’s and watch a Critically-Acclaimed Inspiring Underdog movie on Neflix after work?”. That’s strange, right? And why is that? Because it’s so specific.

Well, on the GMAT you’ll often see questions that ask for something oddly specific; “What is the value of x?” is pretty normal, but “What is the value of 6x – y?” is the equivalent of the specific pizza and odd Netflix category question. Why did they ask that? Often that’s a clue, and if you notice that clue it will help you better set up the problem. Consider this example:

Reflect on what this question is asking about. Not x. Not y. But to paraphrase Netflix, “a partially coefficiented combination of additive variables with a strong horizontal lead.” 6x – y. That’s oddly specific, so your first inclination should be, “Is there an easy way to get 6x – y?” as opposed to, “Let’s start solving for x” (which of course you can’t do here…that’s why E is a trap answer choice).

With that in mind, even if you’ve forgotten (or temporarily blanked on) some exponent rules, you should immediately be thinking, “I have 2x – how does that become 6x,” and, “Where does the subtraction come from?”.

The 6x, of course, comes from breaking 27 down into 3^3, so that you have (3^3)^2x, which then becomes 3^6x. And then with that, you have a fraction:

And that’s where the subtraction comes from. When you divide two exponents of the same base, you subtract the exponents, so now you have your 6x – y ready to go. Of course, from there, you need to get a base of 3 on the other side of the equation, so you can express 81 as 3^4, and now you know that 6x – y = 4, answer choice B.

Most importantly here, when the GMAT asks you an oddly-specific question in the vein of the oddly-specific Netflix category, you should seize on that specificity. Very frequently on the GMAT, it’s easier to solve for that oddly-specific combination of variables than it is to solve for any of the individual variables themselves!

On Problem Solving questions this can save you plenty of time, taking that extra few seconds to ask yourself how you’d arrive at that specific combination. On Data Sufficiency, this practice can be even more a matter of correct or incorrect. Data Sufficiency problems often give you sufficient information to arrive at the oddly-specific combination from the question stem, but insufficient information to determine any of the individual components. Imagine this problem as a Data Sufficiency problem:

Here, as you know from above, Statement 1 is sufficient, but if you go into the problem trying to solve for the variables individually, you’ll likely think that you need Statement 2 so that you can plug the value of y back into Statement 1 to supply the value of x. That way you’ll have the entire picture filled in: x = 1, y = 2, and 6x – y = 4.

But you don’t NEED Statement 2, so on a question like this the GMAT will punish you for not seeing that Statement 1 alone is sufficient. And it’s only sufficient because of that oddly-specific question stem. Check out this follow-up question (with a similar setup, but variables changed to a and b since the actual numbers will change):

Here you cannot use Statement 1 to get directly to the oddly-specific question stem. You can get to 4a – b = 4, but that doesn’t tell you about 6a – b. So here, the answer is C because you need Statement 2 so that you can solve for each variable individually.

More often than not, when the GMAT asks for an oddly-specific combination of variables it provides a way to arrive at it. So pay attention to the question itself: if it’s asking for something out of the ordinary or oddly specific, see that as a thinly-veiled clue that allows you to be the Confident GMAT Problem Solver With Excellent Think Like The Testmaker Skills En Route To A 700+ that you know you can be.

By Brian Galvin.

# GMAT Tip of the Week: Yogi Berra Teaches GMAT Sentence Correction

The world lost a legend this week with the passing of Yogi Berra, a New York Yankee and World War II hero. Yogi was universally famous – his name was, of course, the inspiration for beloved cartoon character Yogi Bear’s – but to paraphrase the man himself, those who knew him didn’t really know him.

As news of his passing turned into news reports summarizing his life, many were stunned by just how illustrious his career was: 18 All-Star game appearances (in 19 pro seasons), 10 World Series championships as a player, 3 American League MVP awards, part of the Normandy campaign on D-Day… To much of the world, he was “the quote guy” who also had been a really good baseball player. His wordsmithery is what we all remembered:

• Never answer an anonymous letter.
• It ain’t over ’til it’s over.
• It gets late early out here.
• Pair up in threes.

And his command (or butchering) of the English language is what you should remember as you take the GMAT. Yogi Berra famously “didn’t say some of the things I said” but he did, however inadvertently, have a lot to say about GMAT Sentence Correction:

Pronouns Matter

What’s funny about his quote, “Always go to other people’s funerals, otherwise they won’t come to yours”?

It’s the pronoun “they.” You know what Yogi means – go to other people’s funerals so that other people will come to yours. But in that sentence, the logical referent for “they” is “other people(‘s)”, and those other people have already been designated in the sentence as people who have already died. So the meaning is illogical: those same people cannot logically attend a funeral in the future. When you use a pronoun, it has to refer back to a specific noun. If that noun cannot logically do what the pronoun is said to be doing, that’s a Sentence Correction, illogical meaning problem.

What’s funny about his quote, “When you come to a fork in the road, take it”?

Again, it’s the pronoun, this time “it.” Since a fork in the road is a place where the road diverges into two paths, you can’t take “it” – you have to pick one path. And this is a good example of another sentence correction theme. In order to fix this thought (and the one above), there’s really not a pronoun that will work. “Them” has no logical referent (there’s only one fork) so the meaning is extremely important.

The only way to fix it is to change something prior in the sentence. Perhaps, “When you come to a turnoff on the road, take it,” or, “when the road presents a turn, take it.” On the GMAT, a pronoun error isn’t always fixed by fixing the pronoun – often the correct answer will change the logic that precedes the pronoun so that in the correct answer the previously-incorrect pronoun is correct.

Modifiers Matter

What’s funny about his quote, “Congratulations. I knew the record would stand until it was broken”?

Of course records stand until they’re broken, but in a grammatical sense Yogi’s primary mistake was his placement of the modifier “until it was broken.” What he likely meant to say is, “Until the record was broken, I thought it might stand forever.” That’s a perfectly logical thought, but we all laugh at the statement he actually made because the placement of the modifier creates a laughable meaning. So learn to spot similarly-misplaced modifiers by checking to make sure the language means exactly what it should.

Redundancy Is Funny (but sometimes has its place)

What’s funny about, “We made too many wrong mistakes,” and “It’s like déjà vu all over again”?

They’re redundant. A mistake is, by nature, something that went wrong. And déjà vu is the feeling that something happened before, so of course it’s “all over again.” Redundancy does come up on the GMAT, but as Yogi himself would point out, there’s a fine line between “redundant (and wrong)” and “a useful literary device”.

Take, for example, his famed, “It ain’t over ’til it’s over” quote. In a sports context, even though the word “over” is repeated, that sentence carries a lot of useful meaning: “when someone might say that the game is over, if there is still time (or outs) remaining there’s always a chance to change the result.” The world chuckles at this particular Yogi quote, but in actuality it’s arguably his most famous because, in its own way, it’s quite poignant.

What does that mean for you on the GMAT? Don’t prioritize redundancy as a primary decision point! GMAT Sentence Correction, by nature, involves plenty of different literary devices and sentence structures, and it’s extremely unlikely that you’ll feel like an expert on all of them.

Students often eliminate correct answers because they perceive redundancy, but a phrase like “not unlike” (a “not” next to an “un-“? That’s a redundant double-negative!) actually has a logical and important meaning (“not unlike” means “it’s not totally different from…there are at least some similarities,” whereas “like” conveys significantly more similarity). Rules for modifiers and pronouns are much more absolute, and you can get plenty of practice with those. Be careful with redundancy because, as Yogi might say, sometimes saying it twice is twice as good as saying it once.

“Baseball is ninety percent mental and the other half is physical.”

To paraphrase the great Yogi Berra, 90% of Sentence Correction is mental and the other half is grammatical. When he talked about baseball, he was talking about the physical tools – the ability to hit, run, throw, catch –  as meaning substantially less than people thought, but the mental part of the game – strategy, mental toughness, stamina, etc. – being more important than people thought. The exact percentages, as his quote so ineloquently suggests, are harder to pin down and less important than the takeaway.

So heed Yogi’s advice as it pertains to Sentence Correction. Memorizing and knowing hundreds of grammar rules is “the other half” (or maybe 10%) of the game – employing good strategy (prioritizing primary Decision Points, paying attention to logical meaning, etc.) is the more-important-but-often-overlooked part of success. However eloquently or inelegantly Yogi Berra may have articulated his lessons, at least he made them memorable.

By Brian Galvin.

# GMAT Tip of the Week: 10 Must-Know Divisibility Rules For the GMAT (#3 Will Blow Your Mind!)

You clicked, didn’t you? You’re helpless when presented with an enumerated list and a teaser that at least one of the items is advertised to be – but probably won’t be – mind-blowing. (In this case it kind of is…if not mind-blowing, it’s at least very powerful). So in this case, let’s use click bait for good and enumerated lists to talk about numbers. Here are 10 important (and “BuzzFeedy”) divisibility rules you should know heading into the GMAT:

1) 1

1 may be the loneliest number but it’s also a very important number for divisibility! Every integer is divisible by 1, and the result of any integer x divided by 1 is just x (when you divide an integer by 1, it stays the same). On the GMAT, the fact that every integer is divisible by 1 can be quite important. For example, a question might ask (as at least one official problem does): Does integer x have any factors y such that 1 < y < x?

Because every integer is divisible by itself and 1, that question is really just asking, “Is x prime or not?” because if there is a factor y that’s between 1 and x, x is not prime, and there is not such a factor, then x is prime. That “> 1” caveat in the problem may seem obtuse, but when you understand divisibility by 1, you can see that the abstract question stem is really just asking you about prime vs. not-prime as a number property. The concept that all integers are divisible by 1 may seem basic, but keeping it top of mind on the GMAT can be extremely helpful.

2) 2

It takes 2 to make a thing go right…in relationships and on the GMAT! A number is divisible by 2 if that number is even (and a number is even if it’s divisible by 2). That means that if an integer ends in 0, 2, 4, 6, or 8, you know that it’s divisible by 2. And here’s a somewhat-surprising fact: the number 0 is even! 0 is divisible by 2 with no remainder (0/2 = 0), so although 0 is neither positive nor negative it fits the definition of even and should therefore be something you keep in mind because 0 is such a unique number.

The GMAT frequently tests even/odd number properties, so you should make a point to get to know them. Because any even number is divisible by 2 (which also means that it can be written as 2 times an integer), an even number multiplied by any integer will keep 2 as a factor and remain even. So even x even = even and even x odd = even.

3) 3

It’s been said that good things come in 3s, and divisibility rules are no exception! The divisibility rule for 3 works much like a magic trick and is one that you should make sure is top of mind on test day to save you time and help you unravel tricky numbers. The rule: if you sum the digits of an integer and that sum is divisible by 3, then that integer is divisible by 3. For example, consider the integer 219. 2 + 1 + 9 = 12 which is divisible by 3, so you know that 219 is divisible by 3 (it’s 3 x 73).

This rule can help you in many ways. If you were asked to determine whether a number is prime, for example, and you can see that the sum of the digits is a multiple of 3, you know immediately that it’s not prime without having to do the long division to prove it. Or if you had a messy fraction to reduce and noticed that both the numerator and denominator are divisible by 3, you can use that rule to begin reducing the fraction quickly. The GMAT tests factors, multiples, and divisibility quite a bit, so this is a critical rule to have at your disposal to quickly assess divisibility. And since 1 out of every 3 integers is divisible by 3, this rule will help you out frequently!

4) 4

Presidential Election and Summer Olympics enthusiasts, be four-warned! You already know the divisibility rule for 4: take the last two digits of an integer and treat them as a two-digit number, and if that’s divisible by 4 so is the whole number. So for 2016 – next year and that of the next presidential election and Brazil Olympics – the last two-digit number, 16, is divisible by 4, so you know that 2016 is also divisible by 4.

If you fail to see immediately that a number is divisible by 4 given that rule, fear not! Being divisible by 4 just means that a number is divisible by 2 twice. So if you didn’t immediately see that you could factor a 4 out of 2016 (it’s 504 x 4), you could divide by 2 (2 x 1008) and then divide by 2 again (2 x 2 x 504) and end up in the same place without too much more work.

5) 5

Who needs only 5 fingers to divide by 5? All of us – divisibility by 5 is so easy you should be able to do it with one hand tied behind your back! If an integer ends in 5 or 0 you know that it’s divisible by 5 (and we’ll talk more about what extra fact 0 tells you in just a bit…).

6) 6

Your favorite character from the hit 1990’s NBC sitcom “Blossom” is also an easy-to-use divisibility rule! Since 6 is just the product of 2 and 3 (2 x 3 = 6), if a number meets the divisibility rules for both 2 (it’s even) and 3 (the sum of the digits is divisible by 3) it’s divisible by 6. So if you need to reduce a number like 324, you might want to start by dividing by 6, instead of by 2 or 3, so that you can factor it in fewer steps.

7) 7

Ah, magnificent 7. While there is a “trick” for divisibility by 7, 7 occurs much less frequently in divisibility-based problems (as do other primes like 11, 13, 17, etc.), so 7 is a good place to begin to think about a strategy that works for all numbers, rather than memorizing limited-use tricks for each number. To test whether a large number, such as 231, is divisible by 7, find an obvious multiple of 7 nearby and then add or subtract multiples of 7 to see whether doing so will land on that number. For 231, you should recognize that a nearby multiple of 7 is 210 (you know 21 is 7 x 3, so putting a 0 on the end of it just means that 210 is 7 x 30). Then as you add 7s to get there, you go to 217, then to 224, then to 231. So in your head you can see that 231 is 3 more 7s than 7 x 30 (which you know is 210), so 231 = 7 x 33.

8) 8

8 is enough! As you saw above with 4s and 6s, when you start working with non-prime factors it’s often easier to just divide out the smaller prime factors one at a time than to try to determine divisibility by a larger composite number in one fell swoop. Since 8 = 2 x 2 x 2, you’ll likely find more success testing for divisibility by 8 by just dividing by 2, then dividing by 2 again, then dividing by 2 a third time. So for a number like 312, rather than working through long division to divide by 8, just divide it in half (156) then in half again (78) then in half again (39), and you’ll know that 312 = 39 x 8.

9) 9

While “nein” may be German for “no,” you should be saying “yes” to divisibility by nine! 9 shares a big similarity with 3 in that a sum-of-the-digits rule applies here too. If you sum the digits of an integer and that sum is a multiple of 9, the integer is also divisible by 9. So, for example, with the number 729, because 7 + 2 + 9 = 18, you know that 729 is divisible by 9 (it’s 81 x 9, which actually is 9 to the 3rd power).

10) 10

We’ve saved the best for last! If a number ends in 0, it’s divisible by 10, giving you a great opportunity to make the math easy. For example, a number like 210 (which you saw above) lets you pull the 0 aside and say that it’s 21 x 10, which means that it’s 3 x 7 x 10.

Working with 10s makes mental (or pencil-and-paper) math quick and convenient, so you should seek out opportunities to use such numbers in your calculations. For example, look at 693: If you add 7, you get to a number that ends in two 0s (so it’s 7 x 10 x 10), meaning that you know that 693 is divisible by 7 (it’s 7 away from an easy multiple of 7) *and* that it’s 7 x 99 because it’s one less 7 than 7 x 100. Because the GMAT rewards quick mental math, it’s a good idea to quickly check for, “If I have to add x to get to the nearest 0, then does that give me a multiple of x?” (297 is 3 away from 300, so you know that 297 = 99 x 3). And since 10 = 2 x 5, it’s also helpful sometimes to double a number that ends in 5 (try 215, which times 2 = 430) to see how many 10s you have (43). That tells you that 215 = 43 x 5 because 215 x 2 = 43 x (2 x 5). Working with 10s can make mental math extremely quick – we’d rate numbers that end in 0 a perfect 10!

Getting ready to take 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: Small Numbers Lead to Big Scores

The last thing you want to see on your score report at the end of the GMAT is a small number. Whether that number is in the 300s (total score) or in the single-digits (percentile), your nightmares leading up to the test probably include lots of small numbers flashing on the screen as you finish the test. So what’s one of the most helpful tools you have to keep small numbers from appearing on the screen?

Have you found yourself on a homework problem or practice test asking yourself “can I just multiply these?”? Have you forgotten a rule and wondered whether you could trust your memory? Small numbers can be hugely valuable in these situations. Consider this example:

For integers x and y, 2^x + 2^y = 2^30. What is the sum x + y?

(A) 30
(B) 40
(C) 50
(D) 58
(E) 64

Every fiber of your being might be saying “can I just add x + y and set that equal to 30?” but you’re probably at least unsure whether you can do that. How do you definitively tell whether you can do that? Test the relationship with small numbers. 2^30 is far too big a number to fathom, but 2^6 is much more convenient. That’s 64, and if you wanted to set the problem up that way:

2^x + 2^y = 2^6

You can see that using combinations of x and y that add to 6 won’t work. 2^3 + 2^3 is 8 + 8 = 16 (so not 64). 2^5 + 2^1 is 32 + 2 = 34, which doesn’t work either. 2^4 + 2^2 is 16 + 4 = 20, so that doesn’t work. And 2^0 + 2^6 is 1 + 64 = 65, which is closer but still doesn’t work. Using small numbers you can prove that that step you’re wondering about – just adding the exponents – isn’t valid math, so you can avoid doing it. Small numbers help you test a rule that you aren’t sure about!

That’s one of two major themes with testing small numbers. 1) Small numbers are great for testing rules. And 2) Small numbers are great for finding patterns that you can apply to bigger numbers. To demonstrate that second point about small numbers, let’s return to the problem. 2^30 again is a number that’s too big to deal with or “play with,” but 2^6 is substantially more manageable. If you want to get to:

2^x + 2^y = 2^6, think about the powers of 2 that are less than 2^6:

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

Here you can just choose numbers from the list. The only two that you can use to sum to 64 are 32 and 32. So the pairing that works here is 2^5 + 2^5 = 2^6. Try that again with another number (what about getting 2^x + 2^y = 2^5? Add 16 + 16 = 32, so 2^4 + 2^4), and you should start to see the pattern. To get 2^x + 2^y to equal 2^z, x and y should each be one integer less than z. So to get back to the bigger numbers in the problem, you should now see that to get 2^x + 2^y to equal 2^30, you need 2^29 + 2^29 = 2^30. So x + y = 29 + 29 = 58, answer choice D.

The lesson? When problems deal with unfathomably large numbers, it can often be quite helpful to test the relationship using small numbers. That way you can see how the pieces of the puzzle relate to each other, and then apply that knowledge to the larger numbers in the problem. The GMAT thrives on abstraction, presenting you with lots of variables and large numbers (often exponents or factorials), but you can counter that abstraction by using small numbers to make relationships and concepts concrete.

So make sure that small numbers are a part of your toolkit. When you’re unsure about a rule, test it with small numbers; if small numbers don’t spit out the result you’re looking for, then that rule isn’t true. But if multiple sets of small numbers do produce the desired result, you can proceed confidently with that rule. And when you’re presented with a relationship between massive numbers and variables, test that relationship using small numbers so that you can teach yourself more concretely what the concept looks like.

The best way to make sure that your GMAT score report contains big numbers? Use lots of small numbers in your scratchwork.

Getting ready to take 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: Eazy E Shows You How To Take Your Quant Score Straight Outta Compton And Straight To Cambridge

If you listened to any hip hop themed radio today, the day of the Straight Outta Compton movie premiere, you may have heard interviews with Dr. Dre. You almost certainly heard interviews with Ice Cube. And depending on how old school the station is there’s even a chance you heard from DJ Yella or MC Ren.

But on the radio this morning – just like on your GMAT exam – there was no Eazy-E. Logistically that’s because – as the Bone Thugs & Harmony classic “Tha Crossroads” commemorated – Eazy passed away about 20 years ago. But in GMAT strategy form, Eazy’s absence speaks even louder than his vocals on his NWA and solo tracks. “No Eazy-E” should be a mantra at the top of your mind when you take the GMAT, because on Data Sufficiency questions, choice E – the statements together are not sufficient to solve the problem – will not be given to you all that easily (Data Sufficiency “E” answers, like the Boyz in the Hood, are always hard).

Think about what answer choice E really means: it means “this problem cannot be solved.” But all too often, examinees choose the “Eazy-E,” meaning they pick E when “I can’t do it.” And there’s a big chasm. “It cannot be solved” means you’ve exhausted the options and you’re maybe one piece of information (“I just can’t get rid of that variable”) or one exception to the rule (“but if x is a fraction between 0 and 1…”) that stands as an obstacle to directly answering the question. Very rarely on problems that are above average difficulty is the lack of sufficiency a wide gap, meaning that if E seems easy, you’re probably missing an application of the given information that would make one or both of the statements sufficient. The GMAT just doesn’t have an incentive to reward you for shrugging your shoulders and saying “I can’t do it;” it does, however, have an incentive to reward those people who can conclusively prove that seemingly insufficient information can actually be packaged to solve the problem (what looks like E is actually A, B, C, or D) and those people who can look at seemingly sufficient information and prove why it’s not actually quite enough to solve it (the “clever” E).

So as a general rule, you should always be skeptical of Eazy-E.

Consider this example:

A shelf contains only Eazy-E solo albums and NWA group albums, either on CD or on cassette tape. How many albums are on the shelf?

(1) 2/3 of the albums are on CD and 1/4 of the albums are Eazy-E solo albums.

(2) Fewer than 30 albums are NWA group albums and more than 10 albums are on cassette tape.

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

Statistically on this problem (the live Veritas Prep practice test version uses hardcover and paperback books of fiction or nonfiction, but hey it’s Straight Outta Compton day so let’s get thematic!), almost 60% of all test-takers take the Eazy-E here, presuming that the wide ranges in statement 2 and the ratios in statement 1 won’t get the job done. But a more astute examinee is skeptical of Eazy-E and knows to put in work! Statement 1 actually tells you more than meets the eye, as it also tells you that:

• 1/3 of the albums are on cassette tape
• 3/4 of the albums are NWA albums
• The total number of albums must be a multiple of 12, because that number needs to be divisible by 3 and by 4 in order to create the fractions in statement 1

So when you then add statement 2, you know that since there are more than 10 albums total (because at least 11 are cassette alone) so the total number could be 12, 24, 36, 48, etc. And then when you apply the ratios you realize that since the number of NWA albums is less than 30 and that number is 3/4 of the total, the total must be less than 40. So only 12, 24, and 36 are possible. And since the number of cassettes has to be greater than 10, and equate to 1/3 of the total, the total must then be more than 30. So the only plausible number is 36, and the answer is, indeed, C.

Strategically, being wary of Eazy-E tells you where to invest your time. If E seems too easy, that means that you should spend the extra 30-45 seconds seeing if you can get started using the statements in a different way. So learn from hip hop’s first billionaire, Dr. Dre, who split with Eazy long ago and has since seen his business success soar. Avoid Eazy-E and as you drive home from the GMAT test center you can bask in the glow of those famous Ice Cube lyrics, “I gotta say, today was a good day.”

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure tofind us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

# GMAT Tip of the Week: Jim Harbaugh Says Milk Does A GMAT Score Good

Someday when he’s not coaching football, playing with the Oakland Athletics, visiting with the Supreme Court, or Tweeting back and forth with Lil Wayne and Nicki Minaj, Jim Harbaugh should sit down and take the GMAT.

Because if his interaction with a young, milk-drinking fan is any indication, Harbaugh understands one of the key secrets to success on the GMAT Quant section:

Harbaugh, who told HBO Real Sports this summer about his childhood plan to grow to over 6 feet tall – great height for a quarterback – by drinking as much milk as humanly possible – is a fan of all kinds of milk: chocolate, 2%… But as he tells the young man, the ideal situation for growing into a Michigan quarterback is drinking whole milk, just as the ideal way to attend the Ross School of Business a few blocks from Harbaugh’s State Street office is to use whole numbers on the GMAT.

The main reason? You can’t use a calculator on the GMAT, so while your Excel-and-calculator-trained mind wants to say calculate “75% of 64” as 0.75 * 64, the key is to think in terms of whole numbers whenever possible. In this case, that means calling “75%” 3/4, because that allows you to do all of your calculations with the whole numbers 3 and 4, and not have to set up decimal math with 0.75. Since 64/4 is cleanly 16 – a whole number – you can calculate 75% by dividing by 4 first, then multiplying by 3: 64/4 is 16, then 16 * 3 = 48, and you have your answer without ever having to deal with messier decimal calculations.

This concept manifests itself in all kinds of problems for which your mind would typically want to think in terms of decimal math. For example:

With percentages, 25% and 75% can be seen as 1/4 and 3/4, respectively. Want to take 20%? Just divide by 5, because 0.2 = 1/5.

If you’re told that the result of a division operation is X.4, keep in mind that the decimal .4 can be expressed as 2/5, meaning that the divisor has to be a multiple of 5 and the remainder has to be even.

If at some point in a calculation it looks like you need to divide, say, 10 by 4 or 15 by 8 or any other type of operation that would result in a decimal, wait! Leaving division problems as improper fractions just means that you’re keeping two whole numbers handy, and knowing the GMAT at some point you’ll end up having to multiply or divide by a number that lets you avoid the decimal math altogether.

So learn from Jim Harbaugh and his obsession with whole milk. Whole milk may be the reasons that his football dreams came true; whole numbers could be a major reason that your business school dreams come true, too.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure tofind us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

# GMAT Tip of the Week: Behind the Scenes of Your GMAT Score

Among the most frequent questions we receive here at Veritas Prep headquarters (sadly, “How much am I allowed to tip my instructor?” is not one of them!) is the genre of “On my most recent practice test, I got X right and Y wrong and only Z wrong in a row… Why was my score higher/lower than my other test with A right and B wrong and C wrong in a row?” inquiries from students desperately trying to understand the GMAT scoring algorithm. We’ve talked previously in this space about why simply counting rights and wrongs isn’t all that great a predictor of your score. And perhaps the best advice possible relates to our Sentence Correction advice here a few months ago: Accept that there are some things you can’t change and focus on making a difference where you can.

But we also support everyone’s desire to leave no stone unturned in pursuit of a high GMAT score and everyone’s intellectual curiosity with regard to computer-adaptive testing. So with the full disclosure that these items won’t help you game the system and that your best move is to turn that intellectual curiosity toward mastering GMAT concepts and strategies, here are four major reasons that your response pattern — did you miss more questions early in the test vs. late in the test; did you miss consecutive questions or more sporadic questions, etc. — won’t help you predict your score:

1) The all-important A-parameter.

Item Response Theory incorporates three metrics for each “item” (or “question” or “problem”): the B parameter is the closest measurement to pure “difficulty”. The C parameter is essentially a measure of likelihood that a correct answer can be guessed. And the A parameter tells the scoring system how much to weight that item. Yes, some problems “count” more than others do (and not because of position on the test).

Why is that? Think of your own life; if you were going to, say, buy a condo in your city, you’d probably ask several people for their opinion on things like the real estate market in that area, mortgage rates, the additional costs of home ownership, the potential for renting it if you were to move, etc. And you’d value each opinion differently. Your very risk-loving friend may not have the opinion to value highest on “Will I be able to sell this at a profit if I get transferred to a new city?” (his answer is “The market always goes up!”) whereas his opinion on the neighborhood itself might be very valuable (“Don’t underestimate how nice it will be to live within a block of the blue line train”). Well, GMAT questions are similar: Some are extremely predictive (e.g. 90% of those scoring over 700 get it right, and only 10% of those scoring 690 or worse do) and others are only somewhat predictive (60% of those 700+ get this right, but only 45% of those below 700 do; here getting it right whispers “above 700” whereas before it screams it).

So while you may want to look at your practice test and try to determine where it’s better to position your “misses,” you’ll never know the A-values of any of the questions, so you just can’t tell which problems impacted your score the most.

2) Content balancing.

OK, you might then say, the test should theoretically always be trying to serve the highest value questions, so shouldn’t the larger A-parameters come out first? Not necessarily. The GMAT values balanced content to a very high degree: It’s not fair if you see a dozen geometry problems and your friend only sees two, or if you see the less time-consuming Data Sufficiency questions early in the test while someone else budgets their early time on problem solving and gets a break when the last ten are all shorter problems. So the test forces certain content to be delivered at certain times, regardless of whether the A-parameter for those problems is high or low. By the end of the test you’ll have seen various content areas and A-parameters… You just won’t know where the highest value questions took place.

3) Experimental items.

In order to know what those A, B, and C parameters are, the GMAT has to test its questions on a variety of users. So on each section, several problems just won’t count — they’re only there for research. And this can be true of practice tests, too (the Veritas Prep tests, for example, do contain experimental questions). So although your analysis of your response pattern may say that you missed three in a row on this test and gotten eight right in a row on the other, in reality those streaks could be a lot shorter if one or more of those questions didn’t count. And, again, you just won’t know whether a problem counted or not, so you can’t fully read into your response pattern to determine how the test should have been scored.

4) Item delivery vs. Score calculation.

One common prediction people make about GMAT scoring is that missing multiple problems in a row hurts your score substantially more than missing problems scattered throughout the test. The thinking goes that after one question wrong the system has to reconsider how smart it thought you were; then after two it knows for sure that you’re not as smart as advertised; and by the third it’s in just asking “How bad is he?” In reality, however, as you’ve read above, the “get it right –> harder question; get it wrong –> easier question” delivery system is a bit more nuanced and inclusive of experimentals and content balancing than people think. So it doesn’t work quite like the conventional wisdom suggests.

What’s more, even when the test delivers you an easier question and then an even easier question, it’s not directly calculating your score question by question. It’s estimating your score question-by-question in order to serve you the most meaningful questions it can, but it calculates your score by running its algorithm across all questions you’ve seen. So while missing three questions in a row might lower the current estimate of your ability and mean that you’ll get served a slightly easier question next, you can also recover over the next handful of questions. And then when the system runs your score factoring in the A, B, and C parameters of all of your responses to “live” (not experimental) questions, it doesn’t factor in the order in which those questions were presented — it only cares about the statistics. So while it’s certainly a good idea to get off to a good start in the first handful of problems and to avoid streaks of several consecutive misses, the rationale for that is more that avoiding early or prolonged droughts just raises your degree of difficulty. If you get 5 in a row wrong, you need to get several in a row right to even that out, and you can’t afford the kinds of mental errors that tend to be common and natural on a high-stakes exam. If you do manage to get the next several right, however, you can certainly overcome that dry spell.

In summary, it’s only natural to look at your practice tests and try to determine how the score was calculated and how you can use that system to your advantage. In reality, however, there are several unseen factors that affect your score that you just won’t ever see or know, so the best use of that curiosity and energy is learning from your mistakes so that the computer — however it’s programmed — has no choice but to give you the score that you want.

Getting ready to take 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: Kanye West’s Everything I Am Teaches Critical Reasoning

“Everything I’m not made me everything I am,” says Kanye West in his surprisingly-humble track Everything I Am. And while, unsurprisingly, much of what he’s talking about is silencing his critics, he might as well be rapping about making you an elite critic on Critical Reasoning problems. Because when it comes to some of the most challenging Critical Reasoning problems on the GMAT, everything they’re not makes them everything they are. Which is a convoluted way of saying this:

On challenging Strengthen and Assumption questions, the correct answer often tells you that a potential flaw with the argument is not true.

Everything that’s not true in that answer choice, then, makes the conclusion substantially more valid.

Consider this argument, for example:

Kanye received the most votes for the “Best Hip Hop Artist” award at the upcoming MTV Video Music Awards, so Kanye will be awarded the trophy for Best Hip Hop Artist.

If this were the prompt for a question that asked “Which of the following is an assumption required by the argument above?” a correct answer might read:

A) The Video Music Award for “Best Hip Hop Artist” is not decided by a method other than voting.

And the function of that answer choice is to tell you what’s not true (“everything I’m not”), removing a flaw that allows the conclusion to be much more logically sound (“…made me everything I am.”) These answer choices can be challenging in context, largely because:

1) Answer choices that remove a flaw can be difficult to anticipate, because those flaws are usually subtle.

2) Answer choices that remove a flaw tend to include a good amount of negation, making them a bit more convoluted.

In order to counteract these difficulties, it can be helpful to use “Everything I’m not made me everything I am” to your advantage. If what’s NOT true is essential to the conclusion’s truth, then if you consider the opposite – what if it WERE true – you can turn that question into a Weaken question. For example, if you took the opposite of the choice above, it would read:

The VMA for “Best Hip Hop Artist” is decided by a method other than voting.

If that were true, the conclusion is then wholly unsupported. So what if Kanye got the most votes, if votes aren’t how the award is determined? At that point the argument has no leg to stand on, so since the opposite of the answer directly weakens the argument, then you know that the answer itself strengthens it. And since we’re typically all much more effective as critics than we are as defenders, taking the opposite helps you to do what you’re best at. So consider the full-length problem:

Editor of an automobile magazine: The materials used to make older model cars (those built before 1980) are clearly superior to those used to make late model cars (those built since 1980). For instance, all the 1960’s and 1970’s cars that I routinely inspect are in surprisingly good condition: they run well, all components work perfectly, and they have very little rust, even though many are over 50 years old. However, almost all of the late model cars I inspect that are over 10 years old run poorly, have lots of rust, and are barely fit to be on the road.

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

A) The quality of materials used in older model cars is not superior to those used to make other types of vehicles produced in the same time period.

B) Cars built before 1980 are not used for shorter trips than cars built since then.

C) Manufacturing techniques used in modern automobile plants are not superior to those used in plants before 1980.

D) Well-maintained and seldom-used older model vehicles are not the only ones still on the road.

E) Owners of older model vehicles take particularly good care of those vehicles.

First notice that several of the answer choices (A, B, C, and D) include “is not” or “are not” and that the question stem asks for an assumption. These are clues that you’re dealing with a “removes the flaw” kind of problem, in which what is not true (in the answer choices) is essential to making the conclusion of the argument true. Because of that, it’s a good idea to take the opposites of those answer choices so that instead of removing the flaw in a Strengthen/Assumption question, you’re introducing the flaw and making it a Weaken. When you do that, you should see that choice D becomes:

D) Well-maintained and seldom-used older model vehicles ARE the only ones still on the road.

If that’s the case, the conclusion – “the materials used to make older cars are clearly superior to those used in newer ones” – is proven to be flawed. All the junkers are now off the road, so the evidence no longer holds up; you’re only seeing well-working old cars because they’re the most cared-for, not because they were better made in the first place.

And in a larger context, look at what D does ‘reading forward’: if it’s not only well-maintained and seldom-driven older cars on the road, then you have a better comparison point. So what’s not true here makes the argument everything it is. But dealing in “what’s not true” can be a challenge, so remember that you can take the opposite of each answer choice and make this “Everything I’m Not” assumption question into a much-clearer “Everything I Am” Weaken question.

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

By Brian Galvin

# GMAT Tip of the Week: Shake & Bake Your Way To Function Success

For many of us, cooking a delicious homemade meal and solving a challenge-level GMAT math problem are equally daunting challenges. So many steps, so many places to make a mistake…why can’t there be an easier way? Well, the fine folks at Kraft foods solved your first problem years ago with a product called “Shake and Bake.” You take a piece of chicken (your input), stick in the bag of seasoning, shake it up, bake it, and voila – you have yourself a delicious meal with minimal effort. So gourmet level cooking is now nothing to fear…but what about those challenging GMAT quant problems?

You’re in luck. Function problems on the GMAT are essentially Shake and Bake recipes. Consider the example:

f(x) = x^2 – 80

If that gets your heart rate and stress level up, you’re not alone. Function notation just looks challenging. But it’s essentially Shake and Bake if you dissect what a function looks like.

The f(x) portion tells you about your input. f(x) = ________ means that, for the rest of that problem, whatever you see in parentheses is your “input” (just like the chicken in your Shake and Bake).

What comes after the equals sign is the recipe. It tells you what to do to your input to get the result. Here f(x) = x^2 – 80 is telling you that whatever your input, you square it and then subtract 80 and that’s your output. …And that’s it.

So if they ask you for:

What is f(9)? (your input is 9), then f(9) = 9^2 – 80, so you square 9 to get 81, then you subtract 80 and you have your answer: 1.

what is f(-4)? (your input is -4), then f(4) = 4^2 – 80, which is 16 – 80 = -64.

What is f(y^2)? (your input is y^2), then f(y^2) = (y^2)^2 – 80, which is y^4 – 80.

What is f(Rick Astley), then your input is Rick Astley and f(Rick Astley) = (Rick Astley)^2 – 80.

It really doesn’t matter what your input is. Whatever the test puts in the parentheses, you just use that as your input and do whatever the recipe says to do with it. So for example:

f(x) = x^2 – x. For which of the following values of a is f(a) > f(8)?

I. a = -8
II. a = -9
III a = 9

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

While this may look fairly abstract, just consider the inputs they’ve given you. For f(8), just put 8 wherever that x goes in the “recipe” f(x) = x^2 – x:

f(8) = 8^2 – 8 = 64 – 8 = 56

And then do the same for the three other possible values:

I. f(-8) means put -8 wherever you see the x: (-8)^2 – (-8) = 64 + 8 = 72, so f(-8) > f(8).
II. f(-9) means put -9 wherever you see the x: (-9)^2 – (-9) = 81 + 9 = 90, so f(-9) > f(8)
III. f(9) means put a 9 wherever you see the x: 9^2 – 9 = 81 – 9 = 72, so f(9) > f(8), and the answer is E.

Ultimately with functions, the notation (like the Shake and Bake ingredients) is messy, but with practice the recipes become easy to follow. What goes in the parentheses is your input, and what comes after the equals sign is your recipe. Follow the steps, and you’ll end up with a delicious GMAT quant 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: Oh Thank Heaven For Seven-Eleven

A week after the Fourth of July, a lesser-known but certainly-important holiday occurs each year. Tomorrow, friends, is 7-11, a day to enjoy free Slurpees at 7-11 stores, to roll some dice at the craps table, and to honor your favorite prime numbers. So to celebrate 7-11, let’s talk about these two important prime numbers.

Checking Whether A Number Is Prime

Consider a number like 133. Is that number prime? The first three prime numbers (2, 3, and 5) are easy to check to see whether they are factors (if any are, then the number is clearly not prime):

2 – this number is not even, so it’s not divisible by 2.
3 – the sum of the digits (an important rule for divisibility by three!) is 7, which is not a multiple of 3 so this number is not divisible by 3.
5 – the number doesn’t end in 5 or 0, so it’s not divisible by 5

But now things get a bit trickier. There are, in fact, (separate) divisibility “tricks” for 7 and 11. But they’re relatively inefficient compared with a universal strategy. Find a nearby multiple of the target number, then add or subtract multiples of that target number. If we want to test 133 to see whether it’s divisible by 7, we can quickly go to 140 (you know this is a multiple of 7) and then subtract by 7. That’s 133, so you know that 133 is a multiple of 7. (Doing the same for 11, you know that 121 is a multiple of 11 – it’s 11-squared – so add 11 more and you’re at 132, so 133 is not a multiple of 11)

This is even more helpful when, for example, a question asks something like “how many prime numbers exist between 202 and 218?”. By finding nearby multiples of 7 and 11:

210 is a multiple of 7, so 203 and 217 are also multiples of 7
220 is a multiple of 11, so 209 is a multiple of 11

You can very quickly eliminate numbers in that range that are not prime. And since none of the even numbers are prime and neither are 205 and 215 (the ends-in-5 rule), you’re left only having to check 207 (which has digits that sum to a multiple of 3, so that’s not prime), 211 (more on that in a second), and 213 (which has digits that sum to 6, so it’s out).

So that leaves the process of testing 211 to see if it has any other prime factors than 2, 3, 5, 7, and 11. Which may seem like a pretty tall order. But here’s an important concept to keep in mind: you only have to test prime factors up to the square root of the number in question. So for 211, that means that because you should know that 15 is the square root of 225, you only have to test primes up to 15.

Why is that? Remember that factors come in pairs. For 217, for example, you know it’s divisible by 7, but 7 has to have a pair to multiply it by to get to 217. That number is 31 (31 * 7 = 217). So whatever factor you find for a number, it has to multiply with another number to get there.

Well, consider again the number 211. Since 15 * 15 is already bigger than 211, you should see that for any number bigger than 15 to be a factor of 211, it has to pair with a number smaller than 15. And as you consider the primes up to 15, you’re already checking all those smaller possibilities. That allows you to quickly test 211 for divisibility by 13 and then you’re done. And since 211 is not divisible by 13 (you could do the long division or you could test 260 – a relatively clear multiple of 13 – and subtract 13s until you get to or past 211: 247, 234, 221, and 208, so 211 is not a multiple of 13. Therefore 211 is prime.

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: Raising Your Data Sufficiency Accuracy From 33% To 99%

You’re looking at a Data Sufficiency problem and you’re feeling the pressure. You’re midway through the GMAT Quantitative section and your mind is spinning from the array of concepts and questions that have been thrown at you. You know you nailed that tricky probability question a few problems earlier and you hope you got that last crazy geometry question right. When you look at Statement 1 your mind draws a blank: whether it’s too many variables or too many numbers or too tricky a concept, you just can’t process it. So you look at Statement 2 and feel relief. It’s nowhere near sufficient, as just about anyone even considering graduate school would know immediately. So you smile as you cross off choices A and D on your noteboard, saying to yourself: “Good, at least I have a 33% chance now.”

You’re better than that.

Too often on Data Sufficiency problems, people are impressed by giving themselves a 33% or even 50% chance of success. Keep in mind that guessing one of three remaining choices means you’re probably going to get that problem wrong! And of more strategic importance is this: if one statement is dead obvious, you haven’t just raised your probability of guessing correctly – you should have just learned what the question is all about!

If a Data Sufficiency statement is clearly insufficient, it’s arguably the most important part of the problem.

Consider this example:

What is the value of integer z?

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

(2) x is not a prime number

Many examinees will be thrilled here to see that statement 2 is nowhere near sufficient, therefore meaning that the answer must be A, C, or E – a 33% chance of success! But a more astute test-taker will look closer at statement 2 and think “this problem is likely going to come down to whether it matters that x is prime or not” and then use that information to hold Statement 2 up to that light.

For statement 1, many will test x = 5 and (x – 1) = 4 or x = 10 and (x – 1) = 9 and other combinations of that ilk, and see that the result is usually (always?) 1 remainder 1. But a more astute test-taker will see that word “prime” and ask themselves why a prime would matter. And in listing a few interesting primes, they’ll undoubtedly check 2 and realize that if x = 2 and (x – 1) = 1, the result is 1 with a remainder of 0 – a different answer than the 1, remainder 1 that usually results from testing values for x. So in this case statement 2 DOES matter, and the answer has to be C.

Try this other example:

What is the value of x?

(1) x(x + 1) = 2450

(2) x is odd

Again, someone can easily skip ahead to statement 2 and be thrilled that they’re down to three options, but it pays to take that statement and file it as a consideration for later: when I get my answer for statement 1, is there a reason that even vs. odd would matter? If I get an odd solution, is there a possible even one?

Factoring 2450 leaves you with consecutive integers 49 and 50, so x could be 49 and therefore odd. But is there any possible even value for x, a number exactly one smaller than (x + 1) where the product of the two is still 2450? There is: -50 and -49 give you the same product, and in that case x is even. So statement 2 again is critical to get the answer C.

And the lesson? A ridiculously easy statement typically holds much more value than “oh this is easy to eliminate.” So when you can quickly and effortlessly make your decision on a Data Sufficiency statement, don’t be too happy to take your slightly-increased odds of a correct answer and move on. Use that statement to give you insight into how to attack the other statement, and take your probability of a correct answer all the way up to “certain.”

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: Talking About Equality

If you’ve ever struggled with algebra, wondered which operations you were allowed to perform, or been upset when you were told that the operation you just performed was incorrect, this post is for you. Algebra is all about equality.

What does that mean?

Consider the statement:

8 = 8

That’s obviously not groundbreaking news, but it does show the underpinnings of what makes algebra “work.” When you use that equals sign, =, you’re saying that what’s on the left of that sign is the exact same value as what’s on the right hand side of that sign. 8 = 8 means “8 is the same exact value as 8.” And then as long as you do the same thing to both 8s, you’ll preserve that equality. So you could subtract 2 from both sides:

8 – 2 = 8 – 2

And you’ll arrive at another definitely-true statement:

6 = 6

And then you could divide both sides by 3:

6/3 = 6/3

And again you’ve created another true statement:

2 = 2

Because you start with a true statement, as proven by that equals sign, as long as you do the exact same thing to what’s on either side of that equals sign, the statement will remain true. So when you replace that with a different equation:

3x + 2 = 8

That’s when the equals sign really helps you. It’s saying that “3x + 2” is the exact same value as 8. So whatever you do to that 8, as long as you do the same exact thing to the other side, the equation will remain true. Following the same steps, you can:

Subtract two from both sides:

3x = 6

Divide both sides by 3:

x = 2

And you’ve now solved for x. That’s what you’re doing with algebra. You’re taking advantage of that equality: the equals sign guarantees a true statement and allows you to do the exact same thing on either side of that sign to create additional true statements. And your goal then is to use that equals sign to strategically create a true statement that helps you to answer the question that you’re given.

Equality applies to all terms; it cannot single out just one individual term.

Now, where do people go wrong? The most common mistake that people make is that they don’t do the same thing to both SIDES of the inequality. Instead they do the same thing to a term on each side, but they miss a term. For example:

(3x + 5)/7 = x – 9

In order to preserve this equation and eliminate the denominator, you must multiply both SIDES by 7. You cannot multiply just the x on the right by 7 (a common mistake); instead you have to multiply everything on the right by 7 (and of course everything on the left by 7 too):

7(3x + 5)/7 = 7(x – 9)

3x + 5 = 7x – 63

Then subtract 3x from both sides to preserve the equation:

5 = 4x – 63

Then add 63 to both sides to preserve the equation:

68 = 4x

Then divide both sides by 4:

17 = x

The point being: preserving equality is what makes algebra work. When you’re multiplying or dividing in order to preserve that equality, you have to be completely equitable to both sides of the equation: you can’t single out any one term or group. If you’re multiplying both sides by 7, you have to distribute that 7 to both the x and the -9. So when you take the GMAT, do so with equality in mind. The equals sign is what allows you to solve for variables, but remember that you have to do the exact same thing to both sides.

Inequalities? Well those will just have to wait for another day.

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

# GMAC Announces Two New GMAT Policies, Both In Your Favor!

MBA applicants, your path to submitting a score report that you can be proud of just got a bit smoother. In an announcement to test-takers today, GMAC revealed two new policies that each stand out as particularly student-friendly:

1) As of July 19, 2015, the designation “C” will no longer appear on score reports to designate a cancelled score. This couples nicely with the recent change to the GMAT’s cancellation policy allowing you to preview your score before you decide whether to “keep” or cancel it. So as of July 19, there is zero risk that anyone but you will ever notice that you had a bad test day (unless, of course, you decide to publish that score). Even better, this policy also applies to previously cancelled scores (not just to tests taken after July 19). If you submit a score report to a school now, and you have multiple test sittings in which you cancelled your score, business schools will never know it.

What does this policy mean for you? For one, you can feel markedly less pressure when you take the GMAT, as a bad score only has to be your business. There is no downside! Furthermore, you can feel confident selecting an aggressive timeline for your GMAT test date, as even if you do not perform to your goals at worst-case that attempt is “an expensive but very authentic practice test.” While in the vast majority of cases, that C never felt to schools like a Scarlet Letter, the stigma in students’ minds was often enough to inspire fear on test day and anxiety in the admissions process. Fear no more!

2) Effective immediately, you only need to wait 16 days (as opposed to 31) before retaking the GMAT. With that waiting period now cut just about in half, you have a few terrific advantages:

• If you decide you need to retake the exam, you can stick on your study regiment just 2.5 more weeks to polish up those last few concepts and you’ll take the test while everything is still fresh and you’re still in “game shape.”
• You’re significantly less likely to end up in limbo between “set the test date that maximizes your chance for success on THAT test” and “set the test date that gives you the safety net of one more try if the first one doesn’t go so well.” That month-plus between administrations made for tricky decisions for applicants in the past. Now you have that much more flexibility when choosing a date to get the test and a backup plan in before your applications are due.

Is there a downside? GMAC wouldn’t likely be as aggressive with the 16-day waiting period if it didn’t have the capacity to allow more GMAT administrations in the busy season, but there is a chance that the ~3 weeks leading up to the major application deadlines could get crowded at test centers. To have your pick of test dates for both your first shot and your backup, you may want to consider taking the GMAT 6 (and maybe 3) weeks before you and others need the score as opposed to 3 weeks and “immediately” before you need it.

Are you getting ready 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: Dave Chappelle’s Friend Chip Teaches Data Sufficiency Strategy

“Officer, I didn’t know I couldn’t do that,” Dave Chappelle’s friend, Chip, told a police officer after being pulled over for any number of reckless driving infractions. In Chappelle’s famous stand-up comedy routine, he mocks the audacity of his (privileged) friend for even thinking of saying that to a police officer. But that’s the exact type of audacity that gets rewarded on Data Sufficiency problems, and a powerful lesson for those who, like Dave in the story, seem more resigned to their plight of being rejected at the mercy of the GMAT yet again.

How does Chip’s mentality help you on the GMAT? Consider this Data Sufficiency fragment:

Is the product of integers j, k, m, and n equal to 1?

(1) (jk)/mn = 1

The approach that most students take here involves plugging in numbers for j, k, m, and n and seeing what answer they get. Knowing that jk = mn (by manipulating the algebra in statement 1) they may pick combinations:

1 * 8 = 2 * 4, in which case the product is 64 and the answer is no

2 * 5 = 1 * 10, in which case the product is 100 and the answer is no

And so some will, after picking a series of arbitrary number choices, claim that the answer must be no. But in doing so, they’re leaving out the possibilities:

1 * 1 = 1 * 1, in which case the product jkmn = 1*1*1*1 = 1, so the answer is yes

-1 * 1 = -1 * 1, in which case the product is also 1, and the answer is yes

And here’s where Chip Logic comes into play: in any given classroom, when the two latter sets of numbers are demonstrated, at least a few students will say “How are we allowed to use the same number twice? No one told us we could do that?”. And the best response to that is Chip’s very own: “I didn’t know I COULDN’T do that.” Since the problem didn’t restrict the use of the same number twice (to do so they might say “unique integers j, k, m, and n”), it’s on you to consider all possible combinations, including “they all equal 1.” Data Sufficiency tends to reward those who consider the edge cases: the highest or lowest possible number allowed, or fractions/decimals, or negative numbers, or zero. If you’re going to pick numbers on Data Sufficiency questions, you have to think like Chip: if you weren’t explicitly told that you couldn’t, you have to assume that you can.

So on Data Sufficiency problems, when you pick numbers, do so with a sense of entitlement and audacity. Number-picking is no place for the timid – your job is to “break” the obvious answer by finding allowable combinations that give you a different answer; in doing so, you can prove a statement to be insufficient. So as you chip away at your goal of a 700+ score, summon your inner Chip. When it comes to picking numbers, “I didn’t know I couldn’t do that” is the mentality you need to know you can use.

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: Making the Most of Your Mental Stamina

One of the most fascinating storylines during the current 2015 NBA Finals is that of LeBron James’ workload and stamina. Responsible for such a huge percentage of Cleveland’s offense and a key component of the team’s necessarily suffocating defense, James needs to parcel out his energy usage much like an endurance athlete does in the Tour de France or Ironman World Championships. And it’s fascinating to watch as he slowly walks the ball up the court (killing time to shorten the game and also buying valuable seconds of rest before initiating the offense) and nervously watches his teammates lose ground while he takes his ~2 minute beginning-of-the-4th rest on the bench. At the final buzzer of each game he looks exhausted but thus far has been exhaustedly-triumphant twice. And watching how he handles his energy can teach you valuable lessons about how to manage the GMAT.

At the end of your GMAT exam you will be exhausted. But will you be exhaustedly triumphant? Here are 5 things you can do to help you tiredly walk out of the test center with a championship smile:

1) Practice The Way You’ll Play

The GMAT is a long test. You’ll be at the test center for about 4 hours by the time you’re done, and even during those 8-minute section breaks you’ll be hustling the whole time. Think of it this way: with a 30-minute essay, a 30-minute Integrated Reasoning section, a 75-minute Quant section and a 75-minute Verbal section, you’ll be actively answering questions for 3 hours and 30 minutes – a reasonable time for someone your age to complete a marathon (and well more than an hour off the world record). If you were training for a marathon, you wouldn’t stop your workouts after an hour or 90 minutes each time; at the very least you’d work up to where you’re training for over two hours at least once a week. And the same is true of the GMAT. To have that mental stamina to stay focused on a dense Reading Comprehension passage over 3 hours after you arrived at the test center, you need to have trained your mind to focus for 3+ hours at a time. To do so:

-Take full-length practice tests, including the AWA and IR sections.
-Practice verbal when you’re tired, after a long day of work or after you’ve done an hour or more of quant practice
-Make at least one 2-3 hour study session a part of your weekly routine and stick to it. Work can get tough, so whether it’s a Saturday morning or Sunday afternoon, pick a time that you know you can commit to and go somewhere (library, coffee shop) where you know you’ll be able to focus and get to work.

2) Be Ready For The 8-Minute Breaks

Like LeBron James, you’ll have precious few opportunity to rest during your “MBA Finals” date with the GMAT. You have an 8-minute break between the IR section and the Quant section and another 8-minute break between the Quant section and the Verbal section…and that’s it. And those breaks go quickly, as in that 8 minutes you need to check out with the exam proctor to leave the room and check back in to re-enter. A minute or more of your break will have elapsed by the time you reach your locker or the restroom…time flies when you’re on your short rest period! So be ready:

-Have a plan for your break, knowing exactly what you want to accomplish: restroom, water, snack. You shouldn’t have to make many energy-draining decisions during that time; your mind needs a break while you refresh your body, so do all of your decision-making before you even arrive at the test center.
-Practice taking 8-minute breaks when you study and take practice tests. Know how long 8 minutes will take and what you can reasonably accomplish in that time.

3) Use Energy Wisely

If you’re watching LeBron James during the Finals you’ll see him take certain situations (if not entire plays) off, conserving energy for when he has the opportunity to sprint downcourt on a fast break or when he absolutely has to get out on a ready-to-shoot Steph Curry. For you on the GMAT, this means knowing when to stress over calculations on quant or details on reading comprehension. Most students simply can’t give 100% effort for the full test, so you may need to consider:

-On this Data Sufficiency problem, do you need to finish the calculations or can you stop early knowing that the calculations will lead to a sufficient answer?
-As you read this Reading Comp passage, do you need to sweat the scientific details or should you get the gist of it and deal with details later if a question specifically asks for them?
-With this Geometry problem, is it worth doing all the quadratic math or can you estimate using the answer choices? If you do do the math, are you sure that it will get you to an answer in a reasonable amount of time?

Sometimes the answer is “yes” – if it’s a problem that you know you can get right, but only if you grind through some ugly math, that’s a good place to invest that energy. And other times the answer is “no” – you could do the work, but you’re not so sure you even set it up right and the numbers are starting to look ugly and you usually get these problems wrong, anyway. Practice is the key, and diagnosing how those efforts have gone on your practice tests. You might not have enough mental energy to give all the focus you’d like all day, so have a few triggers in there that will help you figure out which battles you can lose in an effort to win the war.

4) Master The “Give Your Mind A Break” Problems

Some GMAT problems are extremely abstract and require a lot of focus and ingenuity. Others are very process-driven if you know the process – among those are the common word problems (weighted averages, rate problems, Venn diagram problems, etc.) and straightforward “solve for this variable” algebra problem solving problems. If you’ve put in the work to master those content-driven problems, they can be a great opportunity to turn your brain off for a few minutes while you just grind out the necessary steps, turning your mind back on at the last second to double check for common mistakes.

This comes down to practice. If you recognize the common types of “just set it up and do the work” problems, you’ll know them when you see them and can relax to an extent as you perform the same steps you have dozens of times. If you recognize the testmaker’s intent on certain problems – in an “either/or” SC structure, for example, you know that they’re testing parallelism and can quickly eliminate answers that don’t have it; if a DS problem includes >0 or <0, you can quickly look for positive/negative number properties with the “usual suspects” that indicate those things – you can again perform rote steps that don’t require much mental heavy lifting. The test is challenging, but if you put in the work in practice you’ll find where you can take some mental breaks without getting punished.

The verbal section comes last, and that’s where focus can be the hardest as you face a barrage of problems on a variety of topics – astronomy, an election in a fake country, a discovery about Druid ruins, comparative GDP between various countries, etc. A verbal section will include thousands of words, but only a couple hundred are really operative words upon which correct answers hinge. So be proactive as you read verbal problems. That means:

-Scan the answer choices for obvious decision points in SC problems. If you know they’re testing verb tense, for example, then you’re looking at the original sentence for timeline and you don’t have to immediately focus on any other details. On many questions you can get an idea of what you’re reading for before you even start reading.

-Let details go on RC passages. Your job is to know the general author’s point, and to have a good idea of where to find any details that they might ask about. But in an RC passage that includes a dozen or more details, they may only ask you about one or two. Worry about those details when you’re asked for them, saving mental energy by never really stressing the ones that end up not mattering at all.

-Read the question stem first on CR problems. Before you read the prompt, know your job so that you know what to look for. If you need to weaken it, then look for the flaw in the argument and focus specifically on the key words in the conclusion. If you need to draw a conclusion, your energy needs to be highest on process-of-elimination at the answers, and you don’t have to stress the initial read of the prompt nearly as much.

Know that the GMAT is a long, exhausting day, and you won’t likely get out of the test center without feeling completely wiped out. But if you manage your energy efficiently, you can use whatever energy you have left to triumphantly raise that winning score report over your head as you walk out.

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: No Calculator? No Problem.

For many GMAT examinees, the realization that they cannot use a calculator on the GMAT quantitative section is cause for despair. For most of your high school career, calculators were a featured part of the math curriculum (what TI are we up to now?); nowadays you almost always have Microsoft Excel a click away to perform those calculations for you.

But remember: it’s not that YOU don’t get to use a calculator on the GMAT quant section. It’s that NO ONE gets to use a calculator. And that creates the opportunity for a competitive advantage. If you know that the GMAT doesn’t include “calculator problems” – the testmakers know that you don’t get a calculator, too, so they create questions that savvy examinees can find efficient ways to solve by hand (or head) or estimate – then you can use that to your advantage, looking for “clean” numbers to calculate and saving calculations until they’re truly necessary. As an example, consider the problem:

A certain box contains 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?

(A) 3
(B) 6
(C) 14
(D) 17
(E) 20

If you’re well-versed in “non-calculator” math, you should recognize a couple things as you scan the problem:

1) The 23 oranges represent a prime number. That’s an ugly number to calculate with in a non-calculator problem.
2) 70% is a very clean number, which reduces to 7/10. Numbers that end in 0 don’t tend to play well with or come from double-digit prime numbers, so in this problem you’ll need to “clean up” that 23.
3) The 14 apples are pretty nicely related to the 70%. 14*5 = 70, and 14 = 7 * 2, where 70% is 7/10. So in sum, the 14 is a pretty “clean” number you’re working with to find a relationship that includes that also “clean” 70%. And the 23 is ugly.

So if you wanted to plug in numbers here to see how many oranges should be removed, keep in mind that your job is to get that 23 to look a lot cleaner. So while the Goldilocksian conventional methodology for backsolving is to “start with the middle number, then determine whether it’s correct, too big, or too small,” if you’re preparing for non-calculator math you should quickly see that with answer choice C of 14, that would give you 14 apples and 9 (which is 23-14) oranges), and you’re stuck at that ugly number of 23 as your total number of pieces of fruit. So your goal should be to find cleaner numbers to calculate.

You might try choice A, 3, which is very easy to calculate (23 oranges minus 3 = 20 oranges left), but a quick scan there would show that that’s way too many oranges (still more oranges than apples). So the other number that can clean up the 23 oranges is 17 (choice D), which would at least give you an even number (23 – 17 = 6). Because you’re now dealing with clean numbers (14, 6, and 70%) it’s worth doing the full calculation to see if choice D is really correct. And since 14 apples out of 20 total pieces of fruit is, indeed, 70%, you know that D is correct.

Now, if you follow these preceding paragraphs step-by-step, they should look just as long and unwieldy as the algebra or some traditional backsolving. But to an examinee seasoned in non-calculator math, finding “clean numbers worth testing” is more about the scan than the process. You should know that Odd + or – Odd = Even, but that Odd + or – Even is Odd. So with an even “fixed” number of 14 apples and an odd “changeable” number of 23 oranges, an astute GMAT test-taker looking to save time would probably eschew plugging in C first and realize that it’s just not going to be correct. Then another scan of numbers shows that only 3 and 17 are odd and prone to becoming “clean” when subtracted from the prime 23, so D should start looking tempting within seconds.

Note: this strategy isn’t for everyone or for every problem, but for those shooting for the 700s it can be extremely helpful to develop enough “number fluency” that you can save time not-testing numbers that you can see don’t have a real chance. On a non-calculator test that typically involves “clean” (even, divisible by 10, etc.) numbers, quickly recognizing which numbers will result in good, clean, non-calculator math is a very helpful skill.

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: Snoop Dogg Keeps Your Data Sufficiency Ability Out Of Limbo

Whenever you’re picking numbers on a Data Sufficiency problem, you have to keep one image in your mind: Snoop Dogg at a limbo contest. How will that help you master Data Sufficiency? How can the Doggfather help you beat the Testmaker? Well think about the two questions that Snoop would be asking himself constantly at such a contest:

1) How high can I get? (Snoop’s general state of mind)

2) How low can I go? (Because you know Snoop’s in it to win it)

And that mindset is absolutely crucial in a Data Sufficiency number-picking situation. On these problems, the GMAT Testmaker knows your tendencies well: you’re predisposed to picking numbers that are easy to work with. Consider an example like:

If x is a positive integer less than 30, what is the value of x?

(1) When x is divided by 3 the remainder is 2.

(2) When x is divided by 5 the remainder is 2

On this problem, most can quite quickly eliminate statement 1, as x could be 5, 8, 11, 14, 17, 20, 23, 26, or 29. Typically your quick-thinking methodology will have you look at 3, then add the remainder of 2 (producing 5), then start looking at other multiples of 3 and doing the same (6 + 2 gives you 8, 9 + 2 gives you 11, and so on).

And similarly you can apply that logic to statement 2 and eliminate that pretty quickly. The obvious first candidate is 7 (add the remainder of 2 to 5), and then you should see the pattern: 7, 12, 17, 22, and 27 are your options.

So when you look at these quick lists and see that the only place they overlap is 17 (17/5 is 3 remainder 2 and 17/3 is 5 remainder 2), you might opt for C.

But where does Snoop Dogg’s Limbo Contest come in? Look at the range they gave you: a POSITIVE INTEGER (so anything > 0) LESS THAN 30 (so anything <30). So when you combine those, your range is 0 < x < 30. Then ask yourself:

*How high can you get? Well, on either list you’ve gotten as close to 30 as possible. The next possible number on the first list (5, 8, 11, 14, 17, 20, 23, 26, 29…) is 32, but they tell you that x is less than 30 so you can’t get that high. And the next possible number on the second list (7, 12, 17, 22, 27…) is also 32, but again you’re not allowed to get that high. So you’ve definitely answered that question well.

*How low can you go? On this one, you haven’t yet exhausted the lower limit. Look at the patterns on those lists – on the first one, all numbers are 3 apart but you started at 5. If you move down 3, you get to 2 (2, 5, 8…). And 2/3 is 0 remainder 2, so 2 is a legitimate number on that list, a positive integer that leaves a remainder of 2 when divided by 3. And on the second list, you started at 7 and kept adding 5s. Move 5 spots to the left and you’re again at 2, which does leave a remainder of 2 when divided by 5. So upon closer examination, this problem has two solutions: 2 and 17.

The GMAT does a masterful job of setting ranges that test-takers don’t exhaust, and that’s where the Snoop Limbo mentality comes into play. If you’re always asking yourself “how high can I get and how low can I go?” you’ll force yourself to consider all available options. So for example, if the test were to tell you that:

x^2 < 25 –> This doesn’t just mean that x is less than 5 (how high can you get) it also means that x is greater than -5 (how low can you go)

x is a positive three-digit integer –> make sure you try 100 (how low can you go) and 999 (how high can you get)

x > 0 –> You might want to start with 1, but make sure you consider fractions like 1/2 and 1/8, too (how low can you go? all the way to 0.00000….0001), and try a number in the thousands or millions too (how high can you get?) since most people will just test easy-reference numbers like 1, 2, 5, and 10. A massive number might react differently.

In triangle ABC, angle ABC measures greater than 90 degrees –> remember that “how high can you get” is capped by the fact that the three angles have to add to 180, but this obtuse angle can get up even above 179 (how high can you get?)

x is a nonnegative integer –> the smallest integer that’s not negative is 0, not 1! How low can you go? You’d better check 0.

3 < x < 5 –> it doesn’t have to be 4, as x could be 3.0000000001 or 4.99999999

So keep Snoop’s Limbo Contest in mind when you pick numbers on Data Sufficiency problems. Don’t just pick the easiest numbers to plug in or the first few numbers that come to mind. The GMAT often plays to the edge cases, so always ask yourself how high you can get and how low you can go.

(and for our readers who prefer East Coast rap to West Coast rap, feel free to substitute this with the “Biggie (how big a number can you use) Smalls (how small a number can you use)” method and you can end up with a notoriously big 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: 5 Common Quant Section Mistakes That You Must Avoid

Much of your GMAT preparation will focus on “more” – learning more content, memorizing more rules, feeling more comfortable with the test format, and ultimately getting more questions right. But might impact your score more than “more” is your emphasis on “less” (or “fewer”). Feeling less anxiety, taking less time on tricky problems, having to guess less than in your previous attempts, and this ever-important concept:

Making fewer mistakes.

On an adaptive test like the GMAT, making silly mistakes on problems that you should get right can be devastating to your score. Not only do you get that question wrong, but now you’re being served easier questions subsequent to that, with an even more heightened necessity of avoiding silly mistakes there. So you should make a point to notice the mistakes you make on practice tests so that you’re careful not to make them again. Particularly under timed pressure in a high-stress environment we’re all susceptible to making mistakes. Here are 5 of the most common so that you can focus on making fewer of these:

If someone asked you to pick a number 1-10, you might pick 5 or 6, or maybe you’d shoot high and pick 9 or low and pick 2. But you probably wouldn’t respond with 9.99 or 3 and 1/3. We tend to think in terms of integers unless told otherwise. Similarly, if someone asked “what number, squared, gives you 25” you’d immediately think of 5, but it might take a second to think of -5. We tend to think in terms of positive numbers unless told otherwise.

On the GMAT, a major concept you’ll be tested on is your ability to consider all relevant options (an important skill in business). So before you lock in your answer, ask yourself whether you considered: positive numbers (which you naturally will), negative numbers, fractions/nonintegers, zero, the biggest number they’d let you use, and the smallest number they’d let you use.

An easy way for the GMAT testmaker to chalk up a few more incorrect answers on the problem is to include an extra valuable or an extra step. For example, if a problem asked:

Given that x + y = 8 and that x – y = 2, what is the value of y?

You might quickly use the elimination method for systems of equations, stacking the equations and adding them together:

x + y = 8
x – y = 2
2x = 10
x = 5

But before you pick “5” as your answer, reconsider the question – they made it convenient to solve for x, but then asked about y. And in doing so, they baited several test-takers into picking 5 when the answer is 2. Make sure you always ask yourself whether you’ve answered the right question!

3) Multiplying/dividing variables across inequalities.

By the time you take the test you should realize that if you multiply or divide both sides of an inequality by a NEGATIVE number, you have to flip the sign. -x > 5 would then become x < -5. But the testmakers also know that you’re often trained mentally to only employ that rule when you see the negative sign, –

To exploit that, they may get you with a Data Sufficiency question like:

Is a > 5b?

(1) a/b > 5

And many people will simply multiply both sides of statement 1’s equation by b and get to an ‘exact’ answer: a > 5b. But wait! Since you don’t know whether b is positive or negative, you cannot perform that operation because you don’t know whether you have to flip the sign. When you see variables and inequalities, make sure you know whether the variables are negative or positive!

4) Falling in love with the figure.

On geometry questions, you can only rely on the figure’s dimensions as fairly-reliable measurements if: One, it’s a Problem Solving question (you can never bring in anything not explicitly provided on a DS problem); and, two, if the figure does not say “not drawn to scale”. But if it’s a Data Sufficiency problem *or* if the figure says not drawn to scale, you have to consider various ways that the angles and shapes could be drawn. Often times people will see a “standard” triangle with all angles relatively similar in measure (around 60 degrees, give or take a few), and then base all of their assumptions on their scratchwork triangle of the same dimensions. But wait – if you’re not told that one of the angles could be, say, 175 degrees, you could be dealing with a triangle that’s very different from the one on the screen or the one on your scratchwork. Don’t get too beholden to the first figure you see or draw – consider all the options that aren’t prohibited by the problem.

5) Forgetting that a definitive “no” answer to a Data Sufficiency question means “sufficient.”

Say you saw the Data Sufficiency prompt:

Is x a prime number?

1) x = 10! + y, where y is an integer such that 1 < y < 10

Mathematically, you should see that since every possible value of y is a number that’s already contained within 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1, whatever y is the new number x will continue to be divisible by. For example, if y = 7, then you’re taking 10!, a multiple of 7, and adding another 7 to it, so the new number will be a multiple of 7.

Therefore, x is not a prime number, so the answer is “no.” But here’s where your mind can play tricks on you. If you see that “NO” and in your mind associate that with “Statement 1 — NO”, you might eliminate statement 1 when really statement 1 *is* sufficient. You can guarantee that answer that x is not prime, so even though the answer to the question is “no” the statement itself is “positive” in that it’s sufficient.

So be careful here – if you get a definitive “NO” answer to a statement, don’t cross it out or eliminate it!

Remember, a crucial part of your GMAT study plan should be making fewer mistakes. While you’re right to seek out more information, more practice problems, and more skills, “fewer” is just as important on a test like this. Make fewer of the mistakes above, and your score will take you more places.

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: Cedric the Entertainer becomes Cedric the GMAT Instructor

“They hope. We wish.”

In his classic routine from The Original Kings of Comedy, Cedric the Entertainer talks about the way that two different types of people view confrontation.

Some people hope that there’s no confrontation, worrying all the while that there might be.

Others – including Cedric himself – “wish a would” start some conflict. (Note: Kanye West borrowed this sentiment years later in a lyric for “The Good Life”)

On the GMAT, you want to be on Cedric’s team. Many test-takers go into the reasoning-based exam hoping that they don’t see too much Testmaker trickery, but those poised to score 700+ – the Original Kings of Calm on the test – wish the testmaker would. They’ve prepared to check negative numbers and nonintegers on Data Sufficiency. They’ve prepared to double-check their inferences on Critical Reasoning and Reading Comprehension questions to make sure they “must be true” (correct) and not just “probably true.” They’ve prepared to go back to the question on Problem Solving to make sure that the variable they solved for is the one that the question asked about. They’ve tracked the silly and recurring mistakes that they made in practice and they wish the test tries to sneak that by them on test day.

Why?

A few reasons. For one, any mistake you’ve made more than once in practice is something that you know is going to be difficult for people. By being ready for it, you’re poised to get “cheap” difficulty points (so to speak) when it’s really not that hard. If a question asks:

Starting with a full 12-gallon tank of gas, D.L. drove 225 miles getting 45 miles per gallon of gas burned. How much gas was left in D.L.’s tank at the end of the trip?”

You WANT them to ask about the gas that’s LEFT OVER (7 gallons) and include the amount of gas that was USED (5 gallons) as a trap answer. The math is pretty pedestrian, but that little twist – that you’ll solve for the amount used and then have to take just one more step to finish the problem, subtracting that 5 gallons used from the 12 you started with – will ensure that at least 20% more people get that problem wrong for just not reading carefully or from being in a hurry to finish the math and move on. You want to see those silly little trap answers there because they add difficulty (and therefore points) to your test without being truly “hard.”

Another reason is that there’s nothing more confidence-building than catching the GMAT trying to beat you with a silly trick that you’re more than prepared for. That’s Cedric’s point about concert tickets; sometimes it’s not sitting in great seats that makes you feel truly big-time, it’s being able to prove to someone else that you’ve earned the right to sit in them. That’s why Cedric wishes a would sit in his seats; he wants that pure satisfaction that comes from being justified in kicking them out! That adds happiness and satisfaction to the whole show. Similarly, when you catch the GMAT trying to trick you with a trap you saw coming from a mile away, that’s a huge confidence boost for the rest of the test. And that’s the ultimate point of this post – you can’t go into the test fearful of falling for traps. If that’s your mindset – “I really hope the GMAT doesn’t trick me into forgetting about zero” – then even if you catch that and save your answer, it can breed more stress. In a Data Sufficiency format, that could look like:

What is the value of x?

(1) 8x = x^2

(2) x is not a positive number

But on Cedric’s team – I wish the GMAT would try to sneak numbers like negatives, fractions, and zero past me – that same discussion looks like this (in bold because, well, it’s a bolder way of thinking):

What is the value of x?

(1) 8x = 8^2

<Cedric’s discussion with self: Man I know you want me to say 8 but that’s easy. I think x has to be 8 but I think you may be trying to trick me, GMAT. I’m too quick for that; I’m a grown-ass man dawg. We ain’t through here, you hear me?.>

(2) x is not a positive number

<Cedric’s discussion with self: There you go, always talking in code like that. x is not a positive number…you didn’t say it was negative so what’s the difference there. It’s zero; you don’t think I know that? So I see what you’re doing…I knew you’d try to throw zero at me. 8x = x^2 above? Anything times 0 is 0 so 0 is that second answer up top; I knew it wouldn’t be that easy. Statement 1 isn’t sufficient because of 0 and 8 and statement 2 says it can’t be 8. That’s C, dawg, as in you can’t C me easy like that. What do you have up next there Einstein?>

The real difference? Cedric’s mindset uses his knowledge that the GMAT will hit you with common traps as confidence. He knows it’s coming and he’s happy when he does see it, and catching those traps just breeds more confidence since he knows he’s better than the test and handling at least some of it’s difficulty with ease. The other mindset – even if it leads to a right answer on a particular question – breeds fear and anxiety, and those qualities can take a toll on future questions. By the time you take the GMAT you know what common traps it’s setting for you, so be confident when you see and avoid them! Like in this example:

x and y are consecutive integers such that x > y. What is the absolute value of y?

(1) The product xy is 20.

(2) x is a prime number.

Have you summoned your inner Cedric? Statement 1 begs you to say “oh, well if x is greater than y and they’re consecutive integers that multiply to 20, it’s 4 and 5 and x is the big one so y = 4. But wait – don’t you wish they’d try to throw a trick at you? Are you ready for it when it comes?

Statement 2 looks to just confirm what you saw before. Yep, x = 5 in statement 1, and if you take statement 2 alone it’s nowhere near sufficient. So what’s Cedric thinking? He wishes that the test would try to hit him with some of the low-level trickery it so often does. The test likes nonintegers? No, those don’t apply since the question says that x and y are indeed integers. The test likes 0? That doesn’t really apply either for statement 1 since 0 times anything can’t equal 20. But the GMAT also likes negative numbers, and you were wishing they’d try to get you with those. What other consecutive integers multiply to 20? -4 and -5. And in that case which is the smaller one (again, x > y)? That’s right, -5. So while the amateur might pick A thinking that the absolute value of y has to be 4, you can answer confidently like Cedric in the clip above:

“That’s right. Fo *and* five.”

Statement 1 is not sufficient alone, but statement 2 guarantees that the numbers have to be positive, so the answer is C. And since you wished the GMAT would try to get you with that positive/negative trick, you were looking for it, you answered correctly, and you confidently moved on to the next problem knowing that you’re on a roll.

On the GMAT, don’t hope they don’t try to make it difficult with those tricks that got you in practice. Wish they would make it difficult with those tricks because you’re confident you won’t fall for them again. They hope; you wish.

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: Thinking Out Loud With Drake, Nicki, and Wayne

It’s the hottest song in the country with a beat you just can’t get out of your head. Which is a good thing, because as you go in to take the GMAT you’d be well served to heed some of the lessons that Drake, Nicki Minaj, and Lil Wayne weave into the latest single from Nicki’s album.

The beat itself, with the steady bass line followed by the singsongy “You know…,” is a positive affirmation in and of itself. You DO know. You know how to solve these problems. You know that if you can’t make sense of the question you can often find clues in the answer choices. You know that just getting started and writing down what “you know…” is often the key to lessening anxiety and getting the prompt into an actionable format. You know.

But the master message in this track is the way that the three most prominent rappers in the game start each verse:

“Thinking out loud…”

Why is that important to you, the GMAT test-taker? Because that’s the way that the greatest test-takers start GMAT problems, too.

“Thinking out loud…”

Thinking out loud on the GMAT means having a conversation with yourself about the problem. It means staying relaxed and getting your thoughts together before you panic about the challenge of the problem. It means understanding that many problems won’t have an obvious set of steps that you can begin right away; they’ll require you to start loose and take account of your assets and the strategies in your toolkit. One of the keys to success on the GMAT is thinking out loud.

Check the rapgenius.com annotation for why Drizzy/Nicki/Weezy start each verse that way: All three MCs start their verses with some variation of “I’m thinkin’ out loud,” lending the song a breezy, friends-in-the-booth feeling. The recording was probably not a casual meeting, at all, but they’re good at sounding relaxed.

For that reason alone, thinking out loud is important for you. Their recording wasn’t a casual meeting – as they go on to say in all their lyrics they’re some of the wealthiest and most sought-after people on the planet, so that meeting was a big deal – but they were able to approach it like it was. Similarly your GMAT is, indeed, a big deal, but casual, calm problem solving is the name of the game. Teaching yourself to think out loud – “so I know that x and y must be positive but z could be either positive or negative…” – is a great way to get your mind thinking calmly and proactively as opposed to the all-too-commmon reactive mode of “I don’t even know where to start.”

But thinking out loud isn’t just a psychological tool, it’s also a tactical tool. Tricky GMAT problems are notorious for forcing you to see your assets from different angles before you can package them in a way to solve the problem. Too often students are looking for “the way” to do a problem when really they should be looking for “a way”. Which seems like a trivial difference but going in with the mindset that there may be several ways to solve the problem allows you to be flexible and see assets, not liabilities. Consider the example:

If side AB measures 3 and side BC measures 4, what is the length of line segment BD?

(A) 7/5
(B) 9/5
(C) 12/5
(D) 18/5
(E) 23/5

While many will rush into an abyss of Pythagorean Theorem, thinking out loud can show you a calm, proactive way to do this.

“Thinking out loud…I know that it’s a right triangle so if AB = 3 and BC = 4, it’s a 3-4-5 and side AC is 5. And as much as I want side AC to be cut in half by point D I don’t think I can do that. There are three different right triangles so I could go nuts with Pythagorean Theorem but that’s a lot of work. Thinking out loud, I also know that the perimeter is 3 + 4 + 5 and the area is 1/2(base)(height) so that’s 1/2 (3)(4) = 6. But what can I do with that?

Thinking out loud…the answer choices are all divided by 5…why do they all look like that? The only 5 in the problem so far is the 5 that’s side AC. Why would I multiply or divide by that?

Thinking out loud…BD is definitely going to be smaller than 4 because there’s no way it’s longer than side BC. So it can’t be E. But what else do I know about BD? It’s perpendicular to side AC, and AC is 5 and that’s that 5 in the denominator. Thinking out loud…what if I drew the triangle so that AC was on the bottom and not on the side? Then BD would be the height of triangle ABC and AC would be the base…but wait, I already know the area is 6, so that area 1/2 (side BD)(5) has to be 6, which means that side BD has to be 12/5, answer choice C.”

The takeaway here is that almost no one sees the area relationship with side BD right away, and that’s okay. The key to working on problems like these is staying loose and filling in unknowns. You can’t simply do math on paper and follow a set of steps…you need to do some thinking out loud and talk to yourself as you solve. For each of Drake, Nicki, and Wayne the phrase “thinking out loud” is followed by a wild description of how much money they have. Follow that “thinking out loud” philosophy and you’ll be on a similar pace with the help of an elite MBA.

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: Writing the AWA Without Engaging Your Brain

Writing a Friday GMAT Tip of the Week post on a tight deadline is a lot like writing the AWA essay in 30 minutes.

30 minutes is not a lot of time, many say, and because an effective essay needs to be well-organized and well-written it is therefore impossible to write a 30-minute essay.

Let’s discuss the extent to which we disagree with that conclusion, in classic AWA style.

In the first line of a recent blog post, the author claimed that writing an effective AWA essay in 30 minutes was impossible. That argument certainly has at least some merit; after all, an effective essay needs to show the reader that it’s well-written and well-organized. But this argument is fundamentally flawed, most notably because the essay doesn’t need to “be” well-written as much as it needs to “appear” well-written. In the paragraphs that follow, I will demonstrate that the conclusion is flawed, and that it’s perfectly possible to write an effective AWA essay in 30 minutes or less.

Most conspicuously, the author leans on the 30-minute limit for writing the AWA essay, when in fact the 30 minutes only applies to the amount of time that the examinee spends actually typing at the test center. In fact, much of the writing can be accomplished well beforehand if the examinee chooses paragraph and sentence structures ahead of time. For this paragraph, as an example, the transition “most conspicuously” and the decision to refute that claim with “in fact” were made long before I ever stopped to type. So while the argument has merit that you only have 30 minutes to TYPE the essay, you actually have weeks and months to have the general outline written in your mind so that you don’t have to write it all from scratch.

Furthermore, the author claims that the essay has to be well-written. While that’s an ideal, it’s not a necessity; if you’ve followed this post thus far you’ve undoubtedly seen a number of organizational cues beginning and then transitioning within each paragraph. However, once a paragraph’s point has been established the reader is likely to follow the point even if it’s a hair out of scope. Does this sentence add value? Maybe not, but since the essay is so well-organized the reader will give you the benefit of the doubt.

Moreover, while the author is correct that 30 minutes isn’t a lot of time, he assumes that it’s not sufficient time to write something actually well-written. Since the AWA is a formulaic essay – like this one, you’ll be criticizing an argument that simply isn’t sound – you can be well-prepared for the format even if you don’t see the prompt ahead of time. Knowing that you’ll spend 2-3 minutes finding three flaws in the argument, then plug those flaws into a template like this, you have the blueprint already in place for how to spend that time effectively. Therefore, it really is possible to write a well-written AWA in under 30 minutes.

As discussed above, the author’s insistence that 30 minutes is not enough time to write an effective AWA essay lacks the proper logical structure to be true. The AWA isn’t limited to 30 minutes overall, and if you’ve prepared ahead of time the 30 minutes you do have can go to very, very good use. How do I know? This blog post here took just under 17 minutes…

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: Prepare for the GMAT Using the Study Plan Rule of Thirds

Here on the first Friday of April, we’ve officially ended the first quarter of the year and fiscal reports are streaming in. But who’s in a hurry to finish 2015?

We’re still firmly entrenched in the first third of the year, and if 2015 is the year that you plan to conquer the GMAT you’re in luck. Why?

Because your GMAT study plan should include three phases:

1) Learn

One of the most common mistakes that GMAT studiers make is that they forget that they need to learn before they can execute. Are you keeping an eye on the stopwatch on every question you complete? Are you taking multiple practice tests in your first month of GMAT prep? Have you uttered the phrase “how could I ever do this in two minutes???”? If so, you’re probably not paying nearly enough attention to the learning phase. In the learning phase you should:

• Review core skills related to the GMAT by DOING them and not just by trying to memorize them. You were once a master of (or maybe a B-student at) factoring quadratics and identifying misplaced modifiers and completing long division. Retrain your mind to do those things well again by practicing those skills.
• Learn about the GMAT question types and the strategies that will help you attack them efficiently. For this you might consider a prep course or self-study program, or you can always start by reviewing prep books and free online resources.
• Take as much time as you need to complete and learn from problems. You’ll learn a lot more from struggling through a problem in six minutes than you will from taking two minutes, giving up, and then reading the typewritten solution in the back of the book. Let yourself learn! Again, it’s critical to learn by doing – by actively engaging with problems and talking yourself into understanding – than it is to try to memorize your way to success. The stopwatch is not your friend in the first third of your preparation!
• Embrace mistakes and keep a positive attitude. The GMAT is a hard test; most people struggle with unfamiliar question formats (Data Sufficiency, anyone?) and challenging concepts (without a calculator, too). Recognize that it will take some time to learn/re-learn these skills, and that making mistakes and thinking about them is one of the best ways to learn.

2) Practice

Regardless of how you’ve studied, you’ll need to complete plenty of practice to make sure you’re comfortable implementing those strategies and using those skills on test day. Once you’ve developed a good sense of what the GMAT is testing and how you need to approach it, it’s time to spend a few weeks devouring practice problems. Among the best sources include:

In this phase, you can start concerning yourself with the stopwatch a little and you’ll want to identify weaknesses and common mistakes so that you can emphasize those. Particularly with GMAT verbal, the more official problems you see the more you develop a feel for the style of them, so it’s important to emphasize practice not just for the conscious skills but also for those subconscious feelings you’ll get on test day from having seen so many ways they’ll ask you a question.

3) Execute

Before you take the GMAT you should have taken several practice tests. Practice tests will help you:

• Work on pacing and develop a sense for how much time you’ll need to complete each section. From there you can develop a pacing plan.
• Determine which “silly” mistakes you tend to make under timed pressure and exam conditions, and be hyperaware of them on test day.
• Develop the kind of mental stamina you’ll need to hold up under a 4-hour test day. Verbal strategies can be much easier to employ in a 60-minute study session than at the end of a several-hour test! Make sure that at least a few times you take the entire test including AWA and IR for the first hour.
• Continue to see new problems and hone your skills.

While it’s not a terrible idea to take a practice test early in your study regimen and another partway through the Practice phase, most of your tests should come toward the end of your study process. Why? Because the learning and practice phases are so important. You can’t execute until you’ve developed the skills and strategies necessary to do so, and you won’t do nearly as effective a job of gaining and practicing those if you’re not allowing yourself the time and subject-by-subject focus to learn with an open mind.

So be certain to let yourself learn with a natural progression via the GMAT Study Rule of Thirds. Learn first; then focus on practice; then emphasize execution via practice tests. Studying in thirds is the best way to ensure that you get into a school that’s your first choice.

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: Kanye West Teaches You How To Live The Data Sufficiency Good Life

Welcome back to Hip Hop Month in the GMAT Tip of the Week space, where we know precisely why you want an MBA: so you can live some of the good life. You want a better job with a higher salary and better benefits. You want to invest big chunks of that higher salary to create passive income that brings you even more money per year. And if they hate then let ’em hate and watch the money pile up. Welcome to the Good Life.

Few are living the good life better than the author/performer of “The Good Life,” Kanye West-Kardashian. And while it may seem ironic for “The College Dropout” to provide the best advice for getting into a top graduate school, the way Kanye describes the Good Life provides you with critical advice for obtaining the good life via a high quant score on the GMAT. When you’re practicing Data Sufficiency, pay attention to Yeezy as he says:

“So I roll through good. Y’all pop the trunk; I pop the hood. (Ferrari)
If she got the goods, and she got that ass, I got to look. (Sorry)”

How does this lyric relate to Data Sufficiency? We’ll translate.

As you’re rolling through a standard Data Sufficiency problem, it’s quite common to make your decision on statement 1 alone (pop the trunk) and then on statement 2 alone (pop the hood). And since time is of the essence, you do so quickly (Ferrari). For example, you might see the problem:

Is yz > x?

(1) y > x/z

And then quickly think to yourself “if I take the given statement and multiply both sides by z, I get a direct answer: yz > x, so that’s sufficient. Now let’s look at statement 2 alone because the answer must be A or D.”

But if you’re on your way to the Good Life, you need to play the Data Sufficiency game at a higher level, and that level may be a little different from the status quo. (“50 told me go ‘head switch the style up…”) So read on:

“If she got the goods” refers to the other statement. If “the other statement” seems fairly obvious on its own, most of us will see that as very, very good. We can quickly make our determination, eliminate the last answer choice or two, and move on. But wait:

“And she got that ass, I got to look,” of course, refers to statements having “that assistance.” For example, if statement 2 in this problem were to say:

(2) z < 0

Knowing that z is negative is “that ass(istance)”. It’s clearly insufficient on its own (what about y and x?), but in giving you the goods that z is negative it’s assisting you in avoiding a catastrophic mistake. In statement 1, you multiplied both sides of an INEQUALITY by a variable, z. But statement 2 tells you that the variable is negative, which means that simply multiplying by z without flipping the sign – or at least considering that the sign might need to be flipped – was a mistake. You had to consider negative/positive there – if z were positive, you just multiply; if it were negative, you’d multiply and flip. And since you didn’t know what sign z took when you assessed statement 1 alone, statement 1 actually was not sufficient. You need statement 2’s ass(istance), so the answer is C.

And that’s where Kanye’s lyric is so important. “IF she got that ass(istance), I got to look (Sorry)” means that, while the standard operating procedure for Data Sufficiency is to adhere strictly to: 1 alone, then forget; 2 alone, then forget; if nether was sufficient alone then try them together, that strategy leaves some valuable points on the table. If statement 2 gives you information that you hadn’t considered when you assessed statement 1, you’ve got to look at how that new piece of information would have impacted your decision. Did you need to know that or not? And although this new strategic element may contradict the easy process-of-elimination that helped you learn Data Sufficiency in the first place (Sorry), it’s critical if you’re going to live the 700+ good life – difficult Data Sufficiency is structured to reward those who see the potential for clues in the question stem and in the “other” statement, those who leverage assets that may not be readily apparent to the average test taker.

Note that sometimes that new piece of information is unnecessary. For example, if the question were instead:

Is yz = x?

(1) y > x/z

(2) z < 0

You actually don’t need to know the sign. When you use statement 1 alone and multiply both sides by z, you either get yz > x (if z is positive) or yz < x (if z is negative). It’s either greater than or less than with no room for equals, so you don’t need the sign. So statement 2 isn’t always necessary, but if it appears to give assistance you’ve got to look – you have to at least consider whether it’s important, because that’s where the GMAT has set up the difficulty. On the most difficult problems, the GMAT will tend to reward those who can leverage all available information to think critically and make a good decision, so it pays to at least take a fairly-obvious-on-its-own statement and look at it in the context of the other statement, just in case.

So learn from Yeezy (who in classic yz > x form is a much greater instructor than Xzibit) and remember – the easier statement’s always got the goods, so on the chance that it’s got that ass(istance), you’ve got to look. The good life: it feels like Palo Alto, it feels like Cambridge, it feels like Fontainebleu. If you’ve got a passion for flashing that acceptance letter, when a Data Sufficiency statement looks too obvious on your own, ask yourself what would Yeezus do.

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: Slow Motion Is Better Than No Motion

Welcome back to Hip Hop Month in the GMAT Tip of the Week space, where 3-13 isn’t just a day to honor Eminem’s group “Three and a Third” from 8 Mile (we’ll save that for 10/3). It’s also Common’s birthday, so what better day to let one of the most intellectual rappers in the game help you take your game toward his South Side neighborhood (Chicago-Booth isn’t all that far away) or, we suppose, to the North Side and Kellogg?

Now, while you’re in the thick of the quant section looking for an un-Common-ly high score, the only Common lyric in your head is probably “Go!”. But particularly when you get to dense word problems, you’ll likely have more success if you heed his advice from the beginning and the refrain from “The Food“:

Slow motion better than no motion.

What’s Common trying to tell you about how to approach the quant section? Essentially this: most examinees hurry through their initial read of a problem, taking ~20 seconds to read the entire paragraph prompt, only to get to the question mark, sigh, and go back to the top to get started. That’s “no motion” on your first 20 seconds – which, if you’re holding to an average of 2 minutes per problem, is almost 17% of the time you have to get it done.

What should you do? Slow motion, which is better than no motion. What does that mean? Start writing and thinking while you read. For example, consider this problem:

Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?

(A) 3 and 1/3 weeks
(B) 3 weeks
(C) 2 and 1/2 weeks
(D) 2 and 1/3 weeks
(E) 2 weeks

Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:

Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.

Rate (K) = 1 album / 5 weeks

Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.

Rate (C) = 1 album / x weeks

If the two emcees work together…

I’m adding these rates, so their combined rate is 1/5 + 1/x

…they can drop a full-length platinum compilation LP in 2 weeks.

And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2

Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?

I’m using that equation to solve for Common’s time, so I’m solving for x.

Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:

1/5 + 1/x = 1/2, so let’s get the x term on its own:

1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:

1/x = 5/10 – 2/10

1/x = 3/10, and from here you have options but let’s cross multiply:

10 = 3x, so divide both sides by 3 to get x alone:

10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice A.

What’s the real lesson? It’s like Common says: slow motion (is) better than no motion, so you should read just a little slower but have some scratchwork to show for your initial read of the prompt. If you can:

-assign variables
-jot down relationships or equations
-write down which variable the answer wants

You’ll have a lot more to show for your initial 30 seconds with each problem, and you’ll find that you solve problems much more quickly this way because you have less wasted time. So heed Common’s uncommon wisdom (which is really just common sense): the best way to Go is to remember that slow motion > no motion.

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: LLC Reasoning

In a time-honored tradition here at Veritas Prep, March is Hip Hop Month in the GMAT Tip of the Week space, and no cutting-edge hip hop blog in 2015 would be complete without mentioning the hottest thing from this year’s Grammys:

LL Cool J

Really? It’s been more than 20 years since LL had to start an album with the phrase “don’t call it a comeback; I’ve been here for years.” And yet as America’s favorite award show host and the star of either NCIS or CSI (all we know is that the man loves initials and acronyms), LL Cool J remains a household name in a young man’s game. Which should draw attention to his rather unique moniker:

LL Cool J

Which, of course, stands for Ladies Love Cool James, and also stands as an important Critical Reasoning lesson. When you think about it, LL Cool J’s name is kind of absurd. It’s three initials and a full word, and it forms a complete sentence (L = subject; L = verb; Cool = adjective; J = object). And he somewhat arbitrarily chose to spell out what, in the sentence, is the least important part. Ladies love James is the operative part of the sentence. “Cool” doesn’t add a ton of real value. So why did LL Cool J (James Smith, for those keeping score at home) choose to spell out what seems like the least critical word in the sentence?

Because LL Cool J is a marketing and Critical Reasoning genius.

Think about it: Ladies LCJ would be a terrible name. So would L Love CJ. And LLC James has a nice businessman ring to it, but lacks the kind of street cred it took to rise through the early NYC rap ranks in the 1980s. It had to be LL Cool J.

And what’s more: LL Cool J is telling you how you can master Critical Reasoning by calling attention to the modifier or adjective that adds specificity. Consider these two arguments.

1) The Something Like a Phenomenon award each year goes to the highest selling album of the year. This year, the highest selling album of the year was LL Cool J’s Mr. Smith, so Mr. Smith will be awarded the Something Like a Phenomenon award.

2) The Something Like a Phenomenon award each year goes to the highest selling rap album of the year. This year, the highest selling album of the year was LL Cool J’s Mr. Smith, so Mr. Smith will be awarded the Something Like a Phenomenon award.

What’s the difference? Like the name LL Cool J itself, it really comes down to an adjective. In #2, the first premise has an adjective qualifier – to win the award, it has to be a rap album. And since the second premise doesn’t tell us that Mr. Smith was a rap album, that argument is now vulnerable to criticism…that one adjective that made things a little bit more specific left a hole in the argument for us to attack.

And noticing that hole is everything on Strengthen and Weaken CR questions. If it’s a Strengthen question and we’ve noticed that gap, you should be looking for something that demonstrates that Mr. Smith was a rap album. And if it were a Weaken question, you’re looking for a reason to believe that it wasn’t. But either way, by finding that hole in the argument you now know what you’re looking for.

So the lesson? Train yourself – like the man who could have just been called LLJ did – to spot those extra adjectives or modifiers that make the conclusion or major premise of an argument that much more specific. Look for things like:

“Def Jam Records must find a way to reduce its costs.” vs. “Def Jam records must find a way to reduce its distribution costs.”

“Mr. Smith was host of the Grammys.” vs. “Mr. Smith was host of the 2015 Grammys.”

“LL Cool J proclaimed himself the greatest.” vs. “LL Cool J proclaimed himself the greatest of all time.”

and

“I need a girl.” vs. “I need an around-the-way girl.”

So step one is to notice those (cool) qualifiers that lend themselves to gaps in arguments, in which a more-generic premise just can’t connect to that more-specific statement. Once you’ve identified that potential for a gap in logic, check the other statements to see if they match the specificity. If they don’t – as they generally won’t in GMAT Critical Reasoning – well, then get critical. As mama says…knock it out.

Are you studying for the GM Admissions T? 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 Dress is White and Gold and Your GMAT Score Can Become Golden

The Dress” is white and gold, as all reasonable people can certainly agree. But a sizable, misguided percentage of the internet vehemently disagrees with that fact, proving two major points:

1) You can’t trust what people say on the internet.

2) Your five major senses can deceive you, so you can’t rely on them when approaching GMAT Sentence Correction problems.

If you want to avoid leaving the GMAT test center black-and-blue, beaten up by tricky Sentence Correction problems, make sure you do better than trusting your ear. Much like the powers that launched The Dress on us, the GMAT testmakers know that our senses don’t always hold true to logic and reason, and so they mine Sentence Correction problems with opportunities to be misled by your ear. Consider the example:

While Jackie Robinson was a Brooklyn Dodger, his courage in the face of physical threats and verbal attacks was not unlike that of Rosa Parks, who refused to move to the back of a bus in Montgomery, Alabama.
(A) not unlike that of Rosa Parks, who refused
(B) not unlike Rosa Parks, who refused
(C) like Rosa Parks and her refusal
(D) like that of Rosa Parks for refusing
(E) as that of Rosa Parks, who refused

For many, the phrase “not unlike” is a red (or black-and-blue) flag right away. Your ear may very well abhor that language, and if so you’ll quickly eliminate the white-and-gold answer A and answer B right away. But A is actually correct, as this sentence requires:

-“that of” (to compare Jackie Robinson’s courage with Rosa Parks’s courage)
-“who refused” (to make it clear that Rosa Parks was the one who refused to the back of the bus; with “for refusing” in D it’s unclear who that last portion of the sentence belongs to)

And only choice A includes both, so it has to be right. What makes this problem tricky? The GMAT testmakers know that:

1) You read left to right and top to bottom
2) Your ear likely won’t take kindly to “not unlike” even though it’s not wrong. “Not unlike” is saying “it’s not totally different from, even though it’s not the same thing,” whereas “like” indicates a much closer relationship. There’s a continuum there, and the phrase “not unlike” has a valid meaning on that continuum of similarity.

And so what do the testmakers do? They:

1) Make “not unlike” vs. “like” the first difference between answer choices, daring you to use your ear before you use your Sentence Correction strategy (look for modifiers, verbs, pronouns, and comparisons first)

2) Put the answer you won’t like (but should pick) first at answer choice A, making it easy for you to eliminate the right answer right away before you start considering the core skills listed in the parentheses above

And the lesson?

Don’t trust your ear as your primary deciding factor on Sentence Correction problems. Your senses – as The Dress shows – are prone to deceiving you, and what’s more the testmakers know that and will use it against you! They want to reward critical thinking, the use of logic and reason, the adherence to proven systems and processes. So they give you the opportunity to use your not-always-reliable senses, and reward you for learning the lesson of The Dress. Your senses can fool you, so on important decisions like The Dress and Sentence Correction, don’t simply rely on your senses: they may just leave you black and blue.

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: Data Sufficiency and The Imitation Game

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

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

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

Is x – y > a – b?

(1) x + b > a + y

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

x – y > a – b

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

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

(1) bc = a

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

c = a/b

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

Is x – y > a – b?

(1) a > x and y > b

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

a + y > x + b

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

a – b > x – y

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

By Brian Galvin

# Should You Purchase The New Enhanced Score Report?

For anyone who has ever underperformed their goals on the GMAT, the first question they’ve asked is usually “where did it all go wrong?”. And for those who have asked that question since October 1, 2013, or will ask it soon, there may be an answer waiting for you.

The GMAT Enhanced Score Report is here.

This new add-on report, which costs \$24.95 USD, will provide you with diagnostic feedback from your official GMAT exam, including such information as:

-Performance (percentile ranking) by question type, with question types including Data Sufficiency vs. Problem Solving; Arithmetic vs. Algebra/Geometry; Critical Reasoning vs. Sentence Correction vs. Reading Comprehension

-Time management by question type, broken down by the same categories above

-Time management by correct vs. incorrect answers for Integrated Reasoning

-Percent of Integrated Reasoning questions answered correctly

So those are the features, but the question remains…is this worth \$25? And the answer is a little less concrete than you might like: it depends. Why?

*The report won’t give you question-by-question feedback, so you’ll never know if you got that crazy coordinate geometry problem at #17 right or wrong, and you won’t know which individual problems you spent way too much time on. You’ll get much more aggregate data, which may or may not help.

*If your performance was pretty similar to that of your practice tests – which ought to be the case for most examinees who have taken several practice tests – the report should likely match your expectations. If you’ve prepared well for the test, there shouldn’t be many surprises in that report.

*However, some users will see some VERY enlightening information. Say, for example, you were quite strong on Critical Reasoning and Reading Comprehension (~80th percentile each) but significantly less adept on Sentence Correction (

So who will benefit from the report? Those who have some outliers or anomalies in their performance. If you were 60th percentile on quant, and a combination of 55th, 62nd, 63rd, and 59th on DS, PS, Arith, Alg/Geo, you’re not going to learn very much from that report. But if one area is significantly higher or significantly lower than the others, you’ll learn something.

-If you’re going to retake the exam, the Enhanced Score Report is essentially a 10% increase on your next registration fee, and has the potential to be pretty enlightening. Especially if you’re likely to spend \$25 over the next month on Starbucks or Amazon impulse purchases or anything else extraneous, it’s a good idea to put that \$25 toward the score report. You might not learn anything, but the chance that you’ll learn something is substantial enough that you should leave no stone unturned.

-But if you have \$25 left in your GMAT budget and the choice is between the Enhanced Score Report or a tool like the GMAT Question Pack or one of the Official Guide supplements, choose the extra practice. If you’ve prepared thoroughly there shouldn’t be too many surprises on that report, and whatever you’d learn you’d have to improve by practicing anyway.

So in sum, GMAT retakers should probably pony up the \$25 because the more you know about your performance, the higher the likelihood that you can improve it. Almost all Veritas Prep instructors agree – we want to see those reports from our students! But don’t be surprised if the report only confirms what you suspected. The Enhanced Score Report is a tool to guide your hard work, not a substitute for the effort required to improve.

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

By Brian Galvin

# GMAT Tip of the Week: All About That Base

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

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

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

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

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

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

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

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

2^4 * a = 2^5b

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

a = 2^5b / 2^4

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

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

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

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

By Brian Galvin

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

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

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

Probability

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

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

Probability #2

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

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

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

Critical Reasoning

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

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

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

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

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

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

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

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

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

By Brian Galvin

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

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

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

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

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

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

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

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

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

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

By Brian Galvin

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

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

Thou doth protest too much. Meaning:

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

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

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

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

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

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

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

Or you’ll hear questions like:

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

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

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

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

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

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

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

By Brian Galvin

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

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

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

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

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

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

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

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

Consider this problem:

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

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

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

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

What is the units digit of 2^40?

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

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

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

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

It’s always the last place you look.

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

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

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

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

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

By Brian Galvin

# GMAT Tip of the Week: Serial and Sufficiency

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

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

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

(1) x = 5

(2) y + z = 2

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

x, y, z, 3, x, y, z, 3, x, y, z, 3…

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

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

But let’s interview Sarah Koenig here:

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

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

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

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

By Brian Galvin

# 4 Questions To Ask Yourself On Min/Max GMAT Problems

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

However…

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

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

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

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

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

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

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

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

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

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

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

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

Question 1:

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

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

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

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

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

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

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

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

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

Question 2:

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

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

Here ask yourself the same questions:

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

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

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

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

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

By Brian Galvin

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

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

Why?

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

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

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

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

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

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

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

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

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

What is the perimeter of triangle ABC?

(1) Side AB measures 5 meters.

(2) Side AC measures 12 meters.

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

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

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

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

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

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

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

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

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

By Brian Galvin

# GMAT Tip of the Week: Sentence Correction in Real Life

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

Wait for it.

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

How?

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

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

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

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

Correct:

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

Incorrect:

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

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

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

Signals of verb tense: since, from, until

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

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

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

By Brian Galvin