What does this expression really mean? (Rhetorical question) It means that you followed the logic and executed the calculations properly, but you inputted the wrong parameters. As an example, a problem could ask you to solve a problem about the price of a dozen eggs, but along the way, you have to calculate the price of a single egg. If you’re going too fast and you notice that there’s an answer choice that matches your result, you might be tempted to pick it without executing the final calculation of multiplying the unit price by twelve. While this expression is often used for math problems, the same concept can also be applied to the verbal section of the exam.

The question category that most often exploits erroneous interpretations of a question is Critical Reasoning. In particular, the method of reasoning subcategory appropriately named “Mimic the Reasoning”. These types of questions are reminiscent of SAT questions (or LSAT questions for some) and hinge on properly interpreting what is actually stated in the problem.

Let’s look at an example to highlight this issue:

*Nick**: The best way to write a good detective story is to work backward from the crime. The writer should first decide what the crime is and who the perpetrator is, and then come up with the circumstances and clues based on those decisions.*

*Which one of the following illustrates a principle most similar to that illustrated by the passage?*

**A)** When planning a trip, some people first decide where they want to go and then plan accordingly, but, for most of us, much financial planning must be done before we can choose where we are going.

**B)** In planting a vegetable garden, you should prepare the soil first, and then decide what kind of vegetables to plant.

**C)** Good architects do not extemporaneously construct their plans in the course of an afternoon; an architectural design cannot be divorced from the method of constructing the building.

**D)** In solving mathematical problems, the best method is to try out as many strategies as possible in the time allotted. This is particularly effective if the number of possible strategies is fairly small.

**E)** To make a great tennis shot, you should visualize where you want the shot to go. Then you can determine the position you need to be in to execute the shot properly.

This type of question is asking us to mimic, or copy, the line of reasoning even though the topic may be totally different. The issue is thus to interpret the passage, paraphrase the main ideas in our own words, and then determine which answer choice is analogous to our summary. Theoretically, there could be thousands of correct answers to a question like this, but the GMAT will provide us with four examples to knock out and one correct interpretation (though sometimes it feels like a needle in a haystack).

Let’s look at the original sentence again and try to interpret Nick’s point. The first sentence is: *The best way to write a good detective story is to work backward from the crime. *This means that, wherever we want to go, we should recognize that we should start at the end and work our way backwards. This is a similar principle as solving a maze (or reading “Of Mice and Men”). The second sentence is: *The writer should first decide what the crime is and who the perpetrator is, and then come up with the circumstances and clues based on those decisions. *This means that, once we know the ending, we can layer the text with hints so that the ending makes sense to the audience. Astute readers may even guess the ending based on the clues (R+L = J), and will feel rewarded for their keen observations.

Summarizing this idea, the author wants us to start at the end and work our way backwards so that we end up exactly where we want. The next step is to apply this logic to each answer choice in turn:

For answer choice A, *when* *planning a trip, some people first decide where they want to go and then plan accordingly, but, for most of us, much financial planning must be done before we can choose where we are going*, the first part about choosing a destination is perfect. However, the second part goes off the rails by introducing a previously unheralded concept: limitations. The author was not initially worried about limitations, financial or otherwise, so answer choice A is half right, which is not enough on this test. We can eliminate A.

Answer choice B, *in planting a vegetable garden, you should prepare the soil first, and then decide what kind of vegetables to plant.* While this is good general advice, it has nothing to do with our premise. Starting with the soil is the very definition of starting at the beginning. A more correct (plant-based) answer choice would state that we want to start with which plants we want in the garden and then work backwards to find the right soil. This is incorrect, so answer choice B is out.

Answer choice C, *good architects do not extemporaneously construct their plans in the course of an afternoon; an architectural design cannot be divorced from the method of constructing the building*, changes the timeline (much like Terminator Genysis). We must consider both issues simultaneously, which is not what the original passage postulated. We can eliminate answer choice C.

Answer choice D is: *in solving mathematical problems, the best method is to try out as many strategies as possible in the time allotted. This is particularly effective if the number of possible strategies is fairly small. *This is not only incorrect, but particularly bad advice for aspiring GMAT students. In fact, the author is describing backsolving, because we are starting at the answer and working our way backwards. We are not proposing “throw everything at the wall and see what sticks”. Answer D is out.

This leaves answer choice E, *to make a great tennis shot, you should visualize where you want the shot to go. Then you can determine the position you need to be in to execute the shot properly*. Not only must it be the correct answer given that we’ve eliminated the other four selections, but also it perfectly recreates the logic of planning backwards from the end. Answer choice E is the correct selection.

For method of reasoning questions, and on the GMAT in general, it’s very important to be able to interpret wording. If you cannot paraphrase the statements presented, then you won’t be able to easily eliminate incorrect answer choices. Part of acing the GMAT is not giving away easy points on questions that you actually know how to solve. If you read carefully and paraphrase concepts as they come up, you’ll be interpreting a high score on test day.

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.*

First, take a look at Lesson 1, Lesson 2, Lesson 3, and Lesson 4!

**Lesson Five: **

Procrastinate to Calculate: in much of your academic and professional life, it’s a terrible idea to procrastinate. But on the GMAT? Procrastination is often the most efficient way to do math. In this video, Ravi will demonstrate why waiting until it’s absolutely necessary to do math is a time-saving and accuracy-boosting strategy. So whatever it is you would be doing right now, put that off for later and immediately watch this video. The sooner you learn that procrastination is your friend on the GMAT, the more time you’ll save.

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!

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

*By Brian Galvin*

Some patterns are inexact, or can change dramatically based on external factors. If you think of the stock market or the weather, people often have a general sense of prediction but it is hardly an exact science. Some patterns are more rigid, but can still fluctuate a little. Your work schedule or the weekly TV guide tend to remain the same for long stretches of time, but are not always exactly the same year over year. Finally, there are patterns that never change, like the Earth’s rotation or the number of days in a year (accounting for the dreaded leap year). These patterns are rigid, and can be forecasted decades ahead of time.

On the GMAT, this same concept of rigid prediction is utilized to solve mathematical questions that would otherwise require a calculator. A common example would be to ask for the unit digit of a huge number, as something like 15^16 is far too large to calculate quickly on exam day, but the unit digit pattern can help provide the correct answer. Given any number that ends with a 5, if we multiply it by another number that ends with a 5, the unit digit will always remain a 5. This pattern will never break and will continue uninterrupted until you tire of calculating the same numbers over and over. A similar pattern exists for all numbers that end in 0, 1, 5 or 6, as they all maintain the same unit digit as they are squared over and over again.

For the other six digits, they all oscillate in predetermined patters that can be easily observed. Taking 2 as an example, 2^2 is 4, and 2^3 is 8. Afterwards, 2^4 is 16, and then 2^5 is 32. This last step brings us back to the original unit digit of 2. Multiplying it again by 2 will yield a unit digit of 4, which is 64 in this case. Multiplying by 2 again will give you something ending in 8, 128 in this case. This means that the units digit pattern follows a rigid structure of 2, 4, 8, 6, and then repeats again. So while it may not be trivial to calculate a huge multiple of 2, say 2^150, its unit digit can easily be calculated using this pattern.

Let’s look at a problem that highlights this pattern recognition nicely:

*What is the units digit of (13)^4 * (17)^2 * (29)^3?*

*(A) 9
*

Looking at this question may make many of you wish you had access to a calculator, but the very fact that you don’t have a calculator on exam day is what allows the GMAT to ask you a question like this. There is no reasoning, no shrewdness, required to solve this with a calculator. You punch in the numbers, hope you don’t make a typo and blindly return whatever the calculator displays without much thought (like watching San Andreas). However, if you’re forced to think about it, you start extrapolating the patterns of the unit digit and the general number properties you can use to your advantage.

For starters, you are multiplying 3 odd numbers together, which means that the product must be odd. Given this, the answer cannot possibly be answer choice C, as this is an even number. We’ve managed to eliminate one answer choice without any calculations whatsoever, but we may have to dig a little deeper to eliminate the other three.

Firstly, recognize that the unit digit is interesting because it truncates all digits other than the last one. This means this is the same answer as a question that asks: (3^4) * (7^2) * (9^3). While we could conceivably calculate these values, we only really need to keep in mind the unit digit. This will help avoid some tedious calculations and reveal the correct answer much more quickly.

Dissecting these terms one by one, we get:

3^4, which is 3*3*3*3, or 9*9, or 81.

7^2, which is just 49.

9^3, which is 9*9*9, or 81 * 9, or 729.

The fact that we truncated the first digit of the original numbers changes nothing to the result, but does serve to make the calculations slightly faster. Furthermore, we can truncate the tens and hundreds digits from this final calculation and easily abbreviate:

81 * 49 * 729 as

1 * 9 * 9.

This result again gives 81, which has a units digit of 1. This means that the correct answer ends up being answer choice E. It’s hard to see this without doing some calculations, but the amount of work required to solve this question correctly is significantly less than what you might expect at first blush. An unprepared student may approach it by calculating 13^4 longhand, and waste a lot of time getting to an answer of 28,561. (What? You don’t know 13^4 by heart?) Especially considering that the question only really cares about the final digit of the response, this approach is clearly more dreary and tedious than necessary.

The units digit is a favorite question type on the GMAT because it can easily be solved by sound reasoning and shrewdness. In a world where the biggest movie involves Jurassic Park dinosaurs and a there is a Terminator movie premiering in a week, it’s important to note that trends recur and form patterns. Sometimes, those patterns are regular enough to extrapolate into infinity (and beyond!).

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!

One of my favorite shortcuts that we teach at Veritas Prep, and that will work on a variety of questions, is to use a number line to find the ratio of two elements in a weighted average. Say, for example, that we have a classroom of students from two countries, which we’ll call “A” and “B.” They all take the same exam. The average score of the students from country A is 92 and the average score of the students from country B is 86. If the overall average is 90, what is the ratio of the number of students from A to the number of students in B? We could solve this algebraically. If we call the number of students from county A, “a” and the number of students from country B “b,” we’ll have a total of a + b students, and we can set up the following chart.

Average | Number of Terms | Sum | |

Country A | 92 | a | 92a |

Country B | 86 | b | 86b |

Total | 90 | a + b | 90a + 90b |

The sum of the scores of the students from A when added to the sum of the scores of the students from B will equal the sum of all the students together. So we’ll get the following equation: 92a + 86b = 90a + 90b.

Subtract 90a from both sides: 2a + 86b = 90b

Subtract 86b from both sides: 2a = 4b

Divide both sides by b: 2a/b = 4

Divide both sides by 2: a/b =4/2 =2/1. So we have our ratio. There are twice as many students from A as there are from B.

Not terrible. But watch how much faster we can tackle this question if we use the number line approach, and use the difference between each group’s average and the overall average to get the ratio:

b Tot a

86——–90—-92

Gap: 4 2

Ratio a/b = 4/2 = 2/1. Much faster. (We know that the ratio is 2:1 and not 1:2 because the overall average is much closer to A than to B, so there must be more students from A than from B. Put another way, because the average is closer to A, A is exerting a stronger pull. Generally speaking, each group corresponds to the gap that’s farther away.)

The thing to see is that this approach can be used on a broad array of questions. First, take this mixture question from the Official Guide*:

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%

B. 33 1/3%

C. 40%

D. 50%

E. 66 2/3%

In a mixture question like this, we can focus exclusively on what the mixtures have in common. In this case, they both have ryegrass. Mixture X has 40% ryegrass, Mixture Y has 25% ryegrass, and the combined mixture has 30% ryegrass.

Using a number line, we’ll get the following:

Y Tot X

25—–30———40

Gap: 5 10

So our ratio of X/Y = 5/10 = ½. (Because X is farther away from the overall average, there must be less X than Y in the mixture.) Be careful here. We’re asked what percent of the *overall* mixture is represented by X. If we have 1 part X for every 2 parts of Y, and we had a mixture of 3 parts, then only 1 of those parts would be X. So the answer is 1/3 = 33.33% or B.

So now we see that this approach works for the weighted average example we saw earlier, and it also works for this mixture question, which, as we’ve seen, is simply another variation of a weighted average question.

Let’s try another one*:

During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

a) 180

b) 170

c) 156

d) 150

e) 105

First, we’ll plot the win percentages on a number line.

Remaining Total First 100

50—————70———-80

Gap 20 10

Remaining Games/First 100 = 10/20 = ½.

Put another way, the number of the remaining games is ½ the number of the first 100. That means there must be (½) * 100 = 50 games remaining. This gives us a total of 100 + 50 = 150 games played. The answer is D.

Note the pattern of all three questions. We’re taking two groups and then mixing them together to get a composite. We could have worded the last question, “mixture X is 80% ryegrass and weighs 100 grams, and mixture Y is 50% ryegrass. If a mixture of 100 grams of X and some amount of Y were 70% ryegrass, how much would the combined mixture weigh?” This is what I mean by making horizontal connections. One problem is about test scores, one is about ryegrass, and one is about baseball, but they’re all testing the same underlying principle, and so the same technique can be applied to any of them.

Takeaway: always try to pay attention to what various questions have in common. If you find that one technique can solve a variety of questions, this is a technique that you’ll want to make an effort to consciously consider throughout the exam. Any time we’re stuck, we can simply toggle through our most useful approaches. Can I pick numbers? Can I back-solve? Can I make a chart? Can I use the number line? The chances are, one of those approaches will not only work but will save you a fair amount of time in the process.

*Official Guide questions courtesy of the Graduate Management Admissions Council.

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!

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here. *

So why doesn’t everyone get a perfect score on these questions? Often, it’s simply because they are pressed for time. Reading a 300+ word passage and then answering a question about the subject matter may take a few minutes, especially if English isn’t your first language or you’re not a habitual reader (you’ve only read Game of Thrones once?). Add to that the possibility of two or three answer choices seeming plausible, and you frequently waste time re-reading the same paragraphs over and over again in the passage.

Luckily, there is one type of question in Reading Comprehension that rarely requires you to revisit the passage and search for a specific sentence. **Universal questions** ask about the passage as a whole, not about specific actions, passages or characters. I often define universal questions as the “Wikipedia synopsis” (or Cliff’s notes for the older generation) of the passage. The question is concerned with the overarching theme of the passage, not about a single element. As such, it should be easy to answer these questions after reading the passage only once as long as you understood what you were reading.

Let’s delve into this further using a Reading Comprehension passage (note: this is the same passage I used previously for **function**, **specific **and **inference** questions).

*Nearly all the workers of the Lowell textile mills of Massachusetts were unmarried daughters from farm families. Some of the workers were as young as ten. Since many people in the 1820s were disturbed by the idea of working females, the company provided well-kept dormitories and boarding-houses. The meals were decent and church attendance was mandatory. Compared to other factories of the time, the Lowell mills were clean and safe, and there was even a journal, The Lowell Offering, which contained poems and other material written by the workers, and which became known beyond New England. Ironically, it was at the Lowell Mills that dissatisfaction with working conditions brought about the first organization of working women.*

* The mills were highly mechanized, and were in fact considered a model of efficiency by others in the textile industry. The work was difficult, however, and the high level of standardization made it tedious. When wages were cut, the workers organized the Factory Girls Association. 15,000 women decided to “turn out”, or walk off the job. The Offering, meant as a pleasant creative outlet, gave the women a voice that could be heard by sympathetic people elsewhere in the country, and even in Europe. However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families. The same limitation hampered the effectiveness of the Lowell Female Labor Reform Association (LFLRA), organized in 1844.*

* No specific reform can be directly attributed to the Lowell workers, but their legacy is unquestionable. The LFLRA’s founder, Sarah Bagley, became a national figure, testifying before the Massachusetts House of Representatives. When the New England Labor Reform League was formed, three of the eight board members were women. Other mill workers took note of the Lowell strikes, and were successful in getting better pay, shorter hours, and safer working conditions. Even some existing child labor laws can be traced back to efforts first set in motion by the Lowell Mill Women.*

*The primary purpose of the passage is to do which of the following?*

*(A) Describe the labor reforms that can be attributed to the workers at the Lowell mills
*

The most frequent universal question you’ll see is something along the lines of “what is the primary purpose of this passage”. In essence, it’s asking you to summarize the 300+ word passage into one sentence, and that is difficult to do if you don’t remember anything about the passage. Ideally, you retained the key elements during your initial read. If need be, you can reread the passage, noting the main point of each paragraph in about five words. The synopsis of each paragraph, especially the last one, should give you a good idea about the overall goal of the passage.

In this passage, each paragraph is talking about the labour strife at the Lowell textile mills of Massachusetts in the 1820s. The first paragraph describes the conditions at the mill and sets the stage, the second paragraph describes the worker strike and subsequent resolution, and the third paragraph discusses the legacy of these workers. The overall theme has to capture the spirit of the entire passage, which is often summarized in the final paragraph (often the author’s conclusion). Pay special attention to that paragraph in order to determine why the author wrote this text and what he or she wanted you to learn from it.

Let’s look at the answer choices in order. Answer choice A, *describe the labor reforms that can be attributed to the workers at the Lowell mills*, is a popular incorrect answer. The goal of the passage is to shed light on these events, and describing the labor reforms attributed to these workers seems like a good conclusion, but it is specifically refuted by the first line of the third paragraph: “No specific reform can be directly attributed to the Lowell workers…” This means that answer choice A, while tempting, is hijacking the actual conclusion of the passage, as we cannot describe things that do not exist, and is therefore incorrect.

Answer choice B, *criticize the proprietors of the Lowell mills for their labor practices*, seems like something the reader could agree with, but is completely out of the scope of the passage. The mill is not being scrutinized for their labor practices; rather, the efforts of certain people are being underlined. If anything, the text suggests that the conditions at this mill were better than most at the time (and still today in certain countries). Answer choice B is somewhat righteous, but ultimately wrong in this passage.

Answer choice C, *suggest* *that the Lowell mills played a large role in the labor reform movement*, is supported by what is being said in the final paragraph. The legacy of the Lowell mills is being discussed, and since other workers were inspired by the events that transpired at these mills, the Lowell mills played a significant part in the larger labor reform movement. While this answer focuses somewhat on the third paragraph, don’t forget that the final paragraph has the most sway in the majority of passages, just as the last section of a movie is usually the most important section (the denouement, in proper English). Answer choice C is correct here, as the passage is primarily discussing the legacy of these events.

Let’s continue on for completion’s sake. Answer choice D,* describe the conditions under which the Lowell mills employees worked*, focuses on one small portion of the first paragraph, and even then the conditions are not covered in great detail. It’s a big stretch to try and claim that this is the primary focus of the entire passage, and thus can be eliminated fairly quickly.

Answer choice E, *analyze the business practices of early American factories*, is an answer choice that seems to bring some larger context to the passage, but is even more out of scope than answer choice B because it’s much broader. Only one mill is being examined in the passage, and its business practices were not even the main focus of the passage, so broadening the scope to all American factories is certainly incorrect. Answer choice E can also be eliminated, leaving only answer choice C as the correct selection.

Generally, universal questions do not require a rereading of the passage as the questions are primarily concerned with the broad strokes of the passage. If you didn’t grasp the major facets of the passage when reading through it, you probably didn’t understand the passage at all. If you understand the major elements of the passage as you read through it the first time, noting the primary purpose of each paragraph as you go along, you’ll be ready for any question in the universe.

The good news is, the exam is mandated to have five different answer choices on every question, but some of these answer choices are redundant. While you won’t actually see the same answer choice twice on the test (unless you’re seeing double), many answer choices don’t differ from another answer choice in a meaningful way.

As an example, if you’re looking for the product of two even integers, such as 4 and 6, you know the product can never be odd. So while one answer choice may be 25 and another may be 33, they can both be eliminated for the same reason, greatly streamlining your task if you’re eliminating possible answer choices based on sound reasoning. Sometimes, a question may have two or three answer choices you can eliminate without having to do any math, as long as you can sort multiple answers into the same bucket (think Gryffindor).

Let’s look at such a question and how we can consider eliminating answer choices without actually calculating them longhand:

*If x^4 > x^5 > x^3, which one could be the value of x?*

*A) -3*

*B) -2*

*C) -2/3*

*D) 2/3*

*E) 3*

This question seems complicated because it is very abstract. We’re dealing with some unknown variable x raised to various uncomfortable powers. A great strategy here would be to try and make it easier to understand by using actual numbers. This will allow us to better visualize what is actually happening in the problem.

Let’s begin with the base case. Say we set x to be a simple positive integer, such as 2. If we square 2, we get 4. If we multiply by 2 again, we get 8. This is 2^3. We can continue by multiplying by 2 again and getting 16 for 2^4, and one final time to get 32 for 2^5. It should come as no surprise that the variable gets bigger as the powers increase.

However, this situation does not satisfy our original premise of x^4 > x^5 > x^3 because x^5 is the biggest value. Beyond eliminating the number 2 from contention, we can eliminate 3, 4, and every other positive integer bigger than 1. This is because all positive integers greater than one will increase in amplitude as the powers increase. Knowing this, we can eliminate answer choice E, which follows the same mould.

The remaining answer choices seem to either be negative, fractional or both. We might also recognize that numbers smaller than 1 will follow a different pattern, because successive increases in power will make the number smaller and smaller. Furthermore, negative numbers can break the pattern as well, as they will oscillate between positive results for even powers and negative results for odd powers. In fact, these two axes will be the only determining factors in identifying the correct result. The answer will be only one of the following structures: positive and less than 1, negative and less than 1, positive and more than 1, or negative and more than 1. Our job is to sort these out (like the sorting hat at Hogwarts).

We have already observed that positive and greater than 1 doesn’t satisfy the given inequality, so let’s look at positive and less than 1. We can take ½ as an example and extrapolate that to any result 0 > x > 1. If we square ½, we get ¼. If we continue to multiply by ½, we get 1/8, 1/16 and 1/32 respectively. Unsurprisingly, these are the reciprocals of the values found for x = 2. This batch doesn’t satisfy the inequality either, as x^3 is actually the biggest number here. This eliminates answer choice D. If it’s not obvious, the relative sizes of the exponents are easier to see if we use the number line:

___________________________________________________________________

0 1/32 1/16 1/8 1

x^5 x^4 x^3

Now that we’ve eliminated two possibilities (Hufflepuff and Ravenclaw), let’s look at the remaining choices: -3, -2 and -2/3. At this point, it should make sense that all negative numbers with absolute value greater than 1 will behave the exact same way in this inequality. This means that the answer cannot be either -3 or -2, as they are indistinguishable inputs on this question (also both Slytherin). Thus, if -2 worked, so would -3, and vice versa. Since only one answer choice can be correct, neither of these will be correct, and the answer must be -2/3. Let’s go through the calculation to confirm, but we already know it must be correct.

When we square a negative number, we are multiplying a negative by a negative and yielding a positive. When we multiply that number by a negative again, we revert to negative numbers. Thus, every odd numbered power will be negative and every even numbered power will be positive. Knowing this, we can easily calculate that x = -2/3, then x^2 = 2^2/3^2. Multiplying by -2/3 again, we get -2^3/3^3 for x^3. The next values will be 2^4/3^4 for x^4 and -2^5/3^5 for x^5. If it’s easier to see, you can calculate each of these values and get:

x^2 = 4/9

x^3 = -8/27

x^4 = 16/81

x^5 = -32/243

Using the number line again as a visual aid (roughly to scale):

________________________________________________________________________

-1 -8/27 -32/243 0 16/81 1

x^3 x^5 x^4

This confirms that x^4 is the biggest (most to the right) value while x^3 is the smallest and x^5 is the middle value. This also highlights the issue that -2 and -3 would have, as the amplitude increases, x^5 would be much smaller than x^3. Of the choices given, the only value that works is answer choice C: -2/3.

On the GMAT, one of the five answer choices must always be correct, but the other four can give you insight into what you should consider to solve the question. Oftentimes, you can figure out what the key issues are by perusing the choices provided. And more often than not, you can eliminate swaths of answer choices based on a logical understanding of the question. On test day, you don’t want to waste time considering answer choices that are obviously incorrect. If you can sort through the various answer choices quickly, you’ll end up in the house of your choice (I’d opt for Gryffindor).

**Lesson Four: **

Think Like a Lawyer. Your natural inclination is to just click “I agree” to the iTunes Terms & Conditions, but to lawyers each word in that agreement is carefully chosen to build a case. Thankfully, on the GMAT the Critical Reasoning problems you see will be 99% shorter than those Terms & Conditions, but you’ll need to train yourself to think like a lawyer and notice how carefully chosen those words in the prompt are. In this video, Ravi will demonstrate how his law degree has helped him become a master of GMAT Critical Reasoning, and how you can summon your inner Elle Woods (or Johnnie Cochran) to conquer CR, too.

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!

Want to learn more from Ravi? He’s taking his show on the road for one-week Immersion Courses in San Francisco and New York this summer, and teaches frequently in our new Live Online classroom.

*By Brian Galvin*

When looking through answer choices on Critical Reasoning questions, there is always one correct answer to the question. After all, it wouldn’t be fair if two different answers were both legitimate responses to the query being posed. However, just because the other four answers are incorrect, it doesn’t mean that they aren’t tempting. In fact, there is usually one choice the exam is pointing you towards selecting, even though it isn’t the correct option. This is often referred to as the sucker choice.

The sucker choice is an answer that seems to answer the question on the surface, but in actuality it is only a red herring. Answers like this will frequently provide redundant information, or play into your preconceived notions. As an example, if a couple has two children, and you’re told that child A is taller than child B, you’d naturally think that child A is older than child B. However, this doesn’t have to be the case, as the children could be adults (ironic, no?). A taller child does not necessarily imply an older child, but it’s certainly an assumption a lot of people would make.

Other examples of the sucker choice involve providing known information on a strengthen/weaken question, or giving an answer choice that seems reasonable but not 100% assured on an inference question. The choices will always seem reasonable, and in many cases, they will be the most popular answer choices selected. In many ways, the sucker answer choice is like smoking. It seemed like a good idea at the time, it feels good, and it can be bad for your (GMAT) health long term.

Let’s look at a question that deals with this very topic:

*A system-wide county school anti-smoking education program was instituted last year. The program was clearly a success. Last year, the incidence of students smoking on school premises decreased by over 70 percent.*

Which of the following, if true, would most seriously weaken the argument in the passage?

* (A) The author of this statement is a school system official hoping to generate good publicity for the anti-smoking program.
(B) Most students who smoke stopped smoking on school premises last year continued to smoke when away from school.
(C) Last year, another policy change made it much easier for students to leave and return to school grounds during the school day.
(D) The school system spent more on anti-smoking education programs last year than it did in all previous years.
(E) The amount of time students spent in anti-smoking education programs last year resulted in a reduction of in-class hours devoted to academic subjects*

On this Critical Reasoning weaken question, it’s important to note the conclusion and the supporting evidence. The conclusion is the middle sentence (*The program was clearly a success*) as that is unmistakably the author’s main point in this passage. The evidence is everything else, but especially the last sentence, because a decrease of 70% of student smoking on the premises would seem to support the author’s conclusion. We’re tasked with weakening this conclusion, so we must find evidence that refutes this evidence or otherwise makes the conclusion less likely to occur.

There is one trap answer on this question that a lot of students gravitate towards. I’ll let you reread the choices to see which one you singled out (cue jeopardy music).

The answer choice that most people like is B: *students who smoke stopped smoking on school premises last year continued to smoke when away from school. *After all, the logic seems sound. If students stopped smoking at school, and we’re trying to weaken the conclusion, then it would follow that students smoking everywhere else (at home, in the street, at the Peach Pit…) would weaken the conclusion. Furthermore, this is new evidence that seems to perfectly solve every element we care about. Many students select B here and move on with nary a thought that they just fell into a GMAT trap. (It’s a trap!)

Let’s re-examine the conclusion. The conclusion stated that the program was a success, and the program was defined as a county school anti-smoking education program. This means that the students were being educated in an effort to reduce smoking at school. If incidents of smoking at school decreased by 70%, then the program was a success, regardless of whether the students were smoking elsewhere. Indeed, the goal of the program was to reduce smoking in school, and answer choice B does not weaken that conclusion. It weakens the goal of curbing out smoking altogether, but that is a slightly different conclusion that is beyond the scope of this particular argument.

As such, answer choice B seems like a logical answer, but fails to meet the necessary criteria to be the right response. This means that we need to peruse the other four answer choices to identify the correct choice.

Answer choice A, “*the author of this statement is a school system official hoping to generate good publicity for the anti-smoking program”*, implies that the author may have a hidden agenda. While this may be true, it doesn’t account for the 70% decrease of on-campus smoking, so it doesn’t do a good job of weakening the argument given the evidence presented. We can eliminate this choice.

Answer choice C, “*Last year, another policy change made it much easier for students to leave and return to school grounds during the school day” *does indeed weaken this argument. If your only evidence is the decrease in smoking on campus, then any alternative explanation as to why that happened weakens your argument. The students may not be smoking on the grounds anymore, but they are still smoking at school, just a little further away than before. Indeed, the smoking policy may have had absolutely no effect on students’ habits whatsoever, greatly weakening the conclusion.

Answer choice D, “*The* *school system spent more on anti-smoking education programs last year than it did in all previous years” *actually somewhat strengthens the argument. If the school system put a lot of money into the program, then it would be more likely to succeed. Even if the school overspent, the success of the program is determined by the students’ smoking habits, not the program’s budget.

Answer choice E, “*the amount of time students spent in anti-smoking education programs last year resulted in a reduction of in-class hours devoted to academic subjects” *is also somewhat tempting, because it introduces the concept of side-effects. In the real world, we might do something that has unintended consequences, and look back on the decision as a mistake. Side effects don’t affect the success rate of the program, so this answer choice can be eliminated.

As we saw, answer choice C is the correct selection. However, it may not be the most common selection on this exam, as another answer choice was more enticing for a lot of students. The GMAT is designed to provide tempting answer choices that almost solve the issue at hand, but fall short in one crucial measure. On test day, be wary of these tempting sucker choices, or your exam score will go up in smoke.

Similarly, for all the dizzying content the GMAT requires you to internalize, the exam, more than anything else, is about pattern recognition. There are two ways we can improve at pattern recognition. The first, and most obvious, is that by doing many practice questions, our brains, like those of the aforementioned chess masters, will subconsciously absorb recurring patterns.

The second is to learn to recognize certain signposts and triggers that indicate what’s being tested. In Sentence Correction, for example, there are certain classic trigger words for parallel construction, such as “both,” “either/or,” and “not only/but also.” As soon as we see one of these constructions, we can immediately zero in on this part of the sentence and evaluate whether the items that follow the signpost are parallel to one another. If a phrase begins with “both in x,” for example, I know I want to see the parallel construction, “and in y,” in that same sentence. All of the other grammatical, stylistic, and logical considerations can temporarily be put aside. Once I’ve resolved this issue, if I’m left with more than one answer choice, I’ll look for other differences, but I’ll likely have narrowed my possibilities so much that the problem will be much less taxing than it would have been otherwise.

Take this Official Guide* problem, for example:

Many of the earliest known images of Hindu deities in India date from the time of the Kushan empire, fashioned either from the spotted sandstone of Mathura or Gandharan grey schist.

A) Empire, fashioned either from the spotted sandstone of Mathura or

B) Empire, fashioned from either the spotted sandstone of Mathura or from

C) Empire, either fashioned from the spotted sandstone of Mathura or

D) Empire and either fashioned from the spotted sandstone of Mathura or from

E) Empire and were fashioned either from the spotted sandstone of Mathura or from

The moment I see that “either” I’m focusing on this part of the sentence. Now watch how quickly I can eliminate incorrect options:

A) “either **from** spotted sandstone of Mathura or grey schist.” I want “either **from** x” or “**from**” I don’t have a second “from” here. A is out.

B) “either the spotted sandstone of Mathura or **from** grey schist.” See what they did here. Parallel construction begins when we see the parallel marker “either.” Now there is no “from” before the first item, but we do have it before the second one. “either x or from y” is not parallel. B is out.

C) “either **fashioned from** the spotted sandstone of Mathura or gray schist” Now we’re back to the original error of having “from x or y” rather than the desired “from x or from y.” C is out.

D) “either fashioned **from** the spotted sandstone of Mathura or from **grey**” A little better. We’d prefer “either **fashioned from** x or **fashioned from** y,” but at least we have the preposition “from” in front of both items. But now read that full first clause, “Many of the earliest known images of Hindu deities in India date from the time of the Kushan Empire and either fashioned from the spotted sandstone…” Well, that doesn’t make any sense. We’d want to say that the images *date* from the time of the Kushan Empire and *were fashioned* from the spotted sandstone. Without the verb “were,” the sentence is incoherent. Eliminiate D.

E) “either from the spotted sandstone of Mathura or from grey schist.” Now we see it. “either from x or from y.” We have our parallel construction. E is correct.

Let’s try another example*:

Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.

A) Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted

B) Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both

C) Jazz pianist and composer Thelonious Monk, who produced a body of work rooted

D) Jazz pianist and composer Thelonious Monk produced a body of work that was rooted

E) Jazz pianist and composer Thelonious Monk produced a body of work rooted both

Again, we see one of the parallel trigger words. In this case, “both.” So the first thing I’ll do is examine the items that follow the parallel marker, “both **rooted in** the stride piano tradition.” If I begin a phrase with “rooted **in** x” I’ll want to follow that with “**in** y.” Notice that not only does the original sentence fail to do this, but the portion of the sentence we wish to change isn’t even underlined! Because we cannot produce a parallel construction here, we’ll need to eliminate the parallel marker “both” altogether. That means A, B, and E are all out. Now let’s evaluate C and D.

C) the clause, “who produced a body of work…” is set off by commas and functions as a modifier of Thelonious Monk. This means that the clause is incidental to the meaning of the sentence. But if we read the sentence without the modifier, we get, “Jazz pianist and composer Thelonious Monk, yet in many ways he stood apart from the mainstream jazz repertory.” Well, that doesn’t make any sense. “Yet” should connect two full clauses, but in this case, it connects the noun phrase, “Jazz pianist and composer Thelonious Monk” to the full clause, “in many ways he stood apart from the mainstream jazz repertory.” This is incoherent. Eliminate C.

That leaves us with D, which is our answer. Recognizing the pattern and focusing on parallel construction allowed us to ignore the rest of what was a fairly complex sentence.

Takeaways: The GMAT is less a test of memorization than it is an exercise in pattern recognition. There’s no getting around having to see many examples of questions to prime our brains to recognize these patterns on test day, but there are certain structural clues that provide insight into what a particular question is testing. If we internalize those structural clues, suddenly the patterns we’re tasked with recognizing become far more conspicuous.

*Official Guide questions courtesy of the Graduate Management Admissions Council.

Whatever the Canadian content, I’m always happy to see a question concerning something I already know, because I feel like I start with a leg up on the question. Indeed, I’m motivated whenever I see a question about a familiar topic, but I’m particularly excited when it’s aboot Canada (see what I did there?).

In actuality, questions that arouse your own interests can be dangerous. This is because they can sometimes cloud your judgment or make you feel like you know something that isn’t explicitly stated in the text (I know a 6 cylinder car accelerates faster than 4 cylinder car…). While this may be true in the real world, don’t forget that you can’t bring any outside knowledge with you to the GMAT.

The reason behind this is simple: anybody should be able to solve the question with the information provided in the question. Yes, you might already know something pertinent to the situation, but you cannot use it to solve the question unless it’s explicitly stated in the question. Especially on Critical Reasoning questions, these red herrings can come influence your decision without you even noticing it.

This doesn’t mean that you can’t get excited when a question mentions your favorite team; it just means that you have to maintain your objectivity regardless. I may be one of very few people who get excited when he sees a GMAT question about hockey, but as a Canadian I have to a duty to share as much hockey as possible with the world (and sing the national anthem before every home game).

*There are 16 teams in a hockey league and each team plays each of the others once. Given that each game is played by two teams, how many total games will be played?*

*A) 120
*

Now, ignoring that most leagues don’t play perfect round-robin tournaments because they are time consuming, but this question could be adopted to any sport of choice (perhaps even WWE wrestling) and would be solved the same way. I enjoy the casual mention of hockey in this problem, but you’re free to imagine your favorite sport instead if it makes seeing the pattern easier for you.

Let’s approach this in a brute strength manner first and refine our strategy as we go along. Each team will have to play each other team in the league. This means that the first team, which we’ll call team 1 for simplicity, has to play against team 2, team 3, team 4, etc up until team 16. This would comprise of 15 matches for team 1. Next, we consider team 2. Team 2 already faced team 1, so that game is off the books, and their schedule would start against team 3, then team 4, etc, up until team 16. This would lead to 14 separate matches.

We seem to have something of a pattern here, but let’s do a third team just to compare our hypothesis (H_{0}: It will be 13 matches. H_{A}: We’ll have to find another way). Team 3 has already faced teams 1 and 2, meaning that their schedule begins at team 4, and then goes on to team 5, etc up until team 16. This does indeed add up to 13 more games being played. The pattern seems to hold up logically, every team plays one fewer game than the last because they’ve already faced any opponent with a team number lower than theirs.

Now, this approach gives the correct answer, but yields a difficult sequence to be summed: 15+14+13+12+11+10+9+8+7+6+5+4+3+2+1. We can shortcut this calculation because the sequence is comprised of consecutive integers, which means the total will be the average multiplied by the number of terms. Since the terms run from 1 to 15 (easier to see this forwards than backwards), the average is (1+15)/2 or 8, and there are 15 terms. 15 x 8 is 120, answer choice A, and this is the correct answer.

The brute force approach is rarely the best strategy, but it’s worth noting that it does get you to the correct answer. You can also shortcut this calculation by ignoring the fact that some teams have already played against one another in your initial count. That is to say: Team 1 has to face 15 opponents, and Team 2 has to face 15 opponents as well. Team 3 will end up facing 15 opponents too, and eventually all 16 teams will face 15 opponents, meaning the total number of games should be 15*16. This math isn’t trivial, but you can get to 240 relatively quickly. The problem with 240 is that you have double counted all the games (i.e. 1 vs. 2 and 2 vs. 1). Simply taking this product and dividing it by two will eliminate the double counting and yield the correct answer of 120.

The final strategy I want to point out here is that we’re essentially making all the unordered pairs of a group. This means we can use combinations to get the correct number. If we have n = 16 teams, and we’re trying to make all the combinations of 2 teams (k = 2), then we have a combination of the form:

n! / (k! * (n-k)!)

This formula gives us 16! / (2! * (16-2)!).

Solving for the subtraction gives us:

16! / (2! * 14!)

Simplifying by eliminating the redundant 14! from both numerator and denominator gives:

16 * 15 / 2.

This of course simplifies to 8 * 15 or the aforementioned 120. No matter the approach, you should get the same result, which is still choice A.

The GMAT will ask you all kinds of questions about topics you’ve never heard of, but sometimes it will contain a topic that’s near and dear to your heart. It’s okay to be a little elated; you need some positive moments during the 4 hour GMAT marathon. Just keep in mind that the question will be like any other problem, you solve it using the information contained in the question and your hours of GMAT prep. If you do that properly, you’ll be able to put the puck in the net on test day.