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]]>Fortunately, and contrary to popular belief, the GMAT isn’t “pure evil.” Wherever it provides opportunities for less-savvy examinees to waste their time, it also provides a shortcut for those who have put in the study time to learn it or who have the patience to look for the elevator, so to speak, before slogging up the stairs. And one classic example of that comes with the “at least one” type of probability question.

To illustrate, let’s consider an example:

*In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random and at the same time, what is the probability that at least one of the marbles will be yellow?*

*(A) 5/17*

* (B) 12/17*

* (C) 25/81*

* (D) 56/81*

* (E) 4/9*

Here, you can first streamline the process along the lines of one of those “There are two types of people in the world: those who _______ and those who don’t _______” memes. Your goal is to determine whether you get a yellow marble, so you don’t care as much about “blue” and “black”…those can be grouped into “not yellow,” thereby giving you only two groups: 8 yellow marbles and 10 not-yellow marbles. Fewer groups means less ugly math!

But even so, trying to calculate the probability of every sequence that gives you one or two yellow marbles is labor intensive. You could accomplish that “not yellow” goal several ways:

First marble: Yellow; Second: Not Yellow

First: Not Yellow; Second: Yellow

First: Yellow; Second: Yellow

That’s three different math problems each involving fractions and requiring attention to detail. There ought to be an easier way…and there is. When a probability problem asks you for the probability of “at least one,” consider the only situation in which you WOULDN’T get at least one: if you got none. That’s a single calculation, and helpful because if the probability of drawing two marbles is 100% (that’s what the problem says you’re doing), then 100% minus the probability of the unfavorable outcome (no yellow) has to equal the probability of the favorable outcome. So if you determine “the probability of no yellow” and subtract from 1, you’re finished. That means that your problem should actually look like:

PROBABILITY OF NO YELLOW, FIRST DRAW: 10 non-yellow / 18 total

PROBABILITY OF NO YELLOW, SECOND DRAW: 9 remaining non-yellow / 17 remaining total

10/18 * 9/17 reduces to 10/2 * 1/17 = 5/17. Now here’s the only tricky part of using this technique: 5/17 is the probability of what you DON’T want, so you need to subtract that from 1 to get the probability you do want. So the answer then is 12/17, or B.

More important than this problem is the lesson: when you see an “at least one” probability problem, recognize that the probability of “at least one” equals 100% minus the probability of “none.” Since “none” is always a single calculation, you’ll always be able to save time with this technique. Had the question asked about three marbles, the number of favorable sequences for “at least one yellow” would be:

Yellow Yellow Yellow

Yellow Not-Yellow Not-Yellow

Yellow Not-Yellow Yellow

Yellow Yellow Not-Yellow

Not-Yellow Yellow Yellow

…

(And note here – this list is not yet exhaustive, so under time pressure you may very well forget one sequence entirely and then still get the problem wrong even if you’ve done the math right.)

Whereas the probability of No Yellow is much more straightforward: Not-Yellow, Not-Yellow, Not-Yellow would be 10/18 * 9/17 * 8/16 (and look how nicely that last fraction slots in, reducing quickly to 1/2). What would otherwise be a terrifying slog, the “long way” becomes quite quick the shorter way.

So, remember, when you see “at least one” probability on the GMAT, employ the “100% minus probability of none” strategy and you’ll save valuable time on at least one Quant problem on test day.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, 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: 3 Guiding Principles for Exponent Problems appeared first on Veritas Prep Blog.

]]>But as thoroughly and quickly as you know those rules, this exponent-based problem in front of you has you stumped. You know what you need to KNOW, but you’re not quite sure what you need to DO. And that’s an ever-important part about taking the GMAT – it’s necessary to know the core rules, facts, and formulas, but it’s also every bit as important to have action items for how you’ll apply that knowledge to tricky problems.

For exponents, there are three “guiding principles” that you should keep in mind as your action items. Any time you’re stuck on an exponent-based problem, look to do one (or more) of these things:

**1) Find Common Bases**

Most of the exponent rules you know only apply when you’re dealing with two exponents of the same base. When you multiply same-base exponents, you add the exponents; when you divide two same-base exponents, you subtract. And if two exponents of the same base are set equal, then you know that the exponents are equal. But keep in mind – these major rules all require you to be using exponents with the same base! If the GMAT gives you a problem with different bases, you have to find ways to make them common, usually by factoring them into their prime bases.

So for example, you might see a problem that says that:

*2^x * 4^2x = 8^y. Which of the following must be true?*

*(A) 3x = y*

* (B) x = 3y*

* (C) y = (3/5)x*

* (D) x = (3/5)y*

* (E) 2x^2 = y*

In order to apply any rules that you know, you must get the bases in a position where they’ll talk to each other. Since 2, 4, and 8 are all powers of 2, you should factor them all in to base 2, rewriting as:

2^x * (2^2)^2x = (2^3)^y

Which simplifies to:

2^x * 2^4x = 2^3y

Now you can add together the exponents on the left:

2^5x = 2^3y

And since you have the same base set equal with two different exponents, you know that the exponents are equal:

5x = 3y

This means that you can divide both sides by 5 to get x = (3/5)y, making answer choice D correct. But more importantly in a larger context, heed this lesson – when you see an exponent problem with different bases for multiple exponents, try to find ways to get the bases the same, usually by prime-factoring the bases.

**2) Factor to Create Multiplication**

Another important thing about exponents is that they represent recurring multiplication. x^5, for example, is x * x * x * x * x…it’s a lot of x’s multiplied together. Naturally, then, pretty much all exponent rules apply in cases of multiplication, division, or more exponents – you don’t have rules that directly apply to addition or subtraction. For that reason, when you see addition or subtraction in an exponent problem, one of your core instincts should be to factor common terms to create multiplication or division so that you’re in a better position to leverage the rules you know. So, for example, if you’re given the problem:

*2^x + 2^(x + 3) = (6^2)(2^18). What is the value of x?*

*(A) 18*

* (B) 20*

* (C) 21*

* (D) 22*

* (E) 24*

You should see that in order to do anything with the left-hand side of the equation, you’ll need to factor the common 2^x in order to create multiplication and be in a position to divide and cancel terms from the right. Doing so leaves you with:

2^x(1 + 2^3) = (6^2)(2^18)

Here, you can simplify the 1 + 2^3 parenthetical: 2^3 = 8, so that term becomes 9, leaving you with:

9(2^x) = (6^2)(2^18)

And here, you should heed the wisdom from above and find common bases. The 9 on the left is 3^2, and the 6^2 on the right can be broken into 3^2 * 2^2. This gives you:

(3^2)(2^x) = (3^2)(2^2)(2^18)

Now the 3^2 terms will cancel, and you can add the exponents of the base-2 exponents on the right. That means that 2^x = 2^20, so you know that x = 20. And a huge key to solving this one was factoring the addition into multiplication, a crucial exponent-based action item on test day.

**3) Test Small Numbers and Look For Patterns**

Remember: exponents are a way to denote repetitive, recurring multiplication. And when you do the same thing over and over again, you tend to get similar results. So exponents lend themselves well to finding and extrapolating patterns. When in doubt – when a problem involves too much abstraction or too large of numbers for you to get your head around – see what would happen if you replaced the large or abstract terms with smaller ones, and if you find a pattern, then look to extrapolate it. With this in mind, consider the problem:

*What is the tens digit of 11^13?*

*(A) 1*

* (B) 2*

* (C) 3*

* (D) 4*

* (E) 5*

Naturally, calculating 11^13 without a calculator is a fool’s errand, but you can start by taking the first few steps and seeing if you establish a pattern:

11^1 = 11 –> tens digit of 1

11^2 = 121 –> tens digit of 2

11^3 = 1331 –> tens digit of 3

And depending on how much time you have you could continue:

11^4 = 14641 –> tens digit of 4

But generally feel pretty good that you’ve established a recurring pattern: the tens digit increases by 1 each time, so by 11^13 it will be back at 3. So even though you’ll never know exactly what 11^13 is, you can be confident in your answer.

Remember: the GMAT is a test of how well you apply knowledge, not just of how well you can memorize it. So for any concept, don’t just know the rules, but also give yourself action items for what you’ll do when problems get tricky. For exponent problems, you have three guiding principles:

1) Find Common Bases

2) Factor to Create Multiplication

3) Test Small Numbers to Find a Pattern

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, 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: Taking The GMAT Like It’s Nintendo Switch appeared first on Veritas Prep Blog.

]]>How?

The main feature of the Switch (and the driving factor behind its name) is its flexibility. It can be an in-home gaming system attached to a fixed TV set, but then immediately Switch to a hand-held portable system that allows you to continue your game on the go. Nintendo’s business plan is primarily based on offering flexibility…and on the GMAT, your plan should be to prove to business schools that you can offer the same.

The GMAT, of course, tests algebra skills and critical thinking skills and grammar skills, but beneath the surface it also has a preference for testing flexibility. Many problems will punish those with pure tunnel vision, but reward those who can identify that their first course of action isn’t working and who can then Switch to another plan. This often manifests itself in:

- Math problems that seem to require algebra…but halfway through beg to be back-solved using answer choices.
- Sentence Correction problems that seem to ask you to make a decision about one major difference…but for which the natural choices leave you with clearer-cut errors elsewhere.
- Critical Reasoning answer choices that seem out of scope at first, but reward those who read farther and then see their relevance.
- Data Sufficiency problems for which you’ve made a clear, confident decision on one statement…but then the other statement shows you something you hadn’t considered before and forces you to reconsider.
- The overall concept that if you’re a one-trick pony – you’re a master of plugging in answer choices, for example – you’ll find questions that just won’t reward that strategy and will force you to do something else.

Flexibility matters on the GMAT! As an example, consider the following Data Sufficiency question:

*Is x/y > 3? *

*1) 3x > 9y*

*2) y > 3y*

If you’re like many, you’ll confidently address the algebra in Statement 1, divide both sides by 3 to get x > 3y, and then see that if you divide both sides by y, you can make it look exactly like the question stem: x/y > 3. And you may very well say, “Statement 1 is sufficient!” and confidently move on to Statement 2.

But when you look at Statement 2 – either conceptually or algebraically – something should stand out. For one, there’s no way that it’s sufficient because it doesn’t help you determine anything about x. And secondly, it brings up the point that “y is negative” (algebraically you’d subtract y from both sides to get 0 > 2y, then divide by 2 to get 0 > y). And here’s where, if it hasn’t already, your mind should Switch to “positive/negative number properties” mode. If you weren’t thinking about positive vs. negative properties when you considered Statement 1, this one gives you a chance to Switch your thinking and reconsider – what if y were negative? Algebraically, you’d then have to flip the sign when you divide both sides by y:

3x > 9y : Divide both sides by 3

x > 3y : Now divide both sides by y, but remember that if y is positive you keep the sign (x/y > 3), and if y is negative you flip the sign (x/y < 3).

With this in mind, Statement 1 doesn’t really tell you anything. x/y can be greater than 3 or less than 3, so all Statement 1 does is eliminate that x/y could be exactly 3. Now you have the evidence to Switch your answer. If you initially thought Statement 1 was sufficient, Statement 2 has given you a chance to reassess (thereby demonstrating flexibility in thinking) and realize that it’s not, until you know whether y is negative or positive.

Statement 2 supplies that missing piece, and the answer is thus C. But more important is the lesson – because the GMAT so values mental flexibility, it will often provide you with clues that can help you change your mind if you’re paying attention. So on the GMAT, take a lesson from Nintendo Switch: flexibility is an incredibly marketable skill, so look for clues and opportunities to Switch your line of thinking and save yourself from trap answers.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, 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: As You Debate Over Answer Choices… Just Answer The Freaking Question! appeared first on Veritas Prep Blog.

]]>It’s no surprise that candidate approval ratings are low for the same reason that far too many GMAT scores are lower than candidates would hope. Why?

People don’t directly answer the question.

This is incredibly common in the debates, where the poor moderators are helpless against the talking points and stump speeches of the candidates. The public then suffers because people cannot get direct answers to the questions that matter. This is also very common on the GMAT, where students will invest the time in critical thought and calculation, and then levy an answer that just doesn’t hit the mark. Consider the example:

*Donald has $520,000 in campaign money available to spend on advertising for the month of October, and his advisers are telling him that he should spend a minimum of $360,000 in the battleground states of Ohio, Florida, Virginia, and North Carolina. If he plans to spend the minimum amount in battleground states to appease his advisers, plus impress his friends by a big ad spend specific to New York City (and then he will skip advertising in the rest of the country), how much money will he have remaining if he wants 20% of his ad spend to take place in New York City?*

*(A) $45,000*

* (B) $52,000*

* (C) $70,000*

* (D) $90,000*

* (E) $104,000*

As people begin to calculate, it’s common to try to determine all of the facets of Donald’s ad spend. If he’s spending only the $360,000 in battleground states plus the 20% he’ll spend in New York City, then $360,000 will represent 80% of his total ad spend. If $360,000 = 0.8(Total), then the total will be $450,000. That means that he’ll spend $90,000 in New York City. Which is answer choice D…but that’s not the question!

The question asked for how much of his campaign money would be left over, so the calculation you need to focus on is the $520,000 he started with minus the $450,000 he spent for a total of $70,000, answer choice C. And in a larger context, you can learn a major lesson from Wharton’s most famous alumnus: it’s not enough for your answer to be related to the question. On the GMAT, you must answer the question directly! So make sure that you:

- Double check which portion of a word problem the question asked for. Don’t be relieved when your algebra spits out “a” number. Make sure it’s “the” number.
- Be careful with Strengthen/Weaken Critical Reasoning problems. A well-written Strengthen problem will likely have a good Weaken answer choice, and vice-versa.
- In algebra problems, make sure to identify the proper variable (or combination of variables if they ask, for example “What is 6x – y?”).
- With Data Sufficiency problems, pay attention to the exact values being asked for. One of the most common mistakes that people make is saying that a statement is insufficient because they’re looking to fill in all variables, when actually it is sufficient to answer the exact combination that the test asked for.

As you watch the debate this weekend, notice (How could you not?) how absurd it is that the candidates just about never directly answer the question…and then vow to not make the same mistake on your GMAT exam.

**free online GMAT seminars **running all the time. And as always, 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: Gary Johnson, Aleppo, and What To Do When Your Mind Goes Blank appeared first on Veritas Prep Blog.

]]>In pressure situations, it’s not uncommon for your brain to fail you as you “blank” on a concept you know (or should know). So it’s important to have strategies ready for that moment that very well may come to you. To paraphrase the Morning Joe question to Johnson:

What would you do about “Aleppo?”

Meaning: what would you do if your mind were to go blank on an important GMAT rule or formula?

There are four major strategies that should be in your toolkit for such a situation:

**1) Test Small Numbers**

You should absolutely know formulas like exponent rules or relationships like that between dividend, divisor, and remainder in division, but sometimes your mind just goes blank. In those cases, remember that math rules are logically-derived, not arbitrarily ordained! Math rules will hold for all possible values, so if you’re unsure, test numbers. For example, if you’re forced to solve something like:

*(x^15)(x^9) =*

And you’ve blanked on what to do with exponents, try testing small numbers like (2^2)(2^3). Here, that’s (4)(8) = 32, which is 2^5. So if you’re unsure, “Do I add or multiply the exponents?” you should see from the small example that you definitely don’t multiply, and that your hunch that, “Maybe I add?” works in this case, so you can more confidently make that decision.

Similarly, if a problem asked:

*When integer y is divided by integer z, the quotient is equal to x. Which of the following represents the remainder in terms of x, y, and z?*

*(A) x – yz*

* (B) zy – x*

* (C) y – zx*

* (D) zy – x*

* (E) zx – y*

Many students memorize equations to organize dividend, divisor, quotient, and remainder, but in the fog of war on test day it can even be difficult to remember which element of the division problem is the dividend (it’s the number you start with) and which is the divisor (it’s the one you divide by). So if your mind has blanked on any part of the equation or on which element is which, just test it with small numbers to remind yourself how the concept works:

11 divided by 4 is 2 with a remainder of 3. How do you get to the remainder? You take the 11 you started with and subtract the 8 that you get from taking the divisor of 4 and multiplying it by the quotient of 2. So the answer is y (what you started with) minus zx (the divisor times the quotient), or answer choice C.

Simply put, if you blank on a rule or concept, you can test small numbers to remind yourself how it works.

**2) Use Process of Elimination and Work Backwards From the Answer Choices**

One beautiful thing about the GMAT is that, while in “the real world” if you need to know the Pythagorean Theorem and blank on it, you’re out of luck (well, unless you have a Google-enabled Smartphone in your pocket which you almost certainly do…), on the GMAT you have answer choices as assets. So if your own work stalls in progress, you can look to the answer choices to eliminate options you know for sure you wouldn’t get with that math:

What is x^5 + x^6? You know you don’t add or multiply those exponents, so even if you don’t see to factor out the common x^5, you could eliminate answer choices like x^11 and x^30.

Or you can look to the answer choices to see if they help you determine how you’d apply a rule. For example, if a problem forces you to employ the side ratios for a 45-45-90 triangle and you’ve forgotten them, the presence of some square roots of 2 in the answer choices can help you remember. The square root of 2 is greater than 1, and two sides must match, so if someone spots you “the rule includes a square root of 2” the only thing it can really be is the ratio x : x : x(√2)

Gary Johnson should have been so lucky – had the question been posed as, “What would you do about Aleppo, which is either a DJ on the new Drake album; the epicenter of the Syrian crisis; or a new restaurant in the Garment District?” he would get that question right every single time. Answer choices are your friends…when you blank, consult them!

**3) Think Logically**

Similar to that 45-45-90 “what else could it be?” logic, many times when you blank on a rule, you can work your way to either the rule itself or just to the answer by thinking logically about it. For example, if you end up with math that includes a radical sign in the denominator and can’t quite remember the steps for rationalizing the denominator:

*What is 1/(1 – √2)?*

*(A) √2*

* (B) 1 – √2*

* (C) 1 + √2*

* (D) -1 – √2*

* (E) √2 – 1*

Not all is lost! Sure, algebraically you should multiply the numerator and the denominator by the conjugate (1 + *√*2) but you can also logically work with this one. The numerator is 1, and the denominator is 1 – the square root of 2. You know that *√*2 is between 1 and 2, so what do you know about the denominator? It’s negative, and it’s a fraction (or decimal), so once you’ve taken 1 divided by that, your answer must be a negative number to the left of -1 – only answer choice D would work. So, yeah, you blanked on the steps, but you can still employ logic to back into the answer.

**4) Write Down Everything You Know**

Blanking is particularly troublesome because it’s that moment of panic. You’re trying to retrace your mental steps and the answer is elusive; it’s a moment you’re not in control of at that point. So take control! The more you’re actively working – jotting down other related formulas or facts you know, working on other facets of the diagram or problem and saving that step for last, etc. – the more you’re controlling, or at least actively managing, the situation.

Gary Johnson couldn’t get away with a “Who Wants to Be a Millionaire?” style talk-through-it (“Um, I know it’s not the name of any congressmen; it’s not Zika, it’s not…”) without looking dumb, but no one is going to audit your scratchwork and release it to *Huffington Post*, so you’re free to jot down half-baked thoughts and trial calculations to your heart’s content. Actively manage the situation, and you can work your way through that dreaded “my mind is blank” moment.

So learn from Gary Johnson. No matter how much you’ve prepared for your GMAT, there’s a chance that your mind will go blank on something you know that you know, but just can’t recall in the moment. But you have options, so heed the wisdom above, and let Trump or Clinton handle the gaffes for the day while you move on confidently to the next question.

**free online GMAT seminars **running all the time. And as always, 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: 6 Reasons That Your Test Day Won’t Be A Labor Day appeared first on Veritas Prep Blog.

]]>What does that mean?

On a timed test like the GMAT, one of the biggest drains on your score can be a combination of undue time and undue energy spent on problems that could be done much simpler. “The long way is the wrong way” as a famous GMAT instructor puts it – those seconds you waste, those extra steps that could lead to error or distraction, they’ll add up over the test and pull your score much lower than you’d like it to be. With that in mind, here are six ways to help you avoid too much labor on test day:

QUANTITATIVE SECTION

**1) Do the math in your order, only when necessary.**

Because the GMAT doesn’t allow a calculator, it heavily rewards candidates who can find efficient ways to avoid the kind of math for which you’d need a calculator. Very frequently this means that the GMAT will tempt you with calculations that you’d ordinarily just plug-and-chug with a calculator, but that can be horribly time-consuming once you start.

For example, a question might require you to take an initial number like 15, then multiply by 51, then divide by 17. On a calculator or in Excel, you’d do exactly that. But on the GMAT, that calculation gets messy. 15*51 = 765 – a calculation that isn’t awful but that will take most people a few steps and maybe 20 seconds. But then you have to do some long division with 17 going into 765. Or do you? If you’re comfortable using factors, multiples, and reducing fractions, you can see those two steps (multiply by 51, divide by 17) as one: multiply by 51/17, and since 51/17 reduces to 3, then you’re really just doing the calculation 15*3, which is easily 45.

The lesson? For one, don’t start doing ugly math until you absolutely know you have to perform that step. Save ugly math for later, because the GMAT is notorious for “rescuing” those who are patient enough to wait for future steps that will simplify the process. And, secondly, get really, really comfortable with factors and divisibility. Quickly recognizing how to break a number into its factors (51 = 3*17; 65 = 5*13; etc.) allows you to streamline calculations and do much of the GMAT math in your head. Getting to that level of comfort may take some labor, but it will save you plenty of workload on test day.

**2) Recognize that “Answers Are Assets.”**

Another way to avoid or shortcut messy math is to look at the answer choices first. Some problems might look like they involve messy algebra, but can be made much easier by plugging in answer choices and doing the simpler arithmetic. Other times, the answer choices will lead themselves to process of elimination, whether because some choices do not have the proper units digit, or are clearly too small.

Still others will provide you with clues as to how you have to attack the math. For example, if the answer choices are something like: A) 0.0024; B) 0.0246; C) 0.246; D) 2.46; E) 24.6, they’re not really testing you on your ability to arrive at the digits 246, but rather on where the decimal point should go (how many times should that number be multiplied/divided by 10). You can then set your sights on the number of decimal places while not stressing other details of the calculation.

Whatever you do, always scan the answer choices first to see if there are easier ways to do the problem than to simply slog through the math. The answers are assets – they’re there for a reason, and often, they’ll provide you with clues that will help you save valuable time.

**3) Question the Question – Know where the game is being played.**

Very often, particularly in Data Sufficiency, the GMAT Testmaker will subtly provide a clue as to what’s really being tested. And those who recognize that can very quickly focus on what matters and not get lost in other elements of the problem.

For example, if the question stem includes an inequality with zero (x > 0 or xy < 0), there’s a very high likelihood that you’re being tested on positive/negative number properties. So, when a statement then says something like “1) x^3 = 1331”, you can hold off on trying to take the cube root of 1331 and simply say, “Odd exponent = positive value, so I know that x is positive,” and see if that helps you answer the question without much calculation. Or if the problem asks for the value of 6x – y, you can say to yourself, “I may not be able to solve for x and y individually, but if not, let’s try to isolate exactly that 6x – y term,” and set up your algebra accordingly so that you’re efficiently working toward that specific goal.

Good test-takers tend to see “where the game is being played” by recognizing what the Testmaker is testing. When you can see that a question is about number properties (and not exact values) or a combination of values (and not the individual values themselves) or a comparison of values (again, not the actual values themselves), you can structure your work to directly attack the question and not fall victim to a slog of unnecessary calculations.

VERBAL SECTION

**4) Focus on keywords in Critical Reasoning conclusions.**

The Verbal section simply *looks* time-consuming because there’s so much to read, so it pays to know where to spend your time and focus. The single most efficient place to spend time (and the most disastrous if you don’t) is in the conclusion of a Strengthen or Weaken question. To your advantage, noticing a crucial detail in a conclusion can tell you exactly “where the game is being played” (Oh, it’s not how much iron, it’s iron PER CALORIE; it’s not that Company X needs to reduce costs overall, it’s that it needs to reduce SHIPPING costs; etc.) and help you quickly search for the answer choices that deal with that particular gap in logic.

On the downside, if you don’t spend time emphasizing the conclusion, you’re in trouble – burying a conclusion-limiting word or phrase (like “per calorie” or “shipping”) in a long paragraph can be like hiding a needle in a haystack. The Testmaker knows that the untrained are likely to miss these details, and have created trap answers (and just the opportunity to waste time re-reading things that don’t really matter) for those who fall in that group.

**5) Scan the Sentence Correction answer choices before you dive into the sentence.**

Much like “Answers are Assets” above, a huge help on Sentence Correction problems is to scan the answer choices quickly to see if you can determine where the game is being played (Are they testing pronouns? Verb tenses?). Simply reading a sentence about a strange topic (old excavation sites, a kind of tree that only grows on the leeward slopes of certain mountains…) and looking for anything that strikes you as odd or ungrammatical, that takes time and saps your focus and energy.

However, the GMAT primarily tests a handful of concepts over and over, so if you recognize what is being tested, you can read proactively and look for the words/phrases that directly control that decision you’re being asked to make. Do different answers have different verb tenses? Look for words that signal time (before, since, etc.). Do they involve different pronouns? Read to identify the noun in question and determine which pronoun it needs. You’re not really being tasked with “editing the sentence” as much as your job is to make the proper decision with the choices they’ve already given you. They’ve already narrowed the scope of items you can edit, so identify that scope before you take out the red marking pen across the whole sentence.

**6) STOP and avoid rereading.**

As the Veritas Prep Reading Comprehension lesson teaches, stop at the end of each paragraph of a reading passage to ask yourself whether you understand Scope, Tone, Organization, and Purpose. The top two time-killers on Reading Comprehension passages/problems are re-reading (you get to the end and realize you don’t really know what you just read) and over-reading (you took several minutes absorbing a lot of details, but now the clock is ticking louder and you haven’t looked at the questions yet).

STOP will help you avoid re-reading (if you weren’t locked in on the first paragraph, you can reread that in 30 seconds and not wait to the end to realize you need to reread the whole thing) and will give you a quick checklist of, “Do I understand just enough to move on?” Details are only important if you’re asked about them, so focus on the major themes (Do you know what the paragraph was about – a quick 5-7 word synopsis is perfect – and why it was written? Good.) and save the details for later.

It may seem ironic that the GMAT is set up to punish hard-workers, but in business, efficiency is everything – the test needs to reward those who work smarter and not just harder, so an effective test day simply cannot be a Labor Day. Use this Labor Day weekend to study effectively so that test day is one on which you prioritize efficiency, not labor.

**free online GMAT seminars **running all the time. And as always, 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: The EpiPen Controversy Highlights An Allergic Reaction You May Have To GMAT Critical Reasoning appeared first on Veritas Prep Blog.

]]>But perhaps only a pre-MBA blog could take the stance “but what is Mylan’s goal?” and expect the overwhelming-and-enthusiastic response “Maximize Shareholder Value! (woot!)” Regardless of your opinion on the EpiPen issue, you can take this opportunity to learn a valuable lesson for GMAT Critical Reasoning questions:

**When a Critical Reasoning asks you to strengthen or weaken a plan or strategy, your attention MUST be directed to the specific goal being pursued.**

Here’s where this can be dangerous on the GMAT. Consider a question that asked:

*Consumer advocates and doctors alike have recently become outraged at the activities of pharmaceutical company Mylan. In an effort to leverage its patent to maximize shareholder value, Mylan has decided to increase the price of its signature EpiPen product sixfold over the last few years. The EpiPen is a product that administers a jolt of epinephrine, a chemical that can open airways and increase the flow of blood in someone suffering from a life-threatening allergic reaction.*

*Which of the following, if true, most constitutes a reason to believe that Mylan’s strategy will not accomplish the company’s goals?*

*(A) The goal of a society should be to protect human life regardless of expense or severity of undertaking.*

*(B) Allergic reactions are often fatal, particularly for young children, unless acted on quickly with the administration of epinephrine, a product that is currently patent-protected and owned solely by Mylan.*

*(C) Computer models predict that, at current EpiPen prices, most people will hold on to their EpiPens well past the expiration date, leading to their deaths and inability to purchase future EpiPens.*

Your instincts as a decent, caring human being leave you very susceptible to choosing A or B. You care about people with allergies – heck, you or a close friend/relative might be one of them – and each of those answer choices provides a reason to join the outcry here and think, “Screw you, Mylan!”

But, importantly for your chances of becoming a profit-maximizing CEO via a high GMAT score, you must note this: neither directly weakens the likelihood of Mylan “leveraging its patent to maximize shareholder value,” and that is the express goal of this strategy. As stated in the argument, that is the only goal being pursued here, so your answer must focus directly on that goal. And as horrible as it is to think that this might be the thought process in a corporate boardroom, choice C is the only one that suggests that this strategy might lead to lesser profits (first they buy the product less often, then they can’t buy it ever again; fewer units sold could equal lower profit).

The lesson here? Beware “plan/strategy” answer choices that allow you to tangentially address the situation in the argument, particularly when you know that you’re likely to have an opinion of some sort on the topic matter itself. Instead, completely digest the specifics of the stated goal, and make sure that the answer you choose is directly targeted at the objective. Way too often on these problems, students insert themselves in the larger topic and lose sight of the specific goal, falling victim to the readily available trap answers.

So give your GMAT score a much-needed shot of Critical Reasoning epinephrine – focus on the specifics of the plan, and save your tangential angst for the social media where it belongs.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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]]>The post Quarter Wit, Quarter Wisdom: The Power of Deduction on GMAT Data Sufficiency Questions appeared first on Veritas Prep Blog.

]]>We know that the total number of factors of a number A (prime factorised as X^p * Y^q *…) is given by (p+1)*(q+1)… etc.

So, if we know that a number has, say, 6 total factors, what can we say about the number?

6 = (p+1)*(q+1) = 2*3, so p = 1 and q = 2 or vice versa.

A = X^1 * Y^2 where X and Y are distinct prime numbers.

Today, we will look at a data sufficiency question in which we can use factors to deduce much more information than what we might first guess:

*When the digits of a two-digit, positive integer M are reversed, the result is the two-digit, positive integer N. If M > N, what is the value of M?*

*Statement 1: The integer (M – N) has 12 unique factors.*

*Statement 2: The integer (M – N) is a multiple of 9.*

With this question, we are told that M is a two-digit integer and N is obtained by reversing it. So if M = 21, then N = 12; if M = 83, then N = 38 (keeping in mind that M must be greater than N). In the generic form:

M = 10a + b and N =10b + a (where a and b are single-digit numbers from 1 to 9. Neither can be 0 or greater than 9 since both M and N are two-digit numbers.)

We also know that no matter what M and N are, M > N. Therefore:

10a + b > 10b + a

9a > 9b

a > b

Let’s examine both of our given statements:

*Statement 1: The integer (M – N) has 12 unique factors.*

First, let’s figure out what M – N is:

M – N = (10a + b) – (10b + a) = 9a – 9b

Say M – N = A. This would mean A = 9(a-b) = 3^2 * (a-b)

The total number of factors of A where A = X^p * Y^q *… can be calculated using the formula (p+1)*(q+1)* …

We know that A has 3^2 as a factor, so X = 3 and p = 2. Therefore, the total number of factors would be (2+1)*(q+1)*… = 3*(q+1)*… = 12, so (q+1)*… must be 4.

Case 1:

This means q may be 3 so that (q+1) is 4. Since a-b must be less than or equal to 9 and must also be the cube of a number, (a-b) must be 8. (Note that a-b cannot be 1 because then the total number of factors of A would only be 3.)

So, a must be 9 and b must be 1 in this case (since a > b). The integers will be 91 and 19, and since M > N, M = 91.

Case 2:

Another possibility is that (a-b) is a product of two prime factors (other than 3), both with the power of 1. In that case, the total number of factors = (2+1)*(1+1)*(1+1) = 12

Note, however, that the two prime factors (other than 3) with the smallest product is 2*5 = 10, but the difference of two single-digit positive integers cannot be 10. This means that only Case 1 can be true, therefore, Statement 1 alone is sufficient. This is certainly not what we expected to find from just the total number of factors!

*Statement 2: The integer (M – N) is a multiple of 9.*

M – N = (10a + b) – (10b + a) = 9a – 9b, so M – N = 9 (a-b) . This is already a multiple of 9.

We get no new information with this statement; (a-b) can be any integer, such as 2 (a = 5, b = 3 or a = 7, b = 5), etc. This statement alone is insufficient, therefore our answer is A.

Don’t take the given data of a GMAT question at face value, especially if you are expecting questions from the 700+ range. Ensure that you have deduced everything that you can from it before coming to a conclusion.

*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**!*

*Karishma**, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as **this blog**!*

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]]>The post GMAT Tip of the Week: Making Your GMAT Score SupeRIOr to Ryan Lochte’s appeared first on Veritas Prep Blog.

]]>Whatever it is, it can’t be nearly as bad as being pulled over by fake cops – no lights or nothing, just a badge – then being told to get on the ground and having a gun placed on your forehead and being like, “whatever.” So your big event of 2016 will already go a lot better than Ryan Lochte’s did; you have that going for you.

What else do you have going for you on the GMAT? The ability to learn from the most recent few days of Lochte’s life. Lochte’s biggest mistake wasn’t vandalizing a gas station bathroom at 4am, but rather making up his own story and creating an even larger mess. And that’s a huge lesson that you need to keep in mind for the GMAT:

Don’t make up your own story.

Here’s what that means, on three major question types:

**DATA SUFFICIENCY**

People make up their own story on Data Sufficiency all the time. And like a prevailing theory about Lochte (he didn’t connect the vandalism of the bathroom to the men coming after him for restitution; he really did think that he had been robbed for no reason), it’s not that they’re intentionally lying. They’re just “conveniently” misremembering what they’ve read or connecting dots that weren’t actually connected in real life. Consider the question:

*The product of consecutive integers a, b, c, and d is 5040. What is the value of integer d?*

*(1) d is prime*

*(2) d < c < b < a*

Once people have factored 5040 into 7*8*9*10, they can then quickly recognize that Statement 1 is sufficient: the only prime number in that bunch is 7, so d must be 7. But then when it comes to Statement 2, they’ve often made up their own story. By saying “d is the smallest, and, yep, that’s 7!” they’re making up the fact that these consecutive integers are positive. That was not specifically stated! So it could be 7, 8, 9, and 10 or it could be -7, -8, -9, and -10, making d either -10 or 7. And the GMAT (maybe like an NBC interviewer?) makes it easy for you to make up your own story.

With Statement 1, prime numbers must be positive, so if you weren’t already thinking only about positives, the question format nudges you further in that direction. The answer is A when people often mistakenly choose D, and the reason is that the question makes it easy for you to make up your own story when looking at Statement 2. So before you submit an answer, always ask yourself, “Am I only using the facts explicitly provided to me, or am I somehow making up my own story?”

**CRITICAL REASONING**

Think of your friends who are good storytellers. We hate to break it to you, but they’re probably making at least 10-20% of those stories up. Which makes sense. “It was a pretty big fish,” is a lot less compelling than, “It was the biggest fish any of us had ever seen!” Case in point, the Olympics themselves.

No commentator this week has said that Michael Phelps, Lochte’s teammate, is “a really good swimmer.” They’re posing, “Is he the greatest athlete of all time?” because words that end in -st capture attention (and pageviews). Even Lochte was guilty of going overly-specific for dramatic effect: there was, indeed, a gun pointed at his taxi, but not resting on his forehead. His version just makes the story more exciting and dramatic…and you may very well be guilty of such a mistake on the GMAT. Consider:

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

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

*(A) There were not other lakes in the immediate area before the lava dammed up the river.*

* (B) The lake contained fish that the human ancestors could have used for food.*

* (C) The lava under the lake-bottom sediments did not contain any human fossil remains.*

* (D) The lake was deep enough that a person could drown in it.*

* (E) The bones were already in the sediments by the time the lake disappeared.*

The correct answer here is E (if the bones were not already there, then they’re not good evidence that people were there during that time), but the popular trap answer is C. Consider what would happen if C were untrue: that means that there were human fossil remains that pre-date the time period in question.

But here’s where Lochte Logic is dangerous: you’re not trying to prove that the FIRST humans lived in this period at this time; you’re just trying to prove that humans lived here during that time. And whether or not there were fossils from 2.5 million or 4 million years ago doesn’t change that you still have this evidence of people in that 2 million-1.5 million years ago timeframe.

When people choose C, it’s almost always because they made up their own story about the argument – they read it as, “The earliest human ancestors lived in this place and time,” and that’s just not what’s given. Why do they do that? For Lochte’s very own reasons: it makes the story a little more interesting and a little more favorable.

After all, the average pre-MBA doesn’t spend much time reading about archaeology, but if some discovery is that level of exciting (We’ve discovered the first human! We’ve discovered evidence of aliens!) then it crosses your Facebook/Twitter feeds. You’re used to reading stories about the first/fastest/greatest/last, and so when you get dry subject matter your mind has a tendency to put those words in there subconsciously. Be careful – do not make up your own story about the conclusion!

**READING COMPREHENSION**

A similar phenomenon occurs with Reading Comprehension. When you read a long passage, your mind tends to connect dots that aren’t there as it fills in the rest of the story for you. Just like Lochte, who had to fill in the gap of, “Hey what would I have said if someone pointed a gun at me and told me to get on the ground? Oh right…’whatever’ is my default answer for most things,” your mind will start to fill in details that make logical sense.

The problem then comes when you’re asked an Inference question, for which the correct answer must be true based on the passage. For example, if two details in a passage are:

- Michael swam the fastest race of his life.
- Ryan’s race was one of the slowest he’s ever swam.

You might answer the question, “*Which of the following is a conclusion that can be drawn from the passage?*” with:

*(A) Michael swam faster than Ryan.*

Your mind – particularly amidst a lot of other text between those two facts – wants to logically arrange those two swims together, and with “fastest” for Michael and “slowest” for Ryan, it kind of seems logical that Michael was faster. But those two races are never compared directly to each other. Consider that if Michael and Ryan aren’t Phelps and Lochte, but rather filmmaker Michael Moore and Olympic champion Ryan Lochte, then of course Lochte’s slowest swim would still be way, way faster than Moore’s fastest.

Importantly, Reading Comprehension questions love to bait unwitting test-takers with comparisons as answer choices, knowing that your mind is primed to create your own story and draw comparisons that are probably true, but just not proven. So again, any time you’re faced with an answer that seems obvious, go back and ask yourself if the details you’re using were provided to you, or if instead, you’re making up your own story.

So learn a valuable lesson from Ryan Lochte and avoid making up your own story, sticking only to the clean facts of the matter. Stay true to the truth, and you’ll walk out of the test center saying “Jeah!”

**free online GMAT seminars **running all the time. And as always, 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: What Simone Biles and the Final Five Can Teach You About GMAT Math appeared first on Veritas Prep Blog.

]]>Swimmer Simone Manuel and gymnast Simone Biles each won historic gold medals, and if you’re at all inspired to pursue your own “go for the gold” success in business school (maybe Stanford like Manuel, or UCLA like Biles), you can learn a lot from the Olympic experience. Two lessons, in particular, stand out from the performance of Biles and her “Final Five” teammates:

**Connect Your Skills**

There’s no way to watch Olympic gymnastics and not be overwhelmingly impressed by the skills that each gymnast brings to competition. So at times it’s frustrating and saddening to hear the TV announcers discuss deduction after deduction; shouldn’t everyone at all times just be yelling, “Wow!!!!” at the otherworldly talents of each athlete?

Much like the GMAT, though, Olympic gymnastics is not about the sheer possession of these skills – at that level, everyone has them. It’s more about the ability to execute them and, as becomes evident from the expert commentary of Tim Dagget and Nastia Liukin, to **connect** them. It’s not the uneven bars handstand or release itself that wins the gold, it’s the ability to connect skill after skill as part of a routine. The line, “She was supposed to connect that skill to another…” is always followed by, “That will be a deduction” – both in Olympic gymnastics and on the GMAT.

How does that affect you?

By test day, you had better have all of the necessary skills to compete on the GMAT Quant Section. Area of a triangle, Pythagorean Theorem, Difference of Squares…if you don’t know these rules, you’re absolutely sunk. But to do *really* well, you need to quickly connect skill to skill, and connect items in the problems to the skills necessary to work with them. For example:

If a problem includes a term x^4 – 1, you should immediately be thinking, “That connects really well to the Difference of Squares rule: a^2 – b^2 = (a + b)(a – b), and since x^4 is a square [it’s (x^2)^2] and 1 is a square (it’s 1^2), I can write that as (x^2 + 1)(x^2 – 1), and for good measure I could apply Difference of Squares to the (x^2 – 1) term too.” The GMAT won’t ever specifically tell you, “Use the Difference of Squares,” so it’s your job to immediately connect the symptoms of Difference of Squares (an even exponent, a subtraction sign, a square of some kind, even if it’s 1) to the opportunity to use it.

If you see a right triangle, you should recognize that Area and Pythagorean Theorem easily connect. In a^2 + b^2 = c^2, sides a and b are perpendicular and allow you to use them as the base and height in the area formula. *And* the Pythagorean Theorem includes three squares with the opportunity to create subtraction [you could write it as a^2 = c^2 – b^2, allowing you to say that a^2 = (c + b)(c – b)…], so you could connect yet another skill to it to help solve for variables.

Similarly, if you see a square or rectangle, its diagonal is the hypotenuse of a right triangle, allowing you to use the sides as a and b in the Pythagorean setup, which could also connect to Difference of Squares…etc.

When you initially learned most of these skills in high school (much like when Biles, Aly Raisman, Gabby Douglas, etc. learned handstands and cartwheels in Gymboree), you learned them as individual, isolated skills. “Here’s the formula, and here are 10 questions that test it.” On the GMAT – as in the Olympics – you’re being tested more on your ability to connect them, to see opportunities to use a skill that’s not obvious at first (“Well, I’m not sure what to do but I do have multiple squared terms so let me try to apply Difference of Squares…or maybe I can use a and b in the Area calculation.”), but that helps you build more knowledge of the problem.

So as you study, don’t just learn individual skills. Look for opportunities to connect them, and look for signals that will tell you that a connection is possible. A rectangle problem with a square root of 3 in the answer choices should tell you “the diagonal of this rectangle may very well be connected to a 30-60-90 triangle, since those have the 1, √3, 2 side ratio…” The GMAT is about connections more so than just skills, so study accordingly.

**Stick the Landing**

If you’re like most in the “every four years I love gymnastics for exactly one week” camp, the single most important thing you look for on any apparatus is, “Did he/she stick the landing?” A hop or a step on the landing is the most noticeable deduction on a gymnastics routine…and the same holds true for the GMAT.

Again, the GMAT is testing you on how well you connect a variety of skills, so naturally there are places for you to finish the problem a step short. A problem that requires you to leverage the Pythagorean Theorem and the Area of a Triangle may ask for the sum of sides A and B, for example, but if you’ve solved for the sides individually first, you might see a particular value (A = 6) on your noteboard and in the answer choices and choose it without double checking that you answered the proper question.

That is a horrible and unnecessary “deduction” on your GMAT score: you did all the work right, all the hard part right (akin to the flip-and-two-twists in the air on your vault or the dazzling array of jumps and handstands on the tiny beam) and then botched the landing.

On problems that include more than one variable, circle the variable that the test is looking for and then make sure that you submit the proper answer for that variable. If a problem asks for a combination of variables (a + b, for example), write that down at the top of your scratchwork and go back to it after you’ve calculated. Take active steps to ensure that you stick the landing, because nothing is worse than doing all the work right and then still getting the problem wrong.

In summary, recognize that there are plenty of similarities between the GMAT and **G**y**M**n**A**s**T**ics [the scoring system is too complex for the layman to worry about, the “Final Five” are more important than you think (hint: the test can’t really use the last five questions of a section for research purposes since so many people are rushing and guessing), etc.]. So take a lesson from Simone Biles and her gold-medal-winning teammates: connect your skills, stick the landing, and you’ll see your score vault to Olympian heights.

**free online GMAT seminars **running all the time. And as always, be sure to follow us on **Facebook**, **YouTube**, **Google+** and **Twitter**!

*By Brian Galvin.*

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