For example, look at these graphs:

In the first graph, the answer is E but the author desperately wants you to pick C. In the second, the answer is B but the author is baiting you hard into picking C. And in the third, the answer is C but the author is tempting you with E. In any of these cases, the strategy behind the question is as important – if not more important – than the math itself. Because it’s usually fairly easy for an average (or below) student to eliminate 1-2 answer choices on Data Sufficiency questions, the authors have to “get their odds back” through gamesmanship, by showing you a statement (or two) that look one way (sufficient or not) but that act counterintuitively. And to understand how to play this game well, it may be helpful to see Data Sufficiency through the lens of another popular game, the card game Hearts.

In Hearts, the goal of the game is to avoid getting “points”, and you get points when you end up with any hearts (one point each) or the Queen of Spades (13 points) after having taken a trick. And like with Data Sufficiency, there are really two ways to play: the way you’d play with a middle-schooler who’s learning the game, and the way you’d play with a group of adults who are each trying to win.

Playing Hearts with kids is like doing Data Sufficiency questions below the 550 level – you pretty much just play it straight. In Hearts, that means that when you don’t have any cards of the suit that was led, you try to get rid of your highest point-value cards immediately. If clubs are led and you don’t have clubs, you either get rid of the Queen of Spades if you have it, or you pick your highest heart and unload that. Your goal is to get rid of high cards and point cards quickly so that you end up with as few points as possible.

But if you’re playing with adults, you have to consider the possibility that someone may be trying to “Shoot the Moon” – getting *all* of the points cards in which case they get 0 points and every other player gets 26. What might seem like a counter-intuitive strategy to a 12-year old is often quite necessary when you suspect an opponent may be trying to shoot the moon: even though you may have a chance to get rid of your king-of-hearts, you might hold on to it because you want a high heart in case you need to “win” one of the last tricks to stop the opponent from getting all of the hearts. When you’re playing with adults (or attempting Data Sufficiency questions in the high 600s and into the 700s), you need to see the game with more nuance and develop an instinct for when to avoid the “obvious” play to save yourself from a more-catastrophic outcome.

This is especially true when you notice something suspicious from your opponent; if in one of the first few hands an opponent leads with, say, the jack of hearts, that’s a suspicious play. Why would she fairly-willingly open herself up to taking four points? Or if the first time a heart is played, an opponent swoops in with a high card of the suit that was led, but you know they probably have a lower card that would have let them avoid taking the heart, you again should be suspicious. In either of these cases, an astute player will make a mental note to hold back a high card or two just in case shooting-the-moon is in play. Playing hearts as an adult, you’re often playing the opponent as much as you’re playing the cards.

How does this apply to Data Sufficiency?

Consider this question:

Is a > bc?

(1) a/c > b

(2) c > 3

Playing “middle school hearts”, many test-takers will run through this progression:

Step one: If you multiply both sides by c, you get a > bc so this looks sufficient*. The answer, then, would be A or D.

Step two: Forget everything you learned about statement 1 since you’ve already made your decision about it. Statement 2 is clearly insufficient on its own, so the answer must be A*.

(*we know the math here is slightly flawed; demonstration purposes only!)

But here’s how you’d play the game as an adult, or as a 700-level test-taker:

Step one: Same thing – if you multiply both sides by c you’ll get a > bc, so this one looks sufficient.

Step two: Wait a second – statement 2 is absolutely worthless. And statement one wasn’t *that* hard or interesting. Maybe the author of this question is “shooting the moon”…

Step three: Look at both statements together, reconsidering statement 1 by asking myself if statement 2 matters. If statement 2 is true and c is, say, 10, then a/10 > b would mean that a > 10b, so this still holds. But what if c is -10, and statement 2 is not true. a/(-10) > b would mean that when I multiply both sides by -10 I have to flip the sign, leaving a < -10b. This time it’s not true. Statement 2 *seems* worthless but in actuality it’s essential. Statement 1 is not sufficient alone; as it turns out I need statement 2.

What’s the difference between the two methodologies?

The 500-level, “middle school hearts” approach – NEVER consider the statements together unless they’re each insufficient alone – leaves you vulnerable to the author’s bait. On hard questions, authors love to shoot the moon…that’s their best chance of tricking savvy test-takers.

The 700-level, “playing hearts with grownups” approach seems counterintuitive, much like saving your king of hearts and knowingly accepting points in a hearts game would seem strange to a seventh-grader. But it’s important because it saves you from that bait. On a question like this, it’s easy to think that statement 1 is sufficient; abstract algebra is great at getting your mind away from numbers like negatives, zero, fractions… But statement 2′s worthlessness (ALONE) functions two ways: it’s a trap for the unsuspecting 500-level types, and it’s a reward for those who know how to play the game. That worthless statement 2 is akin to the author leading a high heart early in the game – the novice player sees it as a freebie; the expert considers “why did she do that?” and re-examines statement 1 by asking specifically “what if statement 2 weren’t true; would that change anything?”.

Remember, when you’re taking the GMAT you’re playing against other very-intelligent adults, and so the authors of these questions have a responsibility to “shoot the moon”. While the rules of the game dictate that you don’t want to consider the statements together until you’ve eliminated A, B, and D, there’s a caveat – if you have reason to believe that the author of the question is trying to trick you (which is very frequently the case on 600+ level questions), you have to consider what one statement might tell you about the other; you have to play the game.

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

*By Brian Galvin*

Similarly, when answering a Sentence Correction question, there are many types of errors that can appear in a single sentence. Some questions will be one-trick ponies (I’m looking at you, Bitcoins), in which you can just solve one issue and get the correct answer. However, most will have two or three types of errors that you need to avoid, and identifying these errors will often make the difference between knowing which answers cannot be correct and guessing based on how the sentence sounds.

When looking through the initial sentence, you might notice some errors right away, such as pronoun (she vs. they) or verb agreement (is vs. are) errors. However some errors are more subtle and you must look through the answer choices to confidently narrow down the options. Once you have a good handle on the types of errors occurring in the sentence, you can begin eliminating answer choices that do not dodge (or dodgecoin) the error.

Let’s look at a question that contains multiple issues, but they may not be obvious upon first glance:

*An auteur whose movies define the genre, Jean-Luc Godard’s films are to the French New Wave what Sergio Leone’s The Good, The Bad and The Ugly is to the spaghetti western.*

*(A) **Jean-Luc Godard’s films are to the French New Wave what*

*(B) **Jean-Luc Godard’s films are to the French New Wave like*

*(C) **Jean-Luc Godard’s films are to the French New Wave just as*

*(D) **Jean-Luc Godard directed films that are to the French New Wave similar to*

*(E) **Jean-Luc Godard directed films that are to the French New Wave what*

The sentence begins with a modifier that is not underlined, which means the subsequent underlined portion must necessarily be the subject of the modifier. If it is not, then the sentence will contain a modifier error from the get go and will not be the correct choice. A little further on, a comparison is made between films and other films. If the comparison were to be between two incongruent items (worse than apples and oranges, say apples and androids), the sentence would contain a comparison error. There may be other errors but these are the two most glaring issues to keep in mind.

Looking over the answer choices, we see a 3-2 split between the choices that keep the director’s films as the subject of the verb and the choices that change the subject to the director himself. From a comparison point of view, all the choices seem to keep the comparison between Godard’s films and Leone’s cult masterpiece.

The non-underlined first part of the passage is a modifier that is describing a specific person. The sentence even begins with “An auteur”, which is the French word for author. The subject of the sentence must therefore be a noun that can logically be described by the modifier at the beginning of the sentence. However, the restriction of the comparison also dictates that the sentence compare films with films. The only way to accommodate both limitations is to select either answer choice D or E, both of which keep Jean-Luc Godard as the subject of the phrase while supplying the proper film comparison at the end.

How do we go about differentiating between answer choices D and E (other than flipping a coin)? The difference is in the idiom that connects the underlined portion to the second part of the sentence. The first option indicates that the films are to a certain group *similar to* another movie to a different group. Apart from not being a correct idiom, it also doesn’t make logical sense. The second option indicates that the films are to a certain group *what* another film is to the different group. This is a perfectly acceptable idiom that conveys the meaning properly.

The only answer choice that avoids making a modifier error, a comparison error or a logical error is answer choice E. These errors may not have all been evident at first glance, but we can see why the four other answer choices contain some kind of error. Even though the comparison error ended up being largely irrelevant in this process of elimination, it is the type of error you always need to be aware of when correcting sentences. In fact, juggling many potential error types is a vital skill in solving these types of questions. While not always obvious, the correct answer will be the only option that doesn’t make at least one of the errors you’ve identified. Remember that, no matter how hard the GMAT may seem at times, it is easier (and safer) than juggling flaming chainsaws.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.*

Of course, giving you all the time in the world to break through the confusion would be counterproductive, because then there’d be no way to differentiate between those who understand concepts and those who use brute force to simply try every possible combination of answer choices (think of MacGruber as someone who wastes a lot of time solving problems).

The questions on the quantitative section of the GMAT often appear very complicated and daunting, but can usually be solved quickly using a little logic. Of course, since the exam can potentially ask you hundreds of different questions, you can’t reasonably memorize every type of trick that can be thrown at you. You can, however, identify some recurring themes that appear frequently and understand why they are tricky. On test day, you still have to apply logic on a case by case basis, but some overarching themes are definitely more prevalent than others.

One such theme used frequently is that of turning a math problem into a story that you have to interpret. Today I want to talk about the compound interest problem. This type of problem is common in finance, but most financiers simply input the arguments into their calculators (or abaci) and spit out a solution. The compound interest situation presented is simply a layering mechanism designed to make the underlying exponent problem harder to see. Breaking through the prose of the question and seeing the fundamental problem for what it is can be the difference between a 1-minute solution and a 4-minute solution.

Let’s look at a compound interest problem that highlights the nature of these questions:

*A bank offers an interest of 5% per annum compounded annually on all of its deposits. If 10,000$ is deposited, what will be the ratio of the interest earned in the 4 ^{th} year to the interest earned in the 5^{th} year?*

*(A) **1:5*

*(B) **625 : 3125*

*(C) **100 : 105*

*(D) **100 ^{4} : 100^{5}*

*(E) **725 : 3225*

The first thing to note about this question is that it’s asking about a ratio, which means that the 10,000$ sum will be irrelevant. If you’d put in 100$ instead, or 359$, the ratio would still be the same. The correct answer will therefore not be related to 10,000$ in any way, but it’s also important to try and understand the question being asked before answering in order to avoid getting the right answer to the wrong question.

So what exactly is this question asking? What is the ratio of the interest earned in year 4 to the interest in year 5? This can lead us to some tedious calculations if we’re not careful. We start off with 100$ (or 10,000$, it doesn’t matter). At the end of the first year, we’ll have 5% more, so 105$. I could calculate it for year 2 as well, taking 105$ and multiplying by 1.05. This might take 20 seconds on paper, but will (hopefully) yield a result of 110.25$ I could go through years 3, 4 and 5 to get the respective answers (115.76$, 121.55$ and 127.63$), but that would take a while to calculate by hand.

Moreover, let’s say I have these 5 values; I am now tasked with finding the difference between year 4 and year 5. So now I need to calculate 127.63 / 121.55. Without a calculator… If you get to this point on the exam, you either spend more time trying to figure out the ratio, or you take an educated guess and move to the next question in frustration. Neither of these options is particularly good, so let’s backtrack to see where we veered off the path.

To calculate year one to year two, I took the initial arbitrary amount and multiplied it by 1.05. This is due to the interest compounding annually. The second year, I took the amount after year one and multiplied it by… 1.05 again! Eureka! Now, the pattern emerges. Every year, I take whatever the previous year was, and multiply it by 1.05. This means that, from year n to year n+1, the change will always just be 1.05, or a 5% increase.

Looking over the answers, answer choice C succinctly displays a 5% growth rate, taking whatever 100% of the previous year was and adding on 5%. This will be the correct answer for the growth rate from year one to two, as well as from year four to five. The question would have been much easier had the question been about years one and two, but the GMAT purposefully makes questions more difficult in order to differentiate between those who can identify the pattern and those who try to do each possibly calculation on paper.

On the GMAT, the correct answer can often be achieved by applying a brute force strategy. However, in business, you are rewarded for understanding the underlying concept and not wasting everyone’s time with meandering trial and error experiments. Understanding a concept such as this one about compound interest won’t single-handedly allow you to ace the exam. However, knowing that the exam is trying to appraise your ability to use logic to solve problems should incentivize you to look for the causal logic rather than to undertake tedious calculations.

Remember, there are computers, calculators and smart phones that complete routine computations in seconds. The GMAT is your opportunity to demonstrate not only that you can solve the question, but that you truly understand the question.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

“I am glad that you brought this up! *This is an official question, and the answer choice is the official answer. *I do not understand why you need to be “convinced.” You can trust the official answer to an official question!

In fact, when you saw that your answer was not the correct answer you started looking for ways that you could be right and the official answer wrong. This is not a particularly helpful mindset.

Let’s compare the verbal and the quantitative sections. What do you do when you see that the official answer to a Quant problem is 27 and you thought it was 42? Be honest. You know what you do, you say “27, huh, I must have made a mistake. How did I end up with 42, let me see what I did wrong here so that I do not do it again.”

Right?

You do NOT you say, “I bet it is really is 42 and I am going to think of reasons why it is 42 and not 27.” That would seem strange right? I mean a *Quant* problem only has one correct answer and if you get a different answer you made a mistake and need to figure out why you missed it right?

Okay well here is something that it takes students a long time to learn - **A verbal question only has one correct answer as well. And if you got a different answer you need to say “what did I do wrong and how can I not make this mistake in the future.” **Just as you would on a Quant problem.

I have had tutoring students who wanted to argue the answers on verbal questions, particularly CR and RC, but SC sometimes as well. Eventually I say something along the lines of “This is not the kind of test where you should be debating against the answer key. If you want to get a high GMAT score you need to focus on why you did not get the correct answer and how you can get it right next time.”

Now unofficial questions can often be improved. In fact, when I write original questions of my own I welcome it when students debate the merits of each question. I then edit it to make it better. Every edit makes it a question better. Yet even most unofficial questions are well written and really do have just one correct answer.

What I am saying is that your mind set should be “Why did I get this wrong?” “What can I do better next time?” Rather than “I am not convinced with this official answer to this official question.”

It may seem like a slight difference, but it is the difference between a 600 and a 700.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*David Newland* has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.

Reading comprehension is a category of questions on the GMAT designed to test whether you can read a long (and often pointless, bloated and sleep-inducing) passage and understand the major points covered. This exercise is designed to emulate the various reports and papers you’re likely to read throughout school and work for the next 40 years or so (or until we’re replaced by robots). The passage is presented, and then a series of 3 to 6 questions about the passage will be asked. Ideally, you understood the passage well enough to answer the questions about what you just read. If you grasp the major point the author was trying to get at, you’re likely to get the questions right.

Not every passage you read will ask you about the primary purpose of the passage (say that three times fast!) Sometimes the questions will ask about the author’s tone, the scope of the subject or the organization of the text. However, every passage can potentially ask you about the primary purpose, and at least one will ask you on test day. To avoid losing easy points on this type of relatively straight forward question, it’s important to ascertain which elements are important, and which details are superfluous.

A very good method to ensure you’re following along with the passage is to summarize each paragraph in 3-5 words after you finish reading it. This summary might not have all the details included in the paragraph, but it will succinctly recap the important element(s) of what you have just finished reading. Ideally, you don’t even have to spend time writing these words down, just forming them in your mind’s eye is enough to keep them in your memory for a few minutes. Of course, if you prefer to write this down, or if you want to expand to 6 or 7 words, that’s perfectly acceptable as well. It is important to be mindful of the time constraint, though.

Let’s look at a GMAT passage and answer a question using the organization of the passage (note: this is the same passage I used throughout 2013 for scope, tone and organization.)

*Young Enterprise Services (YES) is a federal program created to encourage entrepreneurship in 14-18 year olds who have already shown a clear aptitude for starting business ventures. The program, started in 2002, has provided loans, grants, and counseling – in the form of workshops and individual meetings with established entrepreneurs – to over 7,500 young people. The future of YES, however, is now in jeopardy. A number of damaging criticisms have been leveled at the program, and members of the Congressional agency that provides the funding have suggested that YES may be scaled down or even dismantled entirely.*

*One complaint is that the funds that YES distributes have disproportionally gone to young people from economically disadvantaged families, despite the program’s stated goal of being blind to any criteria besides merit. Though no one has claimed that any of the recipients of YES funds have been undeserving, several families have brought lawsuits claiming that their requests for funding were rejected because of the families’ relatively high levels of income. The resulting publicity was an embarrassment to the YES administrators, one of whom resigned.*

*Another challenge has been the admittedly difficult task of ensuring that a young person, not his or her family, is truly the driving force behind the venture. The rules state that the business plan must be created by the youth, and that any profits in excess of $1,000 be placed in an escrow account that can only be used for education, investment in the venture, and little else, for a period that is determined by the age of the recipient. Despite this, several grants had to be returned after it was discovered that parents – or in one case, a neighbor – were misusing YES funds to promote their own business ideas. To make matters worse, the story of the returned monies was at first denied by a YES spokesperson who then had to retract the denial, leading to more bad press.*

*In truth, YES has had some real success stories. A 14-year old girl in Texas used the knowledge and funding she received through the program to connect with a distributor who now carries her line of custom-designed cell phone covers. Two brothers in Alaska have developed an online travel advisory service for young people vacationing with their families. Both of these ventures are profitable, and both companies have gained a striking amount of brand recognition in a very short time. However, YES has been pitifully lax in trumpeting these encouraging stories. Local press notwithstanding, these and other successes have received little media coverage. This is a shame, but one that can be remedied. The administrators of YES should heed the advice given in one of the program’s own publications: “No business venture, whatever its appeal, will succeed for long without an active approach to public relations.”*

*The primary purpose of the passage is to _______*

*(A) **detail the approach that should be taken in remedying YES’s public relations problems*

*(B) **defend YES from the various criticisms that have been leveled against it*

*(C) **suggest a way to improve the program*

*(D) **detail several criticisms and problems of the YES program*

*(E) **make the case that YES, despite some difficulties, has been quite successful for some people who have taken part in the program*

If you summarized each paragraph as you read through them, your summary should look something like:

1^{st} paragraph: YES program

2^{nd} paragraph: Problem w/ program

3^{rd} paragraph: Another problem w/ program

4^{th} paragraph: Successes & next steps

With a summary like this, which is all of 13 words, you follow the main point of the story and you’re less likely to get sidetracked by tempting answer choices. Let’s look through the choices and see if any of them encapsulate the main purpose of this passage.

Answer choice A indicates that the goal is to detail the approach in remedying the program’s problems. This answer choice initially makes a lot of sense, as the passage is all about the problems and how to solve them. However, the use of the word “detail” should be sufficient to recognize that this is not what the passage is really doing. The author gives their overarching suggesting of using more PR, but does not detail anything at any point. The choice of words precludes this answer from being considered further.

Answer choice B is about defending YES from criticisms, which is not even something that happens in the text. The author makes no effort to defend the program from the justified criticisms, and merely suggests a course of action moving forward. Answer choice B is thus incorrect.

Answer choice C concisely indicates that the author is suggesting a way to improve the program. This is essentially correct since the author lists a couple of issues with the program, and then outlines a very general way to improve things going forward. We should check the other answer choices, but this choice appears correct and is general enough that it will be hard to eliminate.

Answer choice D stops short at mentioning only the problems and criticisms of the program. This would be correct if the fourth paragraph did not exist, but as it is this choice is summing up the first three paragraphs and ignoring the author’s conclusion. This choice is incorrect as well.

Answer choice E stresses the successes of a few people while acknowledging the managerial incompetence at YES, so it is also a tempting answer choice. However the author mentions one or two success stories mostly for anecdotal reasons, and not to promote the status quo. The program must still be overhauled, despite a couple of feel-good stories. Again this answer choice does not adequately represent the primary purpose of the passage.

As answer choice C is the correct selection here, it is important to note that the answer does not need to recap the entire passage. Such an exercise would be inherently difficult in only a few words, but more so, it is unnecessary. Summarizing something does not necessarily require reiterating every detail, but rather understanding the underlying reason for the writing of the passage. The purpose of this article is to demonstrate that concept (Inception style), and help you save time and maximize your GMAT score on test day.

My friends from the television show *The* *Big Bang Theory* are fond of super heroes. Okay Sheldon and Leonard are not really my friends (unfortunately) but they are certainly fond of super heroes. They love Superman and Batman and the entire Justice League.

What they fail to understand is that they are super heroes themselves…with super powers that translate extremely well to the GMAT. Their biggest super power? Making equations of course!!!

You don’t think that making equations is a super power…did you not hear that music while Sheldon and (Raj) Koothrappali were working on that equation? That was super hero music for sure!

While making equations may not be as cool as flying; on the GMAT the ability to see an equation where others may not is indeed a super power. *A super power that you may already possess.*

All that you need to do in order to create an equation is to set two things equal. Moreover, if any two things are equal to a third then they can be set equal to each other and you have another equation!

This is something that is easiest to illustrate in Geometry. In fact, this is the essence of geometry. If you know that the area of a triangle is Base * Height / 2, and you also know that the area of the triangle is 30, then you drop the thing that they have in common (in this case the area) and create the equation from the other two pieces: Base * Height / 2 = 30, or Base * Height = 60.

You are so used to having this super power at your disposal that you probably do not even think about it when you are using it. The previous example probably did not even impress you. You are like Super Man: when he is rescuing a jumbo jet full of passengers he never seems to stop and think, “Oh, wow! I am actually flying.” He is so focused on using his powers that he never stops to think how awesome they really are.

Try this example from the Veritas Prep Word Problems book. Use your Super Power and create an equation. (If you are having trouble making the equation just remember to find two things that are each equal to a third thing. Drop the thing they have in common and set the other two parts equal to each other).

“Machines A and B always operate independently at their respective constant rates. When working alone machine A can fill the production lot in 5 hours, and machine B can fill the production lot in X hours. Together they can fill the production lot in 2 hours. What is the value of X?

A) 3 1/3

B) 3

C) 2 1/2

D) 2 1/3

E) 1 1/2”

What are the two things that you can set equal to each other? Let’s start with what you know. You know that the rate of A is 1 / 5 (of the job per hour). The rate of B is 1 / X (of the job per hour) and the rate of the two together (the rate of A + B) = 1 / 2 (of the job per hour).

Do you see it now? You know that the rate of A + B is 1 / 2. You can also add the individual rates of A and B, so that (the rate of A) + (rate of B) = 1 / 5 + 1/ X. You now have two different values that is each equal to the rate of A + B. Now you can set them equal to each other. So that “**1 / 5 + 1 / X = 1 / 2**” (the rate of A) + (the rate of B) = the rate of (A + B).

Now you have an equation that you can solve and the rest is Algebra. Find a common denominator for 5 and 2 so that the equation becomes “2 / 10 + 1 / X = 5 / 10.” 1 / X must equal 3 / 10. That means 3X = 10 and X = 3 1/3. The correct answer is A.

You and I might not be quite up to the status of theoretical physicists Sheldon and Koothrappali, but we do have something in common with them. We have the Power to create equations, meaning that we are super heroes, too!

*David Newland* has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.

However, other numbers will show up and need to be inserted into an equation. Some of these numbers will show up on essentially every GMAT exam: numbers like 2, 10 and 100. Each of these numbers will show up in various questions and need to be multiplied, divided or factored out. Nevertheless, a number that will show up frequently is one that is oft overlooked: 60.

The number 60 is inescapable in everyday life. After all, there are 60 seconds in a minute and 60 minutes in an hour. Have you ever wondered why there aren’t 100 seconds in a minute? The answer is that 60 is divisible by almost every important small number you can think of: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30 (hey, you forgot 60!). 100 is divisible by most of these numbers, but not by 3 or any of its multiples. This is the primary reason we restart the count after 59 instead of 99. Even the most die-hard imperial system user could see the value of adopting metric time (Remember this moment: 80 after 2:00 on April 43^{rd}).

However, since we’re unlikely to change timing conventions (no matter how many signatures we get on Facebook), we’ll have to make do with calculating things using the number 60. Specifically, the GMAT likes using conversion problems to demonstrate mathematical proficiency. If you’re going at a certain speed per hour, how far will you go in 80 minutes? These questions can get increasingly difficult when translating times from minutes to hours, and the key is often multiplying or dividing by 60.

Let’s look at an example to underscore the importance of this number:

*A space shuttle orbits the earth at about 8 kilometers per second. This speed is equal to how many kilometers per hour?*

*(A) **480*

*(B) **2,880*

*(C) **4,800*

*(D) **28,800*

*(E) **48,000*

This is the type of question that can bait you into time-consuming calculations, whereas a shrewd test taker can gain valuable time by recognizing that this question is simply asking you to calculate a certain number by 60, and then multiplying it by 60 again (let’s do the time warp!). Even if a question asks you to change one unit into another, you can always do it step by step or all in one shot. There are many ways to solve this, but let’s begin with the detailed process so we make sure we don’t make any mistakes.

If the space shuttle orbits the earth at 8 kilometers per second (you can replace this word by miles if you’re more comfortable), then how many kilometers will it cover in one minute? We can simply multiply 8 by 60 to get 480 kilometers/minute. This is the number in answer choice A, but it is not the correct answer as we’ve only covered a single minute, or about 1.67% of the hour. (There’s still a lot of spinning to go!). If we take the 480 km/minute and multiply it by 60 minutes, we will get to the number of kilometers /hour. 480 x 60 is not obvious, but you ignore the 0’s so it boils down to 48 x 6. Doing this longhand, we can get to 288, and then add back in the two zeros for a total of 28,800. This is answer choice D and the correct answer to this question.

If you followed that strategy, you would get the right answer, but you would miss many opportunities for shortcuts. One of the most glaring shortcuts is to forgo the two-step process and simply multiply the initial speed of 8 km/second by 3,600. This is 60 x 60, and represents the number of seconds in an hour. Since 60 is a number that shows up so frequently on the GMAT, it’s worth knowing that the square of 60 is 3,600 as you may be asked to convert from hour to second and vice versa. Multiplying 8 by 3,600 will also get you to 28,800 in one operation instead of two.

Furthermore, it is possible to solve this question using zero calculations, using the power of order of magnitude. Very simply, if you recognize that there are 3,600 seconds in an hour, and you’re going a little less than 10 kilometers per second, then your answer should be a little under 36,000 kilometers/hour. Since answer choice E is bigger than this, and answer choice C is about five times too small, the answer must be answer choice D. This strategy may be difficult to use if the answer choices are close together, however it is undoubtedly the fastest way to get the correct answer when the answer choices are spread out as they are in this question.

There are also multiple other ways to get the right answer here. One hybrid solution that is pretty intuitive is to multiply 8 kilometers/second by 60 to get 480 kilometers/minute, as we did in the very first step. From there you know you need to multiply 480 by 60 to get the speed per hour, but your trap options are 480 x 10 and 480 x 100, both of which are clearly incorrect at a cursory glance. By order of magnitude, you can again determine that the correct choice must be D.

As will all questions on the GMAT, there are multiple ways to get the right answer, but some question types show up over and over again on the test. If you’re prepared for the common types of problems and can solve them using a variety of solutions such as unit digit, order of magnitude and shortcut math, you’ll see your test score go from 0 to 60 (or 760) on test day.

Let me see if I can make this concept more approachable for you. Think about calculating the Least Common Multiple as if you were a builder getting ready to build a house. The problem is you do not know which house you are going to build. So when you show up on the job site you need to have all of the materials for each of the possible houses. The “houses” are the numbers and the “materials” that you need are the prime factors.

*Try this example (let’s use three numbers to make it more challenging): *

*What is the Least Common Multiple of 9, 20, and 42?*

First you need to get the prime factors of each of the numbers. The prime factors of 9 are 3 * 3 the prime factors of 20 are 2 * 2 * 5 and the prime factors of 42 are 2 * 3 * 7.

Next you need to take each prime factor at the highest power. This is because you need to have all of the materials (prime factors) necessary to build any of the three houses (numbers). So your materials list is 2 * 2 * 3 * 3 * 5 * 7 or in other words 2^{2 }* 3^{2 }* 5 * 7. If you have these prime factors you can build any of the three numbers. For example, if you are asked to build the 20 you have the necessary 2*2*5.

Now you are also a very efficient builder so you do not want to bring more materials than you need. So you have to show up at the job site with the exactly the smallest load of materials with which you can build any of the houses. So that means that you do not want any extra prime factors. That is why the least common multiple on our example is 2 * 2 * 3 * 3 * 5 * 7. There is not a second 5 or another 7 because this is not needed.

You will not be asked to build more than one of the houses at any time. So even though if you list out the prime factors you will see three 2s (there are two of them in the 20 and one in the 42) and three 3s (two in the 9 and one in the 42) you do not need to bring all of these materials. You only need two 3s because you will only need to build the 9 *or* the 42 and not both. You only need two 2s because you will be asked to build the 20 or the 42 but not both.

I hope this helps to explain why you take each prime factor at its highest power. Understanding the reasoning behind the Least Common Multiple can help you to “build” a higher GMAT score.

* David Newland* has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.

The GMAT is not hard, the GMAT is tricky.

Last time, I examined how the GMAT attempts to trick students by using subtle word meaning and blatant misdirection from a predominantly mathematical point of view. Today, I’d like to elaborate on how these same elements apply to the verbal section as well.

A brief recap for those who haven’t read the previous article: The difference between hard and tricky is primarily that the GMAT will not test any material that wasn’t covered in a standard high school curriculum. Obviously, having a degree in English literature will give you an edge on many types of verbal questions, but a post-secondary education in the language is not necessary to solve any problem. The reason for this is to put students on as even a footing as possible. The downside of this is that the material cannot be advanced, by its very nature its high school level material.

The GMAT therefore has to offer difficult questions based on material that’s not inherently too difficult. What are some easy ways to make simple material more challenging? The first one is the timing aspect, so you only have a limited amount of time to answer the questions, but moreover you feel the pressure of time running out on you constantly. If you had unlimited time to answer the questions, most people would score significantly higher on the GMAT, so managing your time is paramount to getting a top score.

This is the same reason as to why there’s no spell check on the AWA. With a spell check, it’s a lot harder to differentiate between someone who has a mastery of the English language and someone who can just rely on the red underline in Word (or my bane: the green underline). It also forces you to have to come up with synonyms or alternatives if you’re unsure of the ideal phrasing (or trying to paraphrase the word “question” again).

To highlight these elements, let’s look at simple question that underscores the trickiness of the GMAT:

*Even today, lions can be seen ruling the African plains, hunting almost any animal that crosses its path and intimidating all but the most intrepid hunters.*

*(A) lions can be seen ruling the African plains*

*(B) lions are able to be seen ruling the African plains*

*(C) lions rule the African plains*

*(D) the lion rules the African plains*

*(E) the lion species rules the African plains*

This sentence correction question asks us to choose among several answers that all sound pretty similar. In fact, the first three answer choices are very similar, just with varying degrees of superfluous text added to each. The other two answers also seem very similar, but play around with the number of the subject. There seems to be a split along the number of the subject, but other than that, the choices seem distressingly similar.

At first glance, many students concentrate on the first part of the sentence and essentially ignore everything after the underlined portion. After all, if it were important, wouldn’t it be underlined? This tends to lead to a differentiation among the first three answer choices, all of which essentially say the same thing. In this case, most students would gravitate towards answer choice C as it is the most succinct version of the text. However the slight meaning difference between answers A and C leads many students to debate the merits of each answer choice. Often this can lead to indecision between the choices and an educated guess just to move on to the next question.

However, if you’ve gone down this path here (or on another similar question), you’ve fallen into a classic GMAT trap. You’ve just spent time deciding between two answer choices that are both incorrect! This process can be very frustrating on practice tests, but you’ll never know whether this situation arose on the actual GMAT because you’ll never know what the correct answer was (the NSA would know, though). What happened in this situation? The GMAT misled you into contrasting two answer choices with virtually identical meanings.

The difference between the first three answer choices and the last two hinges on the number of the subject. If the subject is plural, we need lions; if it’s singular, we need lion or lion species (this is singular even though it doesn’t sound like it!). The key to making this decision lies in the pronoun “its” located at the end of the line. Since the pronoun is singular, the subject must also be singular in order to avoid making an antecedent agreement error. Neither answer choice A nor C can be correct, so it must be either D or E. The correct answer will be D as it is the only one that has a logical meaning. If the subject were the lion species, it would be nonsensical to imagine crossing paths with a species. Answer D is also more succinct, which adds to its appeal (like driving a nice car).

The decisions asked of you on the GMAT do not tend to be hard, but they also do not tend to be straight forward. A lot of questions will try to mislead you or trick you into focusing on the wrong thing. Spending a minute choosing between two incorrect answer choices seems absurd, and yet it happens time and time again on this exam. The rules of grammar being tested on this exam, much like the mathematical rules being tested in the quant section, are not the hardest rules imaginable. However, they are specifically chosen to tricky and deceptive.

Going back to the industrial strength lock analogy I used two weeks ago, the same lessons can be applied in both verbal and quant. If you know the combination to the safe, you will get the correct answer quickly. If you’re attempting a brute force approach with every possible combination, you will certainly run out of time. However if you know which options to eliminate and which options to keep, you’ll do well on the test. As Kenny Rogers put it: You got to know when to hold ‘em and know when to fold ‘em.

In the *Austin Powers* movies the character known as “Dr. Evil” creates an exact version of himself, only smaller, that he calls “Mini-me.” The two characters have identical proportions even though one evil villain is 8 times the size of the other. The hero, Austin Powers, quickly recognizes the similarity, despite the difference in size. This is something that you will need to be able to do on the GMAT!

If you are not familiar with “Dr. Evil” and “Mini-me, watch the following clip:

**This is what similar triangles are all about! Not the evil villain stuff, but the “same proportions, different size.”** When you have proven that you have similar triangles you know that any ratio of a side of one triangle to the corresponding side of the other triangle will hold true for each of the sides and even for the height of those triangles.

As you can see from the diagram below all three angles are equal. The ratio of the lengths of the triangle will remain constant. So if A:a = 2:1 then B:b and C:c and even H:h will stay at that same ratio of 2:1

**Recognizing Similar Triangles**

Often the biggest difficulty that people have with these similar triangle problems is simply recognizing that they are, in fact, “similar.”

**Most similar triangles on the GMAT are not like the diagram above. They are actually overlapping triangles that have one angle in common. Be on the lookout for that “shared angle.” That is usually the first clue that you have similar triangles! **

In addition to the *shared angle* look for one of these other two clues that similar triangles are present:

1) **Parallel lines:** If the triangle has a shared angle AND parallel lines then you have a similar triangle. For the diagram below you would be told that DE is parallel to AC. This creates similar triangles BDE and ABC.

2) **Right angles:** If the triangles each have a right angle AND a shared angle then you have a similar triangle. In the diagram below you see that angle “D” is shared and that angles DCE and ABC are right angles. This means that you have similar triangles ABD and CDE.

**Don’t wait for the GMAT to make similar triangles as obvious as Dr. Evil and Mini-Me. Watch out for shared angles, parallel lines, and right angles. And remember that easily recognizing similar triangles is “groovy baby, yeah!”**

If you plan on taking the GMAT soon, we have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

* David Newland* has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.