The post GMAT Tip of the Week: Movember and Moving Your GMAT Score Higher appeared first on Veritas Prep Blog.

]]>Because while the Movember Foundation is committed to using mustaches as a way to increase both awareness of and funding for men’s health issues (in particular prostate and testicular cancer), many young men focus solely on the mustache-growth facet of the month. And “I’m growing a mustache for Movember” without the fundraising follow-through is akin to the following quotes:

“I’m growing a mustache for Movember.”

“I’m running a marathon for lymphoma research.”

“I’m dumping a bucket of ice water over my head on Facebook.”

“I’m taking a GMAT practice test this weekend.”/”I’m going to the library to study for the GMAT.”

Now, those are all noble sentiments expressed with great intentions. But another thing they all have in common is that they’re each missing a critical action step in their mission to reach their desired outcome. Growing a mustache does very little to prevent or treat prostate cancer. Running a marathon isn’t what furthers scientists’ knowledge of lymphoma. Dumping an ice bucket over your head is more likely to cause pneumonia than to cure ALS. And taking a practice test won’t do very much for your GMAT score.

Each of those actions requires a much more thorough and meaningful component. It’s the fundraising behind Movember, Team in Training, and the Ice Bucket Challenge that advances those causes. It’s your effort to use your mustache, sore knees, and Facebook video to encourage friends and family to seek out early diagnosis or to donate to the cause. And it’s the follow-up to your GMAT practice test or homework session that helps you increase your score.

This weekend, well over a thousand practice tests will be taken in the Veritas Prep system, many by young men a week into their mustache growth. But the practice tests that are truly valuable will be taken by those who follow up on their performance, adding that extra step of action that’s all so critical. They’ll ask themselves:

*Which mistakes can I keep top-of-mind so that I never make them again?*

*How could I have budgeted my time better? Which types of problems take the most time with the least probability of a right answer, and which types would I always get right if I just took the extra few seconds to double check and really focus?*

*Based on this test, which are the 2-3 content areas/question types that I can markedly improve upon between now and my next practice test?*

*How will I structure this week’s study sessions to directly attack those areas?*

And then they’ll follow up on what they’ve learned, following the new week’s plan of attack until it’s time to again take the first step (a practice test) with the commitment to take the substantially-more-important follow-up steps that really move the needle toward success.

Taking a practice test and growing a Movember mustache are great first steps toward accomplishing noble goals, but in classic Critical Reasoning form, premise alone doesn’t guarantee the conclusion. So make sure you don’t leave the GMAT test center this November with an ineffective mustache and a dismal score – put in the hard work that has to accompany that first step, and this can be a Movember to Remember.

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Trick or Treat appeared first on Veritas Prep Blog.

]]>But as we head into Halloween weekend, it’s an appropriate time for you to think back to the phrase that earned you pounds and pounds of candy (and maybe tons if you followed Jim Harbaugh’s double-costume strategy): Trick or Treat.

In a GMAT context, that means that on these challenging questions, what tricks one examinee is the “treat” or reward for those who buy into the critical thinking mindset that the GMAT is set up to reward. The GMAT testmakers themselves are defensive about the idea of the “trap” answer, preferring to see it as a reward system; the intent isn’t to “trick” people as much as it is to “treat” higher-order thinking and critical reasoning. Consider the Data Sufficiency example:

Is x > 3z?

(1) x/z > 3

(2) z > 0

Here the “trick” that the testmaker employs is that of negative numbers. Many people will say that Statement 1 is sufficient (just multiply both sides by z and Statement 1 directly answers the questions, x > 3z), but it’s important to remember that z could be negative, and if it were negative you’d have to flip the sign, as you do in an inequality problem when you multiply or divide by a negative. In that case x < 3z and the answer is an emphatic no.

Now, those test takers who lament the trick after getting it wrong are somewhat justified in their complaint that “you forgot about negatives!” is a pretty cheap trick. But that’s not the entire question: Statement 2 exists, too, and it’s a total throwaway when you consider it alone. Why is it there? It’s there to “treat” those who are able to leverage that hint: why would it matter if z is greater than 0? That statement provides a very important clue as to how you should have been thinking when you looked at Statement 1.

If your initial read of Statement 1 – under timed pressure in the middle of a test, mind you – had you doing that quick algebra and making the mistake of saying that it’s sufficient, that’s understandable. But if you blew right past the clear hint in the second statement, you missed a very important opportunity to seize the treat. To some degree this problem is about the math, but the GMAT often adds that larger degree of leveraging hints – after all, much of business success comes down to your ability to find an asset that others have overlooked, or to get more value out of an asset than anyone else could.

So as you study for the GMAT, keep that Halloween spirit close by. When you miss a problem because of a dirty “trick,” take a second to also go back and see if you missed a potential treat – a reward that the GMAT was dangling just out of reach so that only the most critical thinkers could find it and take advantage. GMAT problems aren’t all ghosts, goblins, and ghouls out to frighten and trick you; often they include very friendly pieces of information just disguised or camouflaged enough that you have to train yourself to spot the treat.

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Percents Are Easy, Words Are Hard appeared first on Veritas Prep Blog.

]]>[Answers: $12.80; 55%; 75%]

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?

So what are the answers?

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.

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Your GMAT Verbal (Donald) Trump Card appeared first on Veritas Prep Blog.

]]>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.”

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: What To Do When The GMAT Gets All Netflix On You appeared first on Veritas Prep Blog.

]]>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.

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: Yogi Berra Teaches GMAT Sentence Correction appeared first on Veritas Prep Blog.

]]>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.

**It’s all in your head.**

*“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.

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: There's a Hole in the Bucket... But Not in Your GMAT Score! appeared first on Veritas Prep Blog.

]]>Henry: There’s a hole in the bucket (dear Liza, dear Liza, dear Liza…)

Liza: Then fix it (dear Henry, dear Henry, dear Henry…)

Henry: With what shall I fix it?

Liza: With straw.

Henry: The straw is too long.

Liza: Well, cut it.

Henry: With what shall I cut it?

Liza: With an axe.

Henry: The axe is too dull.

Liza: Then sharpen it.

Henry: With what shall I sharpen it?

Liza: With a stone.

Henry: The stone is too dry.

Liza: Then wet it.

Henry: With what shall I wet it? (Editor’s note: really, Henry?)

Liza: With water.

Henry: With what shall I fetch it?

Liza: With a bucket.

Henry (and his redemption): There’s a hole in the bucket.

*<Repeat over and over again>*

Now, what makes that song such a children’s and family favorite? In some part it’s popular because it repeats upon itself, but mostly it’s popular because even small children have to laugh at Henry’s heroic lack of critical thought. Henry simply can’t function unless Liza directly hands him the specific next step.

…and Liza and Henry’s conversation is not all that much unlike many GMAT tutoring sessions.

Among the pool of GMAT test-takers, there are plenty of Henrys. And as much as you may laugh at him, you’re playing the part of Henry just a little too much when you:

- Stop working on a problem in less than 2 minutes and flip to the back of the book for the solution. (“With what shall I solve it, dear textbook, dear textbook…”)
- Give up on the calculations without first checking the answer choices to see if they afford you a shortcut. (“The calculation is too long, dear GMAT, dear GMAT”)
- Frustratedly ask “but how am I supposed to see that I should do that?”. (“But how should I know that, dear teacher, dear teacher…”)
- Write off the question as flawed because you disagree with the correct answer. (“The solution is just wrong, dear answer key, dear answer key…”)

Eavesdrop on a GMAT tutoring session at your local library or coffee shop and there’s a good chance you’ll hear more Liza-and-Henry than you’d expect. Students frequently ask for the rule but not the lesson, and tutors often simply oblige. But to avoid Henrydom on test day (this conversation should last 3-5 seconds, not be a song that kids will sing for an entire field trip bus ride. Figure it out, Henry!) you need to train yourself to ask and answer those questions for yourself.

We at Veritas Prep suggest the “toolkit” approach as opposed to a “if it’s this kind of problem I will steadfastly use this method without critical thought” mindset. When the bucket has a hole or the straw is too long, ask yourself what other tools are in your toolkit.

For example, if you blank on a rule, try proving it with small numbers. Unsure whether Even + Odd is Even or Odd? Just try 2 + 1 (an even plus and odd) and recognize that the answer is 3 (Odd!). Or if the algebra looks too messy, see if you can plug in an answer choice to get a better feel for the solutions’ relationship to the problem.

What makes “There’s a Hole in the Bucket” funny is what could ultimately make your own GMAT test experience miserable: you (and Henry) have to employ a combination of critical thinking, trial-and-error, and patience to solve problems. The exam simply isn’t testing your ability to memorize a “Liza List” of steps to solve each problem; many hard problems are designed specifically to reward those who overcome the adversity of the “obvious” method leading you down a rabbit hole of awful algebra or those who find a familiar theme in a completely unfamiliar setup. So to train yourself to be an anti-Henry:

- Force yourself to fight and struggle through hard practice problems. The written solution isn’t likely to be nearly as helpful as your having had to struggle to gain understanding.
- Think in terms of your “toolkit” – if your first inclination doesn’t lead to success, rummage around your toolkit to see what other types of concepts might apply to that problem.
- When you don’t know or can’t remember a rule, test the concept with small numbers to see if you can retrain your brain or prove the relationship to yourself.
- Hold your tutor accountable – they should be asking you probing questions like Socrates, not handing you one-time solutions and steps like Liza (she’s not totally innocent in this either…she enables Henry way too much!)

The way the song goes, there will be a hole in Henry’s bucket forever, but if there’s a hole in your GMAT score you can fix it with a new study mindset (even if the straw is too long…).

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

*By Brian Galvin.*

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]]>The post GMAT Tip of the Week: 10 Must-Know Divisibility Rules For the GMAT (#3 Will Blow Your Mind!) appeared first on Veritas Prep Blog.

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**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*

The post GMAT Tip of the Week: 10 Must-Know Divisibility Rules For the GMAT (#3 Will Blow Your Mind!) appeared first on Veritas Prep Blog.

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]]>Small numbers on your noteboard.

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*

The post GMAT Tip of the Week: Small Numbers Lead to Big Scores appeared first on Veritas Prep Blog.

]]>The post GMAT Tip of the Week: Eazy E Shows You How To Take Your Quant Score Straight Outta Compton And Straight To Cambridge appeared first on Veritas Prep Blog.

]]>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

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

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

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*

The post GMAT Tip of the Week: Eazy E Shows You How To Take Your Quant Score Straight Outta Compton And Straight To Cambridge appeared first on Veritas Prep Blog.

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