Firstly, if you’ve never heard the song, please feel free to listen to it now. The chorus is discussing how Ariana would have “one less problem” without the person she’s currently serenading (surprisingly this isn’t a Taylor Swift song). The issue with the lyric is that problems are countable, and as such she should actually be singing “one fewer problem without you”. Perhaps the extra syllable messed up the harmony, or perhaps the songwriter hadn’t brushed up on their grammar prior to writing the song, but this is the type of issue students often struggle with because they don’t understand the underlying rule.

When it comes to counting things, there are two broad categories: items that are countable, and items that are not countable. The former comprises most tangible things we can imagine: computers, cars, cats, cookies, cans of Coke and countless conceivable commodities (This sentence brought to you by the letter C). The latter comprises things that are uncountable, such as water, sand or hair. You can count grains of sand or strands of hair, but you cannot count actual sand or hair, so these words get treated a little differently.

The rule is that for any noun that is countable, you must use “fewer” if you are going to decrease it. For any noun that is not countable, you must use “less” to decrease it. As an example, I want less water in my cup; I do not want fewer water in my cup. That example makes sense to most people. However, the converse is just as true: I want fewer bottles of water, not less bottles of water. If the item in question is scarce, similar words will be used. You can say that there is little water, but you wouldn’t say that there is few water left. Note how these words have the same etymology as “less” and “fewer”, respectively.

If the sentence calls for an increase, more is acceptable for both countable and uncountable elements. As an example, you can say that you want more water in your cup, or you can say that you want more bottles of water. Other synonyms exist as well, of course, but the delineation is much cleaner for decreases than for increases, so that structure appears more often on the GMAT. If the item in question is in abundance, similar words will also be used. You can say that there is much water, but you can’t say that there is many water. Much and many follow these same countable/uncountable rules.

The difference between items that are countable or uncountable is not unique to the GMAT, these rules apply to everyday language, they are simply enforced more rigorously on this test. Failure to choose the proper word in a Sentence Correction problem will result in an incorrect answer choice. As such, it behooves us to be aware of the grammatical difference between countable and uncountable elements, as it regularly comes up on the GMAT.

Let’s look at an example to illustrate the point:

*The controversial restructuring plan for the county school district, if approved by the governor, would result in 20% fewer teachers and 10% less classroom contact-time throughout schools in the county. *

*A) **in 20% fewer teachers and 10% less *

*B) **in 20% fewer teachers and 10% fewer *

*C) **in 20% less teachers and 10% less *

*D) **with 20% fewer teachers and 10% fewer *

*E) **with 20% less teachers and 10% less*

Looking at the answer choices, it becomes fairly clear that the correct answer will hinge primarily on the difference between “fewer” and “less”. If we recall the rules for countable vs. uncountable, anything that we can count must use the adjective “fewer”, while anything that is not countable must use the adjective “less”.

For this example, the first reduction is in the number of teachers. Teachers are human beings (often handsome ones!), and are therefore countable. You can want to spend less time with a specific teacher, but you cannot (correctly) say that you want the school to have less teachers. The request must be for fewer teachers. This already eliminates answer choices C and E because they use the incorrect term.

The second reduction is about classroom time. Time is a wondrous and magical thing (or so young people tell me), but it is not countable. Yes, you can break up time into countable units, such as seconds or minutes, just as you can break up sand into grams or ounces, but holistically time is intangible and therefore uncountable. The plan calls for less time in the classroom, not fewer time. This eliminates answer choices B and D because they use the incorrect term. Only answer A remains and it is indeed the correct answer.

As mentioned earlier, the rules around countable and uncountable nouns are fairly precise, but you are unlikely to be corrected in everyday conversation if you misuse a term. Since the GMAT is testing logic, precision and general attention to detail, it is a perfect type of question to try and trap hurried students who don’t always notice the difference. In daily conversation (and on the radio), you can often get away with imprecision in language. However, if you understand the nuances between countable and uncountable nouns, to paraphrase Ariana Grande, you’ll have one fewer problem on the GMAT.

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*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.*

The major difference between the GMAT and high school exams is that the questions are unpredictable. In high school, we’re taught to memorize certain pieces of information, and then regurgitate them on the final exam. If the question on the exam differed even slightly from the question we’ve committed to memory, we tended to panic, guess and generally fail to see the relationship between what we learned and what we were being asked to solve. As an example, if you know 12^2, you’re already 85.2% of the way to solving 13^2 (you know, roughly…). There is a fairly simple way to go from one perfect square to another, but before we talk about the general case solution, let’s go back to the beginning.

This pattern holds with 0^2, but for simplicity’s sake, let’s starts with 1^2. 1^2 expanded is 1 x 1, and this gives us a product of 1. Let’s look at the next perfect square: 2^2. 2 x 2 = 4. This is an increase of 3 from the first perfect square. The next perfect square is 3^2. 3 x 3 = 9. This represents an increase of 5 from the previous perfect square. Let’s do one more to cement the pattern: 4^2. 4 x 4 = 16. From the previous perfect square, we’ve increased by 7. The next perfect squares are 25, 36 and 49, representing subsequent increases of 9, 11 and 13, respectively. Indeed, each increase between subsequent perfect squares is a positive odd integer, and they’re in sequential order. It turns out that this pattern holds for all perfect squares, allowing us a shortcut to calculate them quickly. Let’s look at why this pattern holds.

From the initial perfect square of 1^2, we increase to 2^2. Consider this in two parts. We start with 1 x 1, and then we go to 1 x 2, and then finally to 2 x 2. What happens at each step? The first step brings up the total by 1, as we are adding another one of the initial element. The second step brings us up by 2, as we are adding another one of the new (n+1) element. This difference is what makes the perfect square 2^2 increase by (1+2=) 3 from the previous perfect square 1^2. Similarly, going from 2^2 to 3^2 can stop by the intermediary step of 2 x 3, and then 3 x 3. The first increase is of 2, and the second is of 3, giving a total of 5. For the general case, we can see that n^2 becomes (n+1) ^2 if we simply take n^2 and increase it by n and then increase it by n+1.

While this level of mathematics is not required on the GMAT, it certainly makes certain calculations much faster. Let’s return to our initial example of 12^2. Most (non-GMAT aficionado) people don’t know 13^2 offhand, but since elementary school has indoctrinated us with the multiplication table up to 12, the majority of people can easily recall that 12^2 is 144. Using this shortcut, we can see that 13^2 is 144 + 12 + 13. Adding these together, we get 169, the correct answer. 14^2 will similarly be 169 + 13 + 14, or 196, and so on.

I don’t consider this strategy a trick in any way, but rather a result of deeply understanding mathematical properties. This is the type of skill that’s rewarded on the GMAT, and it’s often rewarded by solving questions like this in under 2 minutes:

225, or 15^2, is the first perfect square that begins with two 2s. What is the sum of the digits of the next perfect square to begin with two 2s.

(A) 7

(B) 9

(C) 13

(D) 16

(E) 21

This is the type of question that could easily take 5 minutes on the GMAT. We have very little information, only that the number we want is a perfect square that begins with two 2s. Also, that it’s not 225, which is one a lot of people might know (especially if you live in a country with 15% sales tax). Even with a calculator, this question isn’t particularly trivial, so we’ll need to devise a strategy before randomly squaring numbers and hoping they begin with 22…

First things first, the next perfect square cannot possibly be 22x. The next perfect square after 15^2 is 16^2, which is 256 (you can get here any way you like). This means that the next perfect square has to be 22xx. This gives us an order of magnitude to shoot for. Until we have a better idea on which numbers to hone in on, let’s use easy numbers to get a sense of where we’re going:

20^2 = 400

30^2 = 900

40^2 = 1,600

50^2 = 2,500

Okay, so the number must be somewhere between 40 and 50. From here, it may be obvious that we need to be closer to 50, since 22xx is more than halfway between 1,600 and 2,500. As such, an astute test taker might try something like 47^2 or 48^2 and see how close they got. However, instead of guessing, let’s use our perfect square strategy to see how quickly we can calculate the correct number.

50^2 is 2,500. This means that if I were to calculate 49^2, I could simply take 2,500 and remove 50, then remove 49. This is the reverse of adding them together to get from 49^2 to 50^2. You can also think of this subtraction as 2,500 – 99, which means that 49^2 must be 2,401. A cursory test of the unit digit reveals that 9 x 9 would yield a unit digit of 1, so we’re on the right track. Similarly, going to 48^2 from 49^2 involves taking 2401 and subtracting 49 then 48. This would be 2,401 – 97, or 2,304. We got close to 22xx, but we’ll need one more step. 47^2 will be 48^2 – 47 – 48. This is equivalent to 2,304 – 95, leaving us with 2,209.

The number we need is a perfect square that begins with 22, so 2,209 is the correct term. From here, we need to add together the digits and get the total of 13, which is answer choice C.

While there is no direct method to answer questions such as these, it’s important to not use blind guessing, as this can waste a lot of time and won’t help you solve a similar question next time. Back solving is useless in a situation like this as well, so our options are somewhat limited. A simple strategy such as calculating signpost perfect squares like 30^2 and 40^2 is helpful, and in a case such as this can negate much of the difficulty of the problem. Since this exam is a test of how you think, don’t forget that any perfect square is just a hop, skip and a jump from the next perfect square.

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Most of the terms you hear are just general math and verbal times that you’ve seen before, but likely not in many years (“gerunds” and “isosceles” come to mind immediately). However, some expressions exist only on the GMAT. As an example, have you come across the term “The C trap” yet? This idiom is used to describe the erroneous assumption that answer choice C is disproportionately chosen on Data Sufficiency questions. As a quick reminder, this choice indicates “both statements taken together are sufficient to answer the question, but neither statement alone is sufficient”. (If you knew it verbatim by heart, congratulations, you’re in GMAT mode).

Why do people select this choice on roughly 30-40% of their data sufficiency questions? The answer is that, since you have two independent statements to evaluate, choosing to use both typically gives you the maximum amount of information. Of course, that doesn’t mean that using both statements is what will provide sufficient information to answer the question. It also doesn’t mean that you can’t get the same information from only one of the two statements. Despite this, test takers consistently feel most comfortable picking answer choice C than any other choice on questions where they’re unsure how to proceed. It seems as if answer choice C makes them feel safe. Unfortunately, time and time again, it’s a trap.

Let’s look at question that highlights this issue:

*An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?*

*(1) No cats were adopted on Tuesday.*

*(2) 4 dogs were adopted on Tuesday.*

*(A) **Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked*

*(B) **Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked*

*(C) **Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient*

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

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

Let’s begin by taking stock of what we know. This question is asking about ratios. At a certain shelter, the ratio started off as 5:11 for cats : dogs. During the course of the day, some animals were potentially adopted. The question asks about the ratio at the end of the day. The most important thing to note here is that we being with a ratio but not absolute numbers, which means if we get ratios (i.e. half the cats got adopted) we might know the end ratio. If we get absolute numbers, we have almost no chance of having sufficient data. The stimulus gives us no further information, so we need to start looking at the statements.

For simplicity’s sake, let’s start with statement (1). Remember that you can always start with statement (2) if you prefer (or if it seems easier) as both statements are independent. The first statement tells us that no cats were adopted. However, we don’t know anything about the dogs (other that they’re four legged mammals). This statement alone will clearly be insufficient. We can eliminate answer choices A and D.

Looking now at statement 2, we know that exactly four dogs were adopted over the course of the day. This statement will suffer from the same problem as statement 1: we have no information about the cats. This statement will be insufficient on its own, and answer choice B can be eliminated as well.

Looking now to combine the statements, we can consider that the number of dogs dropped by four while the number of cats remained the same. Since we know about both animals, many people believe that the two statements together are sufficient. This would be true if we knew the actual number of each animal at the beginning of the day. Regrettably, we only know the ratio of one to the other, meaning that a change in absolute number is meaningless.

To use concrete numbers, there could have been 5 cats and 11 dogs at the beginning of the day, and the loss of four dogs would change the ratio to 5:7. Just as likely, we had 50 cats and 110 dogs at the beginning of the day, and the new ratio would be 50:106 (which we could simplify to 25:53 for completeness’ sake). Since either of these scenarios (and a dozen more) is possible, the answer must be answer choice E. The statements together do not provide enough information.

There is one caveat worth mentioning with ratios. Since the ratio does not tell us about absolute numbers, adding 10 or subtracting 15 is meaningless because we don’t know the original numbers. There is, however, one interesting exception: If you added 5 cats and 11 dogs, then the ratio would naturally remain unchanged. Indeed, as long as the change was in the ratio of 5:11, the ratio would be known: still 5:11. If the ratio deviates in any way, this does not hold. Interestingly, for subtraction, this problem does not occur because removing 5 cats and 11 dogs introduces the non-negligible possibility that there are now 0 cats and 0 dogs left at the shelter. In general, absolute number data is meaningless on ratios. Keep the one exception (adding by the exact same ratio) in mind when considering these types of problems.

In general, people are far too enticed by answer choice C on Data Sufficiency questions. Indeed, answer choice E was the most common answer for this question, but choice C was not far behind. Having more information is always tempting, even if it has almost no bearing on the actual question. Many students report feeling more secure selecting answer choice C, especially if they don’t know the answer and are guessing (educated guess, hopefully) the correct answer. The problem is that the test makers know that answer choice C is the most popular answer choice and specifically design problems to lure you to that conclusion. However, (as admiral Ackbar warned in 1983) it’s a trap!

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One reason people spend a lot of time on these questions is that they try to read the entire passage thoroughly. This is normal because this is how most reading is done, be it in newspapers or periodicals or novels. However, on the GMAT, speed is the name of the game. If I were doing a book report on Shakespeare’s works, then I would read the text multiple times, looking for nuance and symbolism. The goal on the GMAT is quite different: you have roughly eight minutes to read a passage and then answer four questions about it. That isn’t much time, but it can work if you’re question-focused.

Why be question focused? (Rhetorical question) A typical passage may have 300-400 words, and you could be asked 20-30 different questions about the information contained within it. In reality, you will only be asked 3-4-5 questions about this text, so becoming an expert on the minutiae contained within seems like a complete waste of time. In fact, considering that you only have ~2 minutes per question, it is not only a waste of time but a distraction that will waste precious time and lower your score. The vast majority of questions will require you to go back to the passage and reread the relevant portion, so your initial read is only there to give you a general sense of the text. After the initial read, you should be able to answer broad, universal questions. However, for questions that deal in specifics, you’ll have to go back to the text.

Specific questions deal with (drum roll please) specific elements of the passage. At first glance, you wouldn’t necessarily recall such minute details, but if you know where to go back in the text, it becomes a trivial case of rereading until you find it. As an example, you might not remember what Luke Skywalker was wearing on Tatooine when he first meets Obi-Wan Kenobi, but you could just rewatch the first act of Star Wars and see for yourself. There is no need to memorize every minor detail, as long as you know where to find the answer, you can just look it up.

Let’s look at a GMAT passage and answer a question that deals with a specific element of the passage (note: this is the same passage I used in October for a function question).

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.

According to the passage, which of the following contributed to the inability of the workers at Lowell to have their demands met?

(A) The very young age of some of the workers made political organization impractical.

(B) Social attitudes of the time pressured women into not making demands.

(C) The Lowell Female Labor Reform Association was not organized until 1844.

(D) Their families depended on the workers to send some of their wages home.

(E) The people who were most sympathetic to the workers lived outside of New England.

If you’ve been following the Veritas technique on Reading Comprehension, then you should have spent about two minutes reading through the passage and summarizing each paragraph in a couple of words. If you didn’t do this, feel free to go back and do it now. Once completed, your summaries of each paragraph should be something like:

1) Lowell Mills and context

2) Labor strife and consequences

3) Legacy of Lowell Mills

Your exact wording may vary, but you want to keep it at about 3-5 words or so. This should give enough of a framework so you know where to go in every question. If we look at the question at hand, it asks why were the workers at Lowell unable to have their demands met. This has to be in the second paragraph, as that was the part that dealt with the actual worker strife.

Rereading this paragraph, we go through a description of what prompted the strike and then how many people participated. Directly following this is the line: “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”. This was their downfall: they needed money to support themselves and their loved ones (unsurprisingly the downfall of most strikes). The wording used may be somewhat obtuse, but the context makes it quite clear that the issue was money. Going through the answer choices, D is the only option that is remotely close to what we want, and is therefore the correct answer.

On Reading Comprehension questions, it’s very easy to experience information overload (TL;DR for the new generation). A lot of information is contained in each passage, and this is not an accident. The test is designed to try and waste your time with frivolous sentences, so your goal is to read for overarching intent and know that you’ll have to revisit the text on most questions. Specific questions tend to ask about something minor, or possibly tangential, and therefore usually require you to reread the passage. Practice Reading Comprehension timing and you will find that you can answer these specific questions faster.

So if geometry isn’t useful in your studies, why would the GMAT regularly contain 4-6 questions that deal specifically with geometry? The answer is: the people making the exam want to know how you think. That’s all. The GMAT is a test designed to measure your critical thinking skills and your ability to reason out conclusions. The fact that geometry is being used as a vehicle to accomplish these goals is only because geometry is a key part of the high school curriculum. Similar questions could easily be formulated about linear algebra, calculus or other mathematical disciplines (please no one tell the GMAC about manifolds). However, the fact that not everyone has seen these disciplines before would give some people an unfair advantage. The GMAT may be many things, but unfair is not usually one of the qualities mentioned (cruel comes up a lot, though).

The other issue about geometry is it seems that it’s a subject that requires a lot of memorization. While it’s true that many formulae (or formulas) need to be committed to memory before taking the test, most questions revolve around how to use that information. On occasion, it may seem that there’s a different formula for every situation, the majority of questions will require you to apply a simple concept or formula in an unfamiliar situation.

Let’s look at an example of a geometry question that doesn’t require any special formula, but stumps a lot of students:

If the radius of a circle that centers at the origin is 5, how many points on the circle have integer coordinates?

(A) 4

(B) 8

(C) 12

(D) 15

(E) 20

There is a necessity to understand some of the verbiage in this question in order to be able to answer it properly. Firstly, a circle that is centered at the origin is centered at point {0,0}. The radius is 5, which means we know the diameter (2*r), the circumference (2*π*r) and the area (π * r^2). However, none of that information really helps us to answer this question. We are interested in how many points on the circle have integer coordinates. Quite simply, a circle has an infinite number of discrete points, so it’s easier to answer this question in the reverse: For each integer coordinate, is that point on the circle?

Let’s start with the obvious ones. The point {5,0} has to necessarily be on the circle. If the origin is {0,0} and the radius is 5, then not only must point {5,0} be on the circle, but so must point {-5,0}. The circle extends in all four directions, so we cannot forget the negative values. Similarly, the points {0,5} and {0,-5} will also be on the points, effectively covering the four cardinal points from the original circle. The circle could look something like this:

After solving for these four points, we must evaluate whether other integer coordinates could be on the circle. One thing should be clear: if the radius is 5, then any integer point above 5 will necessarily not be on the circle, as it is beyond the reach of our radius. We’ve already covered zero, so the only options we have left are one, two, three and four. Of course all of these numbers have negatives and can be considered on either the x or y axis, but still we have a finite number of possibilities to consider.

Another important thing that might not be as obvious is that the answer to this question will necessarily be a multiple of four. Given that a circle extends in all directions by the same distance, it is impossible for point {x, y} to be on the circle and for points {x,-y}, {-x,y} and {-x,-y} to not also be on the circle. This is an important property of all circles and one of the reasons they’re so common in everything from architecture to cooking (and to alien crop circles, if you believe in that). This rule also guarantees that any answer choice that’s not a multiple of four can be eliminated. We can thus eliminate answer choice D (15).

How do we go about finding other points on the circle? (Why am I asking rhetorical questions?) By using the Pythagorean Theorem, of course! Any point on the circle naturally forms a right angle triangle with the radius as the hypotenuse, and the radius is always five. Therefore, if the two other sides can be formed out of integers, we have a point on the circle with integer coordinates. The graph below will highlight this principle:

Since the Pythagorean Theorem states that the squares of the sides will be equal to the square of the hypotenuse, we only need to look for numbers that satisfy the equation a^2 +b^2 = r^2. And given that r is 5, r^2 must always be 25. So if we plug in a as one, we find that 1 + b^2 = 25. This gives us b^2 = 24, or b = √24, which is not an integer. We only have to plug this in three more times, so there’s no reason not to try all the possibilities. If a = 2, then we get 4 + b^2 = 25. The value of b would be √21, which again is not an integer value.

If a = 3, however, we quickly recognize the vaunted 3-4-5 triangle, as 9 + b^2 = 25, meaning b^2 is 16 and therefore b is 4. This means that the points {3,4}, {-3,4}, {3,-4} and {-3,-4} are all on the circle. We’ve brought the total up to 8, but we’re not done. The final value is when a equals four, which will again work and bring in the converse of the last iteration: {4,3}, {-4,3}, {4,-3} and {-4,-3}. These values are distinct from the previous ones, so we now have a total of 12 points. We’ve already checked five, so we can stop here. The answer to this question is answer choice C. There will be 12 distinct values with integer coordinates, as crudely demonstrated below (or on any analog clock).

In geometry, even if it feels like you have to constantly commit more rules to memory, remember that the rules are not nearly as important as knowing how to apply them. This problem can be solved with just the Pythagorean Theorem and a little elbow grease (or a graphing calculator). The GMAT is very much a test of how you think, not of what you know. If you think about geometry problems as cases that must be solved, or obstacles to be overcome, you’ll be in good shape to solve them.

The most common constructs that come in pairs are idioms, which are accepted turns of phrase, and elements requiring parallel structure. Both of these concepts can come up in sentence correction questions, and both play into whether a sentence has been properly constructed. Idioms often come up in pairs because one part of a sentence necessitates a parallel structure down the road. Similarly, parallel structure needs to have consistent elements or the sentence loses efficacy and becomes hard to read (like reading the word efficacy in a non-GMAT context).

A common example of the duality of idioms is the “Not only… but also…” idiom, whereby something will be described as “not only this… but also that”. If you don’t have the second part of the idiom, the first part doesn’t make much sense. You can say: “Ron is eating turkey”, but if you say “Not only is Ron eating turkey.” There must be some logical conclusion to that sentence, or you’re committing a sentence construction error. As an example: “Not only is Ron eating turkey, but he’s also eating yams.” Now the sentence is complete, as the idiom requires a second portion to complete the entire thought.

A common example of the importance of parallel structure is when making lists (and checking them twice). As an example, consider: “Ron likes eating turkey, watching football and to spend time with family”. The parallel structure is not maintained in this sentence because the first two are participial verbs and the third is an infinitive. You could rewrite this example as “Ron likes eating turkey, watching football and spending time with family” and it would be fine. However, that is not the only option. You could also rewrite this as “Ron likes to eat turkey, to watch football and to spend time with family”, or even “Ron likes to eat turkey, watch football and spend time with family”. Any of these constructions would be acceptable, because they all maintain the consistency required in parallel structures.

Now that we’ve seen how important it is to stick together, let’s look at an example that highlights these concepts in sentence correction:

In a plan to stop the erosion of East Coast beaches, the Army Corps of Engineers proposed building parallel to shore a breakwater of rocks that would rise six feet above the waterline and act as a buffer, so that it absorbs the energy of crashing waves and protecting the beaches.

(A) act as a buffer, so that it absorbs

(B) act like a buffer, so as to absorb

(C) act as a buffer, absorbing

(D) acting as a buffer, absorbing

(E) acting like a buffer, absorb

One ongoing difficulty in sentence correction is that a problem is rarely about only one concept. Frequently multiple issues must be addressed, such as agreement, awkwardness and antecedents of pronouns (and that’s just the letter A!) As such, it’s paramount to identify the decision points and see which types of errors could potentially occur in this sentence. It may not be as obvious on test day as it is now to note that this sentence has some issues with parallelism, but the fact that some verbs are underlined while others are not can help guide your approach here.

There is a verb (rise) before the underlined portion, and another verb (protecting) after the underlined portion. (Rise and protect make me think this sentence is about Batman). The correct answer choice will have to work with both verbs effortlessly, so let’s evaluate them one at a time. The first decision point we have in the underlined portion is deciding between “act” and “acting”, and this verb must match up with the previous verb “rise” as both are being commanded by the wall of rocks that is their shared subject. Since “rise” is an infinitive, and it is not underlined, the correct match must be with “act”. This parallel structure eliminates answer choices D and E, as both have the verb in its participle form. As an aside, please note that you don’t need to know the grammatical terms; they’re listed primarily for clarity.

The second decision point is the other verb, which comes in three different forms (absorbs, absorb, absorbing) in the three answer choices. Since the verb at the end of the sentence is in its participle (protecting), the parallel structure dictates that the answer choice must be answer choice C, as it is the only remaining choice with “absorbing”. We have thus eliminated four answer choices using only parallel structure. While answer choice C is indeed the correct answer, we can also note the idiom “act as a buffer”, which is used correctly, as opposed to “act like a buffer” in answer choice B. This decision point could be sufficient on its own, but you can often knock out a single incorrect answer choice for multiple reasons. Answer choice C is the only choice that does not contain any sentence construction errors.

Often, I compare the concept of parallelism to the banal notion of wearing socks. Any two socks are acceptable as long as they match, but wearing unmatched socks is a sure-fire way to get mocked (by me). Similarly, parallel structure only requires that you remain consistent within the same sentence, not that lists must be constructed exclusively in a certain way. Parallelism is very important in sentence correction, as it’s often the only reason to eliminate an answer choice that otherwise makes grammatical sense.

If you’re studying for the GMAT during the holidays this year, I wish you the best of luck, and remember that studying well and succeeding on the GMAT go hand in hand.

Now, some numbers are spelled out down to the decimals, but other numbers, such as 11!, seem unnecessarily abstract. 11 factorial is a big number, but wouldn’t it be simpler if I had a concrete number in front of me instead of a shorthand notation for 10 multiplications. The answer is: not really. If you wanted to expand 11! To get a longhand answer, you’ll end up with a large concrete number that is no easier to manipulate than the shorthand you had before. For example, 11! is actually 39,916,800. Does that make it any easier to use? Again, the answer is: not really.

In essence, every time you see a big number like this, the GMAT is baiting you into performing tedious calculations that don’t help you in any way. Having a cumbersome number is the GMAT’s way of saying “Don’t try and solve this with brute force, there’s a concept here you should recognize”. While it’s uncommon for the GMAT to actually speak, given that it’s an admissions exam, it actually is telling you loud and clear that concentrating on the number is a trap. There will always be some element that will help highlight the underlying issue without performing tedious math.

There are many concepts that may come into play, and it’s hard to approach these questions with a single standard approach, but some elements repeat more frequently than others. One of the first things to look for is the units digit. The units digit gives away many properties of a number. As an example, 39,916,800 ends with a 0, indicating that it is even, and that it is divisible by 10. Different units digits can yield different number properties, so you can learn a lot from one simple digit. The factors of the number in question can often unlock clues as to which numbers to look for among the answer choices. Finally the order of magnitude can also play a pivotal role in determining how to approach a question.

Since we don’t have one definitive strategy, let’s test our mental agility on an actual GMAT question:

For integers x, y and z, if ((2^x)^(y))^(z) = 131,072, which of the following must be true:

(A) The product xyz is even

(B) The product xyz is odd

(C) The product xy is even

(D) The product yz is prime

(E) The product yz is positive

This question is significantly easier if you recognize which power of two 131,072 is off the bat (I knew that Computer Science degree would be good for something). However, let’s approach this knowing that 131,072 is a multiple of two, but that calculating which one would require more time than the two minutes we have earmarked for this question. Furthermore, simply knowing that 131,072 is a power of 2 gives us all the information we really need to solve this question.

We know x, y and z will combine to form some integer, but we’re not sure which. Let’s call it integer R (as in Ron) for simplicity’s sake. Moreover, the way the equation is set up, the powers will all be multiplied by one another, meaning that their exact order won’t matter. As such, the commutative law of mathematics confirms that if ((2^5)^(3))^(2) is the exact same thing as ((2^3)^(2))^(5). If the order doesn’t matter, then there are a lot of potential situations that could occur. So R will equal x + y + z, but the order won’t change anything. Let’s look at the answer choices, and start from the end because they’re easier to eliminate.

Answer choice E asks us whether y*z must be positive. If y*z gives us some positive number, then x would just be whatever is left over to form R. It doesn’t matter is y*z is positive or negative, as x can just come and make up the difference. Let’s say y*z = 4, then x would just be R – 4. If, instead, y*z = -4, then x would just be R – 12 and there would be no difference. In other words, as long as one variable is unrestricted, it will always be able to make up for the restriction on the other two. If you recognize this, you can eliminate C, D and E for the same reason. Two out of three ain’t bad, but in this case, it ain’t enough.

This brings us down to answer choices A and B, which are complimentary. Either the product of the three numbers is even, or it is odd. One of these, logically, must be true. Unfortunately, the best way to verify this appears to be doing the calculation longhand (like the petals of a flower: she loves me, she loves me not). Herein lays a potential shortcut: the units digit. Since the number is a power of two, we can simply follow the pattern of multiples of two and see what we get. Considering primarily the units digit (underlined for emphasis):

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^7 = 128

2^8 = 256

2^9 = 512

You probably don’t have to go this far to notice the pattern, but it doesn’t hurt to confirm if you’re not sure after 2^5. Essentially, the unit digit oscillates in a fixed pattern: 2, 4, 8, 6, and then repeats. This is helpful, because the number in question ends with a 2, and every power of two that ends with a 2 is either 2^1, 2^5, 2^9, etc. All of these numbers are odd powers of 2, repeating every fourth element. With this pattern clearly laid out, it becomes apparent that the answer must be that the product of these three variables must be odd. As such, answer choice B is correct here. We can also probably deduce from order of magnitude that 131,072 is 2^17.

When it comes to large numbers on the GMAT, you should never try to use brute force to solve the problem. The numbers are arbitrarily large to dissuade you from trying to actually calculate the numbers, and they can be made arbitrarily larger on the next question to waste even more of your time. The GMAT is a test of how you think, so thinking in terms of constantly calculating the same numbers over and over limits you to being an ineffective calculator. Your smart phone currently has at least 100 times your computational power (but not the ability to use it independently… yet…). Brute force may break some doors down, but mental agility is a skeleton key.

**What motivates you to be a GMAT instructor?**

*“I have been teaching the GMAT for 10 years because I absolutely love what the test is designed to assess and how it makes you learn and think. This is not a content regurgitation test, but rather it is one that assesses who is good at taking basic content and using that to solve very difficult problems and reasoning puzzles. I believe that the skills and thinking processes the GMAT assesses are invaluable not only in business but in all walks of life. I really enjoy unlocking this way of thinking for students and teaching them to love a test that they may have at first despised!”*

**If you could give three pieces of advice to future GMAT test takers, what would they be?**

*“1) Do not waste 3 months preparing on your own, receive a low score, and THEN sign up for a **high quality GMAT prep course**. Take our **full GMAT course** before you even open a book or read about the GMAT. It will save you so much time, energy, and frustration.*

*Click here for Chris’ other two points of advice.*

**Is there a common misconception of the GMAT or of what is a realistic GMAT score?**

*“I think there are many important misconceptions about the test as a whole and the scoring system in particular. As I have intimated earlier, the biggest misconception about the GMAT is that it is a content test in which memorizing all the rules and the underlying content will allow you to do well. This is certainly not the case and it is why so many students get frustrated when they prepare on their own. The GMAT is so different from the tests that you were able to ace in college with memorization ‘all-nighters.’ Also, I think people underestimate how competitive and difficult the GMAT really is. Remember that you are competing against a highly selective group of college graduates from around the world who are very hungry to attend a top US business school. This test is no joke and requires an intensive preparation geared toward success in higher order thinking and problem solving.”*

Read the rest of the interview here!

Now, at a restaurant, you may be particularly hungry and decide to order both the soup and the salad (and the frog legs while we’re at it). Similarly, on forms, someone who selects both options is being confusing. Perhaps you’ve smoked once and didn’t like it. Perhaps you smoke only on long weekends when the Philadelphia Eagles have a winning record. Sometimes people decide they don’t want to pick between the two choices given. However, if the question were changed to “have you ever smoked a cigarette?” and then given yes or no options, the decision becomes much easier. You have to be in one camp or the other, there is no sitting on the fence (like Humpty Dumpty).

For questions that set up this kind of duality, the entire spectrum of possibilities is essentially covered in these two options. There is no third option; there is no “It’s Complicated” selection. There isn’t even a section for you to explain yourself in the comments below. On these questions, you have to either be on one side or the other, you cannot be in both. Equally, you cannot be in the “neither” camp either. Necessarily, to this point in your life, you have either smoked a cigarette or you have not. Since one of them must be true, this certainty offers some insight on inference questions in critical reasoning.

As you probably recall, inference questions require that an answer choice must be true at all times. This isn’t always easy to see as many answer choices seem likely, but simply are not guaranteed. Sometimes, on inference questions, you get two answer choices that are compliments of one another. You get two choices that say something to the effect of “Ron is always awesome” and “Ron is not always awesome”. Even I would go for the latter here, but clearly one of these must be correct. They cannot both be correct, but they also cannot both be false. Having two answer choices like this guarantees that one of them must be the correct answer, and makes your task considerably easier.

Let’s look at an example:

A few people who are bad writers simply cannot improve their writing, whether or not they receive instruction. Still, most bad writers can at least be taught to improve their writing enough so that they are no longer bad writers. However, no one can become a great writer simply by being taught how to be a better writer, since great writers must have not only skill but also talent.

Which one of the following can be properly inferred from the passage above?

(A) All bad writers can become better writers

(B) All great writers had to be taught to become better writers.

(C) Some bad writers can never become great writers.

(D) Some bad writers can become great writers.

(E) Some great writers can be taught to be even better writers.

Since this is an inference question, we must read through the answer choices because there are many possible answers that could be inferred from this passage. When reading through the passage, you probably note that answers C and D are somewhat complimentary. Either the bad writers can become great writers, or they can’t. However, some people might be miffed by the fact that “some writers” is vague and could mean different people in different contexts. However, while the term “some writers” is undoubtedly abstract, it can refer to any subset of writers one or greater (and up to the entire group). Any group of bad writers is thus conceivable in this passage, but the answer choice must be true at all times, so the groups comprised of “some writers” can mean anyone, and these two groups can be considered equivalent.

If you recognize that either answer choice C or answer choice D must be the answer, then you can easily skip over the other three choices. For completeness’ sake, let’s run through them quickly here. Answer choice A directly contradicts the first sentence of this passage: Some bad writers simply cannot improve their writing. Answer choice B contradicts the major point of this passage, which is that great writers have a combination of skill and talent, and you cannot teach talent. Answer choice E makes sense as an option, but it doesn’t necessarily have to be true. This is a classic example of something that’s likely true in the real world, but not necessarily guaranteed by this particular passage.

This leaves us with two options to consider. Can bad writers become great writers, or can they never become great writers? As mentioned above, great writers are born with some level of talent that cannot be mimicked by practice alone. The passage explicitly states “no one can one can become a great writer simply by being taught how to be a better writer”. Even though some bad writers can improve their writing with some help (perhaps even writing a Twilight Saga), some cannot improve their writing at all. If these bad writers cannot improve their writing, they necessarily will never become great writers. Answer choice C must be true based on the passage.

Looking at answer choice D in contrast, it states: “some bad writers can become great writers”. Perhaps some can, but this cannot be guaranteed in any way from the passage. It’s possible that all the writers are terrible even after year of practice. In fact, since we know that some will never improve (the opposite), this conclusion is certainly is not guaranteed. Answer choice C is supported by the passage, answer choice D seems conceivable in the real world, but it is certainly not assured.

On the GMAT, as in life, when confronted with two complimentary choices, you have to end up making a choice. In this instance, because you typically have five choices to consider, whittling the competition down to two choices already saves you time and gives you confidence. Recognizing which option must always be true is all that’s left to do, and that often comes down to playing Devil’s Advocate. When you’re tackling a decision such as this, consider what has to be true, and you’ll make the right choice.

A common strategy in puzzles is to build the outsides or the corners first, as these pieces are more easily identifiable than a typical piece, and then try and connect them wherever possible. Indeed, you are unlikely to have ever solved a puzzle without needing to jump around (except for puzzles with 4 pieces or so).

Similarly, you are often faced with GMAT questions that seem like intricate puzzles, and this same strategy of jumping around can be applied. If you start at the beginning of a question and make some strides, you may find your progress has been jammed somewhere along the way and you must devise a new strategy to overcome this roadblock. Jumping around to another part of the problem is a good strategy to get your creative juices flowing.

Let’s say a math question is asking you about the sum of a certain series. A simplistic approach (possibly one used by a Turing machine) would sequentially count each item and keep a running tally. However, a more strategic approach might involve jumping to the end of the series, investigating how the series is constructed, and finding the average. This average can then be multiplied by the number of terms to correctly find the sum of a series in a couple of steps, whereas the brute force approach would take much longer. Since the GMAT is an exam of how you think, the questions asked will often reward your use of logical thinking and your understanding of the underlying math concepts.

Let’s look at a sequence and see how thinking out of order can actually get our thinking straight:

In the sequence a1, a2, a3, an, an is determined for all values n > 2 by taking the average of all terms a1 through an-1. If a1 = 1 and a3 = 5, then what is the value of a20?

(A) 1

(B) 4.5

(C) 5

(D) 6

(E) 9

This question is designed to make you waste time trying to decipher it. A certain pattern is established for this sequence, and then the twentieth term is being asked of us. If the sequence has a pattern for all numbers greater than two, and it gave you the first two numbers, then you could deduce the subsequent terms to infinity (and beyond!). However, only the first and third terms are given, so there is at least an extra element of determining the value of the second term. After that, we may need to calculate 16 intermittent items before getting to the 20th value, so it seems like it might be a time consuming affair. As is often the case on the GMAT, once we get going this may be easier than it initially appears.

If a1 is 1 and a3 is 5, we actually have enough information to solve a2. The third term of the sequence is defined as the average of the first two terms, thus a3 = (a1 + a2) / 2. This one equation has three variables, but two of them are given in the premise of the question, leading to 5 = (1 + a2) /2. Multiplying both sides by 2, we get 10 = 1 + a2, and thus a2 has to be 9. The first three terms of this sequence are therefore {1, 9, 5}. Now that we have the first three terms and the general case, we should be able to solve a4, a5 and beyond until the requisite a20.

The fourth term, a4 is defined as the average of the first three terms. Since the first three terms are {1, 9, 5}, the fourth term will be a4 = (1 + 9 + 5) / 3. This gives us 15/3, which simplifies to 5. A4 is thus equal to 5. Let’s now solve for a5. The same equation must hold for all an, so a5 = (1 + 9 + 5 + 5) /4, which is 20/4, or again, 5. The third, fourth and fifth terms of this sequence are all 5. Perhaps we can decode a pattern without having to calculate the next fourteen numbers (hint: yes you can!).

A3 is 5 because that is the average of 1 and 9. Once we found a3, we set off to find subsequent elements, but all of these elements will follow the same pattern. We take the elements 1 and 9, and then find the average of these two numbers, and then average out all three terms. Since a3 was already the average of a1 and a2, adding it to the equation and finding the average will change nothing. A4 will similarly be 5, and adding it into the equation and taking the average will again change nothing. Indeed all of the terms from A3 to A∞ will be equal to exactly 5, and they will have no effect on the average of the sequence.

You may have noticed this pattern earlier than element a5, but it can nonetheless be beneficial to find a few concrete terms in order to cement your hypothesis. You can stop whenever you feel comfortable that you’ve cracked the code (there are no style points for calculating all twenty elements). Indeed, it doesn’t matter how many terms you actually calculate before you discover the pattern. The important part is that you look through the answer choices and understand that term a20, like any other term bigger than a3, must necessarily be 5, answer choice C.

While understanding the exact relationship between each term on test day is not necessary, it’s important to try and see a few pattern questions during your test prep and understand the concepts being applied. You may not be able to recognize all the common GMAT traps, but if you recognize a few you can save yourself valuable time on questions. If you find yourself faced with a confusing or convoluted question, remember that you don’t have to tackle the problem in a linear fashion. If you’re stuck, try to establish what the key items are, or determine the end and go backwards. When in doubt, don’t be afraid to skip around (figuratively, literal skipping is frowned upon at the test center).