Needless to say, having a sound understanding of the theory and logic of a question is ideal. Completely understanding the possibilities, rules and potential traps of a certain topic regularly leads you to select the correct answer choice. However, it is almost inevitable that a topic, notion or concept will come up that you don’t fully comprehend (or comprehend at all). In that case, it’s often best to try and determine a logical answer and double check it with some manual verification.

Obviously, if an answer asks you to sum all the integers from 1 to 150, you hopefully have a better strategy than simple brute force. Solving such a question without a calculator in less than 2 minutes is a fool’s errand. If you begin adding 1 to 2 to 3 to 4, you know you’re in trouble (unless you’re 5½ years old). Nonetheless, many questions can be solved via brute force within the given time constraints, if only with the help of a little bit of logic to narrow down the answer choices.

Let’s look at a Data Sufficiency problem that highlights these issues:

If P and Q represent the hundreds and tens digits, respectively, in the four-digit number x=8PQ2, is x divisible by 8?

(1) P = 4

(2) Q = 0

(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 but neither statement is sufficient alone.

(D) Each statement alone is sufficient to answer the question.

(E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

This is a fairly straight forward divisibility question asking about whether a certain number is divisible by 8. However, there is one caveat: two of the digits can change. This question allows for different tens and hundreds digits, and this oscillation allows for no fewer than 100 distinct options to consider for divisibility. A brute force approach would take far too long, so we need to undertake a logical approach to a divisibility rule that is often overlooked because it is uncommon (as opposed to mythic rare).

To be divisible by 8, the rule you might know is that the last 3 digits must be divisible by 8. This essentially truncates anything bigger than the hundreds, and is due to the fact that 1,000 is divisible by 8, so any multiple of 1,000 can be ignored as it is necessarily also divisible by 8. Knowing this, we can ignore the “8” at the beginning of the number and concentrate on the 3-digit PQ2. Determining the divisibility of the last 3 digits isn’t too hard if those numbers are static. If they vary, though, the answer may be harder to pinpoint.

Let’s start with statement 1: P=4. If this is true, then we’ve turned the abstract question into the more straight forward determination of whether 4Q2 is divisible by 8, which really is just asking if {402, 412, 422, …, 492} are all divisible by 8. This is small enough that we can brute force it, especially if we recognize that 400 is divisible by 8 (the quotient would be exactly 50). 402 is then logically not divisible by 8, since it is only 2 away from a known multiple of 8. 412 is similarly not divisible by 8, and neither is 422. However, 432 is divisible by 8 (yielding a quotient of 54). This means that we have at least one value that is divisible by 8 (432) and at least one value that is not (402). Statement 1 will thus be insufficient.

Logically, this inconsistency should make sense. We are taking an even number and adding 10 to it. While 10 is not divisible by 8, multiples of 10 will be divisible by 8, and we’ll eventually cycle through a few numbers that are perfectly divisible by 8. Even if we can’t easily see this logic on test day, a strategic brute force will confirm these suspicions. There are only 10 numbers to check in the worst case, and we can stop whenever we can confidently say whether the statement is sufficient or not. This leaves only answer choices B, C and E possible.

Let us now look at statement 2: Q = 0. This ultimately means we must check the divisibility of P02, which is {102, 202, 302, …, 902}. This is not necessarily trivial, but if we check for 102, we know that 80 is divisible by 8, thus so is 88, 96 and 104. Since 102 falls in the gap between two multiples, it is not a multiple of 8. Next we can check 202, and if you recognize that 200 is a multiple of 8 (8×25), you’ll know fairly quickly that 202 is not a multiple. You can check the remaining eight choices quickly if you use your logic and start from numbers you know to be divisible by 8 (400, 600, 800). Even using this painstaking method, you can determine that all ten choices are not divisible by 8 within a minute. If none of the choices work, then we can confidently assert that this statement is sufficient to get a consistent answer of no on this question. Answer choice B is correct.

There are more logical tenets that help guide you on these types of questions, but they’re not necessarily well known. For example, any number that is divisible by 8 must also be divisible by 4, meaning that dividing by 4 can be used as an easy filter (like coloring inside the lines). Any number that ends in 02 will not be divisible by 4, no matter what the hundreds digit is. Therefore, this statement will always produce an answer of no. Even if you utilized this property and were leaning towards answer choice B, it doesn’t hurt to double check your answers manually. Often, double checking your answers can lead to double digit improvements on your GMAT score.

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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.*

Usually, order is a positive thing that gives structure to what we’re doing. Today I’m studying reading comprehension, tomorrow I will study algebra. This method allows our brains to classify different concepts and keep them neatly separated in our minds. The alternative is to have things haphazardly stored in our memories and try to recall the information as it comes up. It’s the same principle as a library. If the books are stored by alphabetical order, then it’s easy to find the book you’re looking for (say Fifty Shades of Gray), whereas a pile of books scattered on the floor may or may not contain the book you want.

However, with this order comes some level of compartmentalization, which can be problematic on compound problems. For example, if a question deals with geometry, it may also contain some elements of algebra. Typically, when you see a triangle, your brain is busy scanning through the properties it recognizes (area, isosceles rules, etc), and doesn’t bother with perfect squares or exponent rules. More difficult questions require you to combine seemingly disparate concepts and utilize them on the same question. This becomes difficult because it breaks the order we’ve neatly established and requires us to sometimes jumble information.

This phenomenon is not limited to math problems. Indeed, it shows up very frequently on “Mimic the Reasoning” questions, in which we’re asked to construct a similar argument to the one in the question stem. The problem is the logic is almost never in the same order in the answer choices as in the question stem. Let’s review one and see how we can approach these questions:

Some political observers believe that the only reason members of the state’s largest union supported Senator Hughes in his recent re-election campaign was that the union’s leaders must have been assured by Hughes that, if elected, he would stay out of their coming negotiations with the union’s national leadership, whose members have been financial backers of several close associates of Hughes. More likely, the union’s members believed that Hughes deserved to serve another term in office.

Which of the following best parallels the method of argument used by the author?

(A) The popularity of Deap, a powerful carpet cleaning system that can be used by the homeowner is, some industry observers say, due to an agreement made by a leading professional carpet cleaning company to supply Deap with the chemicals that are sold as accessories. This does not, however, fully explain the sudden popularity of the product in the last three months.

(B) After a rocky start, Shade, a new cosmetics line, is now selling briskly. The reason for the turnaround is almost certainly that Shade is now being marketed to women in their twenties, not just to teens. This has helped the product achieve a more sophisticated appeal, which has translated into greater sales in every age group.

(C) The Shakelight, a small flashlight that can be powered for several minutes by a shaking motion, has once again proven a popular gift item this holiday season. Other similar devices are available, but none has been as successful, and the reason is simple: the cost of The Shakelight has fluctuated so that it has always been at least one dollar less than that of any competitor. The manufacturers’ claim that they have a better product is nonsense.

(D) The continued success of the Daddo line of toys is due to the simple appeal that these toys have for kids between three years of age and six. Others disagree. One industry journal ascribed the brand’s popularity to a deal made with a major toy retailer guaranteeing that the retailer would carry the coming line of Daddo products exclusively for three months.

(E) As with last year, this year’s best selling foreign policy journal is World Opinion. It may be that the content in World Opinion is simply more exhaustive and better presented than that of similar publications, or it may be that the journal’s publishers have the substantial support of their parent company, which has been a good friend to bookstores and other outlets.

One of the uncontestable issues with a question like this is that it’s very long. A quick word count reveals that this question is over 400 words, but thankfully we’re skimming the answer choices looking for a match to the original argument. The passage states that there are two potential reasons for the re-election of a certain Senator, one that’s more conspiracy-oriented and one that’s more straight forward (we may want Occam’s Razor for this). We must now peruse the other answer choices looking for a similar pattern of reasoning.

Answer choice A only gives one explanation and then elaborates on how this may not actually be correct because it doesn’t explain everything. No alternative is given. The logic is not the same and therefore this choice can be eliminated.

Answer choice B similarly gives one explanation and then defends it as the only plausible choice. While this is a reasonable logic to follow, it does not mimic that of the passage.

Answer choice C is a little closer. The Shakelight is known to be a popular gift, and there is one reason given. Another possible reason is mentioned, but ignored out of hand because it is preposterous. This choice at least presents the illusion of two possibilities, even if one of them is never seriously considered. The logic is not the same as the original passage, but it is closer than the two previous choices.

Answer choice D is essentially the same logic as that of the passage. Two possible choices are given, and one is more likely than the other. Both choices are considered, even if one choice is given more credence. This is a good match to the original passage and answer choice D is the correct answer.

For completion’s sake, let’s also look at answer choice E. This logic is not that far from the original, but it is in the opposite direction from answer choice C. Two possibilities are given, but neither one is decreed to be more likely than the other. This logic is again similar to the original passage, but not exactly the same.

This question somewhat mirrors the goldilocks parable. Answer choice E postulates that either possibility could be good (too big), while answer choice C completely disregards the second option (too small). Only answer choice D (just right) correctly mirrors the logic in the original passage, albeit in a different order. It is important on the GMAT to be able to see the logic in the statements, even if it’s presented in a different order than you’re used to. The exam rewards those test takers who demonstrate mental agility and can correctly decode order from the chaos.

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I often tell my students this quote: “The better you are at math, the less math you do.” This seems counter-intuitive at first. Lebron James is very good at basketball, and he plays a lot of basketball (when he’s not choosing cities to play in). It is reasonable to assume that proficiency in something makes you more likely to want to do it. However, on the GMAT, simply understanding what will happen is often enough to answer the question. The math can be used to confirm your thought, but it is not necessary and often will just slow you down.

A simple example would be to answer the question: “At a red light, there are 4 cars in 3 lanes. Is there at least one lane that has at least 2 cars?” The answer must be yes (by the pigeonhole principle, actually), because you have more cars than lanes. You don’t have to actually try the combinations to know the answer, but if you wanted to, you could imagine scenarios of the cars all in one lane, in two lanes, or in all three lanes. The math skills required to try every combination aren’t actually needed to solve a question like this, only an understanding of the permutation rules.

Despite many people swearing that the math on the GMAT is very hard, it’s often more a question of understanding than of math skills. Let’s look at an example that highlights this type of question:

Submarine A and Submarine B are equipped with sonar devices that can operate within a 3,000 yard range. Submarine A remains in place while Submarine B moves 2,400 yards south from Submarine A. Submarine B then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine B continue to move and still be within the sonar range of Submarine A?

I. North

II. South

III. West

A) I only

B) II only

C) I and II only

D) II and III only

E) I and III only

The submarines have a 3,000 yard sonar range in all directions, which essentially makes a circle around the ship. Submarine B moves a certain number of yards south and then a certain number of yards east. The question then asks which direction the sub could move in without losing contact.

This seems like a geometry question, and there are some numbers provided in this question. Let’s look through it quickly for the sake of completion, but you may have already noticed they won’t help in any meaningful way and are only there to bait you into tedious calculations. If submarine A has a circular range of 3,000 yards and submarine B moves south for 2,400 yards and then east, how far will it go east? The answer is actually a triangle inscribed within a circle, something like the figure below.

Given that submarine B ends up at the edge of the 3,000 yard range, the hypotenuse of the triangle is 3,000 yards, and the y-axis is 2,400 yards. The x-axis displacement is easy to calculate if you recognize this pattern as a glorified 3-4-5 triangle. Multiply those values by 600 and you get an 1,800-2,400-3,000 right triangle. Thus the sub moved east by exactly 1,800 yards. However, this information won’t really be helpful in answering the question as we’re being asked for directions, not distances.

The graph may help clarify the issue, but you can solve it without even using the graph either. Clearly the sub on the edge of the triangle can head back west and be within sonar range. Similarly, it can travel due north and stay within range as well. The only two directions that are not allowed are east and south. The answer must this be I and III together, which is answer choice E (also Kanye West’s daughter).

While proficiency in mathematics is helpful on the GMAT (and in life in general), it is often not a necessary skill in solving “math” questions on the exam. Remember that the main goal is to test your reasoning skills and determine whether you can correctly solve problems. Being a business student isn’t about being an expert at math, but rather using the information provided to swiftly reach the correct conclusion. Oftentimes, the better you are at math, the less math you’ll actually end up using.

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The GMAT is an exam that tests many different facets of understanding, and some questions are designed to test your ability to finish a thought. In Critical Reasoning, we are often asked to establish which answer choice is the correct answer to a given question. However, sometimes there is no actual question posed, but simply an unfinished thought that must be completed. The thought cannot end in multiple different ways, but rather, it must end in the only answer choice that is coherent with the rest of the passage. These questions combine elements of strengthen, weaken and inference questions and ask you to best complete the passage given.

These questions do tend to be harder than a typical Critical Reasoning question, and therefore may not show up that frequently on any one test. However, they are important to understand because they ______________

A) Build confidence

B) Underscore important concepts

C) Squirrel!!

The answer to my little trivia game was B, but you could make a case for any of the given answers. Let’s try it again with an actual GMAT question:

*Environmentalists support a major phase-down of fossil fuels and substitution of favored ‘non-polluting’ energies to conserve depleting resources and protect the environment. Yet energy megatrends contradict those concerns. Fossil-fuel resources are becoming more abundant, not scarcer, and promise to continue expanding as technology improves, world markets liberalize, and investment capital expands. However, these facts do not mean a smaller role of the non-polluting sources of energy in the long run given that ______________*

*A) The costs of producing energy from non-polluting sources of energy have remained constant in the last five years.
*

The correct answer must correctly finish the thought as if it were always supposed to be there. If there are any contradictions or illogical conclusions drawn, that answer choice must be incorrect. The thought began by discussing fossil fuels and how environmentalists are calling for decreasing their use. However, the worldwide trend is that their use is increasing (#FossilFuels). These facts must somehow combine to indicate that non-polluting sources of energy will still be prevalent in the future, and we must select the answer choice that supports that. Let’s examine them one by one.

Answer choice A *“The costs of producing energy from non-polluting sources of energy have remained constant in the last five years”* introduces cost into the equation. There was no mention of cost prior to this, so it seems illogical that cost will be a determining factor in this issue. We can safely eliminate A.

Answer choice B *“The availability of fossil fuels does mean an increased use of the same”* is actually a 180°. If this were true, then there would be ever more fossil fuel use, and the alternatives would be significantly reduced. Answer choice B may seem tempting, but it’s going the wrong way.

Answer choice C *“The amount of confirmed deposits of fossil fuels is sufficient to serve the world energy needs at least over the next two centuries”* brings up an arbitrary timeframe for the purposes of sounding grandiose. Two centuries seems like a long time, but it’s also unfounded and irrelevant to the process. What if the answer choice had been two decades instead? Or two millennia? Would that make it more or less likely to be true? The arbitrary timeframe does not have any bearing on this thought, so we must eliminate answer choice C.

Answer choice D *“There is an increasing sense of acceptance across the world on the harmful effects of the use of fossil fuels on the environment”* brings the argument back to the cause of the environmentalists. This harkens back to the first sentence of the passage, and logically concludes why the facts may indicate something, but the long term trend will eventually indicate something else. Answer choice D is correct.

Answer choice E *“Non-polluting sources of energy are less cost-effective than fossil fuels“* can be particularly tempting, because it is actually true in real life. However, just like with answer choice A, the concept of cost is parachuted into the passage with no antecedent to build upon. This factoid may be largely true in 2014, but does that mean it will be true in 2015 or 2025? We cannot select answer choices that seem correct in real life but are unsupported in the text. Answer choice E can also be eliminated.

When it comes to finishing a thought, it is important to note that the conclusion is often the most interesting part. Even if you’re already contemplating the next element or task, ensure that you do a thorough job finishing up the previous job. No one likes to leave loose threads, and it completely undermines your conclusion when the last portion is unclear or unfinished. Above all, the most important thing is to always…

There is one mathematical discipline that dominates the Quant section of the GMAT: Algebra. The majority of the math questions that you will see on test day involve algebra.

Many questions involve pure algebra, such as expressions and equations involving variables, roots, and exponents. Another large group of questions is word problems, most of which are best addressed using algebraic equations. Geometry is another significant subject on the GMAT; and geometry is simply a delivery mechanism for algebra. Even things like ratios can often best be addressed by using equations with “x” as the multiplier.

It seems that the “A” in “A Game” really does stand for Algebra! It’s a good thing that there are topics, such as statistics, that involve real numbers instead of algebra. Yet even these questions can often best be solved using Algebra.

Here is a statistics question that can be addressed several ways. Try to solve this question using algebra.

“The average of the five numbers is 6.8. If one of the numbers is multiplied by 3, the average of the numbers increases to 9.2. Which of the five numbers is multiplied by 3?

(A) 1.5

(B) 3.0

(C) 3.9

(D) 4.0

(E) 6.0

You can do this problem in a few different ways, but perhaps the best way is Algebra! No matter how you choose the address the question you will need to determine the magnitude of the increase. Since “sum (total) = average * # of terms” You can take the average of 6.8 times the five terms and get a beginning total of 34. The new total is 9.2 times 5 which equals 46. So the increase is 12.

In order to create an equation you need to ask yourself “what happened to cause that increase of 12?” The question stem tells you that one of the numbers was multiplied by 3. So when one of the numbers (we can call that number “x”) was multiplied by 3 the total increased by 12.

The equation formed from this information is simply “3x = x + 12.” The “3x” is because the number is multiplied by 3 and the “x + 12” is because you had the x to start with (there were five numbers right? and x was one of them) and you added 12 because of the increase to the sum.

So if “3x = x + 12” then x = 6. So the correct answer is E.

This question can be done based on knowledge of number properties and can even be done by working directly with the answer choices. However, neither of these methods is as reliable for most students as the algebra is. I have worked with the question for years and I can tell you that more people choose D than choose the correct answer. Yet very few of the people who get this wrong used algebra. Those who use algebra generally seem to get this question right.

Make sure that you are very comfortable with algebra, after all, bringing your “A Game” is essential to your success on the Quant section!

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

Within the confines of the GMAT, the expectations for students are well known. You will be faced with 37 math and 41 verbal questions, have to select from five multiple choice answers, and complete each section within 75 minutes. However, sometimes certain questions will set up arbitrary rules within this game. An obvious example is data sufficiency: a question type that always provides two statements and asks whether a certain question can be answered using these statements. Why are there not three statements? Or four statements? The official answer will be to standardize the questions and allow for easier preparation, but the truthful answer is something most parents have had to utter countless times: “Because I said so”.

The only reason these rules apply is because they were established by the GMAC to test logical thinking. However, other rules could have been set up and test takers would have had to adhere to them. In fact, any question can set up arbitrary rules and then require you to analyze the situation and provide insight. Within the game that is the GMAT, a sub-game is created with each new question, and some of these questions have very specific rules (GMAT Inception).

The difficulty with some of the arbitrary question-specific rules is that the situation is only applicable to the exact question, meaning that you don’t have long to acclimate to the circumstances. Usually, the question will provide rules that are indispensible to solving the query, so we must adhere to them or risk falling into a trap.

Let’s look at an example that highlights the sub-game nature of certain GMAT questions:

An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?

(A) 1/16

(B) 37/256

(C) 5/32

(D) 219/256

(E) 15/16

As always, let’s begin by paraphrasing the question. A student is blindly guessing on a True/False question, and thus will likely get half the questions right by default. It is conceivable that he could get 0% or 100% as well, meaning this is likely a probability question of sorts. However it’s a probability question within a probability question. Once we have accepted the premise that this exam will take place, we can only analyze the possible results of the student taking this test (the irony of which is enormous).

Another excellent trick is to look at the answer choices for easily removable options. If Brian did not study a single line of text, then the expected value of his blind guesses is 50%. This means it is possible that he can pass this test if he gets lucky, but he is not expected to do well. As such, any probability above 50% can be eliminated. We will need to do the calculations to determine exactly which answer is correct, but we already know it cannot be D or E as they are both too high.

Picking among the next three choices, each with a different denominator and fairly close values would be tricky. Statistically speaking, this question is identical to a coin flip question, where True is Heads and False is Tails (or vice versa if you prefer). The chances of getting all 8 correct, just as 8 straight Heads, would be (½)^8 or 1/2^8 or 1/256. This would yield a result of 100% on the exam. Brian would undoubtedly be surprised by such a result, but it is possible for him to pass the test without getting every question right. Since there are 8 questions, each question is worth 1/8 of the final score or 12.5%. Thus Brian could miss 1 question and still manage an 87.5%. He could even squeak by with 2 errors, giving him a result of 75% on the test. Anything lower would put him below the failure threshold.

There are three ways to calculate the remaining options, so let’s look at a more likely scenario: the possibility of getting 7 correct answers on the test. This result could be achieved if Brian missed the first question and got the next 7 right, or missed the last question after getting the first 7 right, or any other such breakdown. Logically, you can deduce that there are 8 different spots where the error could be, and the remaining 7 spots are all correct. Thus if each combination of answers has a 1/28 possibility of occurring, we should end up with 8/28 or 23/28 (cancelling to) 20/25 or 1/32. We can also use the combination formula for selecting 7 elements out of 8 where the order doesn’t matter. The formula would be n!/k!(n-k)!, where n is the total (8) and k is the number of choices (7). This would yield 8!/1!*7!, which simplifies to 8. This means there are 8 possible choices to select 7 correct answers. The final step is to divide by the total number of possibilities, which still stands at 28. The last option is to determine the numerator with the repeating elements formula n!/t!f!, where t and f are the number of repeating True and False answers. The result will still be 8!/1!7!, so 8 possibilities out of the same 256 options.

Using the same strategies on 6 correct answers and 2 false answers, we can get 8!/2!6!, which is 8*7/2 or 28 possibilities. The denominator won’t change for any of these, so the probability of getting exactly 6 correct answers is 28/256 (a little less than 11%). While I’m on the subject, I’ll simply draw attention to the fact that picking two correct answers and six incorrect answers on a binary test such as this one will yield the same results as picking two incorrect answers and six correct answers. The nature of the exercise (and the formulas) makes it so symmetry is guaranteed. This may be helpful at some point on the GMAT or in life, so try to ensure you can shortcut some calculations in this manner.

Putting together our three results, the chances of passing this exam are 1/256 + 8/256 + 28/256. This sum gives exactly answer choice B: 37/256. Although it seems unlikely that going into an exam with absolutely no preparation could yield a 15% chance of passing, those are the rules stipulated on this question. The entire GMAT exam has fixed rules, so it’s important to know how to approach each question on the exam. Moreover, it’s also important to understand the adjunct rules on particular questions in order to correctly solve the problem. As Jigsaw would rhetorically ask in any Saw movie: “Would you like to play a game?”

I replied to the student by discussing the *Process Pyramid for Sentence Correction.* Here is what the pyramid looks like.

Brevity

Clarity Specificity

Logic Grammar

**Logic and Grammar Come First**

You can see that the bottom level – the foundation of sentence correction – is logic and grammar, (including proper comparisons and parallelism). This is where your analysis should begin. If the answer choice has a flaw in grammar, such as subject-verb agreement or an error in logic, such as an illogical modifier then that answer choice should be eliminated.

This type of error is less subjective than something like an ambiguous modifier. That is why you should begin with logic and grammar, these errors are not a matter of judgment and the rules are easier to master. In particular students get a tremendous return on investment from mastering the rules of the common modifiers, including participial phrases, prepositions, appositives, and relative clauses.

**Next Clarity and Specificity**

The initial level of analysis should eliminate most answer choices based on flaws in grammar and logic. However, sometimes there will be more than one answer choice that has (or seems to have) no errors in grammar or logic. At this point you can move to clarity and specificity as a way to distinguish between answers. This is when it is appropriate to eliminate answer choices that have pronouns that are not clearly matched to antecedents.

The Official Guide for GMAT Review, 13^{th} Edition (written by the people who make the GMAT exam) states that a correct answer should avoid being “awkward, wordy, redundant, imprecise, or unclear” and that an answer that is any of these things can **be eliminated** **even if it is “free of grammatical errors.”** This group of secondary errors is referred to as problems with “rhetorical construction.”

The following answer choice is from question #44 of the sentence correction portion of the Official Guide 13^{th} Edition:

“The plot of the Bostonians centers on the active feminist, Olive Chancellor, and the rivalry with the charming and cynical cousin Basil Ransom, when they find themselves drawn to the same radiant young woman whose talent for public speaking has won her an ardent following.”

This answer choice is eliminated not for a grammatical flaw, but because it is lacks clarity and specificity. It is unclear in this particular answer choice that “Olive Chancellor is a party to the rivalry” with Basil Ransom.

**Finally, Brevity**

At the top of the Process Pyramid is Brevity. Most sentence correction questions do not require you to climb so high on the pyramid. It is only when two or more answers are logically and grammatically acceptable AND are each clear and specific that you need to bring brevity into the equation. However, the Official Guide describes many answer choices as “unnecessarily wordy.” So if you do find that you have two or more answer choices that satisfy the first two levels of the process pyramid only then do you eliminate the one that is “wordy.”

Looking for an error such as an ambiguous pronoun is fine; just make sure that you do so at the proper time. Use the process pyramid to organize errors and address those errors in the proper order: Grammar and logic, clarity and specificity, and finally, brevity.

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

Last week, I discussed timing issues on a quantitative question, and many of the concepts covered are applicable to the verbal section as well. Maintaining a good pace and avoiding spending undue time on perplexing questions are fundamental elements of a good GMAT score. However, I wanted to delve further into a particular type of question that often causes timing issues on the exam. Particularly when exhausted near the end of the test, students often dread coming across protracted Reading Comprehension passages.

Reading Comprehension (or RC for friends and family) poses a unique challenge on the GMAT. Every quantitative question and every other type of verbal question is entirely self-contained. A question will ask you about something, and then the following problem will be a completely different question about a completely different topic. Reading Comprehension questions ask you three, four and even five questions about the same prompt, and the prompts can be dozens of lines. Indeed, the first question on Reading Comprehension expects you to read through the entire passage, creating an inherent timing concern. Surely you can’t be expected to read through the entire passage in 2 minutes? (You are expected to do so, and don’t call me Shirley.)

Indeed, you can read through the passage in about two minutes, but you’re unlikely to be able to both read the passage and answer the (first) question posed during that span. For RC questions, I often find the best strategy is to separate the passage from the questions. If you read the question first, you risk skewing the analysis of the passage towards the question you have in mind, so it’s best to read the passage first without reading the question on the opposite side of the screen. The goal of this initial reading is to be able to identify the main idea of each paragraph and the primary purpose of the passage as a whole. You can read the passage in about 2 minutes and then spend about 1.5 minutes on each question, yielding a total of 8 minutes for 4 questions, roughly what you’d expect to spend holistically.

Let’s try this approach on a GMAT Reading Comprehension passage. At the end of each paragraph, try to summarize the main idea in about 3-5 words. You can even write these words down if you want, but it should be sufficient to think about the ideas.

*Biologists have advanced two theories to explain why schooling of fish occurs in so many fish species. Because schooling is particularly widespread among species of small fish, both theories assume that schooling offers the advantage of some protection from predators. Proponents of theory A dispute the assumption that a school of thousands of fish is highly visible. Experiments have shown that any fish can be seen, even in very clear water, only within a sphere of 200 meters in diameter. When fish are in a compact group, the spheres of visibility overlap. Thus the chance of a predator finding the school is only slightly greater than the chance of the predator finding a single fish swimming alone. Schooling is advantageous to the individual fish because a predator’s chance of finding any particular fish swimming in the school is much smaller than its chance of finding at least one of the same group of fish if the fish were dispersed throughout an area.*

* However, critics of theory A point out that some fish form schools even in areas where predators are abundant and thus little possibility of escaping detection exists. They argue that the school continues to be of value to its members even after detection. They advocate theory B, the “confusion effect,” which can be explained in two different ways. Sometimes, proponents argue, predators simply cannot decide which fish to attack. This indecision supposedly results from a predator’s preference for striking prey that is distinct from the rest of the school in appearance. In many schools the fish are almost identical in appearance, making it difficult for a predator to select one. The second explanation for the “confusion effect” has to do with the sensory confusion caused by a large number of prey moving around the predator. Even if the predator makes the decision to attack a particular fish, the movement of other prey in the school can be distracting. The predator’s difficulty can be compared to that of a tennis player trying to hit a tennis ball when two are approaching simultaneously.*

*According to one explanation of the “confusion effect,” a fish that swims in a school will have greater advantages for survival if it *

*(A) **tends to be visible for no more than 200 meters.*

*(B) **stays near either the front or the rear of a school.*

*(C) **is part of a small school rather than a large school.*

*(D) **is very similar in appearance to the other fish in the school.*

*(E) **is medium-sized.*

This passage only has two main paragraphs, and really each one is mostly about a theory as to why fish form schools (theory C: to get business degrees). We can summarize the first paragraph as the evasion theory and the second paragraph as the confusion theory. Overall the passage is primarily concerned with differing theories as to why fish tend to regroup in many disparate situations.

Looking over the question, it is specifically concerned with the “confusion effect”, which was theory B in the second paragraph. We can now focus our attention on the second paragraph to answer the question about survival. Rereading the passage, nothing was mentioned about the front or back of a school, as well as the size of the school, which eliminates answer choices B and C. Answer choice E similarly makes decisions based on the size of the fish, which was only discussed in terms of small fish. We can fairly quickly eliminate this choice as being a medium sized fish was never even mentioned.

Only answer choices A and D remain. Answer choice A is mentioned in the general sense for all fish in schools, and so would be a dubious choice as a great advantage since it applies to all fish in a given school. This is equivalent to saying we should promote Bob because he breathes oxygen. Answer choice D offers a logical choice, which is almost verbatim in the middle of the second paragraph “*In many schools the fish are almost identical in appearance, making it difficult for a predator to select one.”* This answer lines up with the text and we’ve eliminated the other four choices, making D an easy selection (also possibly recalling memorable moments from Disney’s Finding Nemo).

The questions on Reading Comprehension tend to be somewhat less tricky than the other verbal sections (Sentence Correction and Critical Reasoning). This difference is somewhat due to the fact that reading through passages takes time and inherently contributes to the difficulty of the question. The trouble isn’t just finding the right answer, it’s reading through 300 words of drivel without falling asleep and then isolating the important aspect to answer the given question. Especially since the verbal section is the last section of this test, it’s important not to waste too much time and get mentally fatigued. A good timing strategy is crucial to getting the best possible result on your GMAT.

This problem speaks to the inherent time management skill required to succeed on the GMAT. Almost any question you will face on test day can be solved with a brute force approach. However, you won’t have a calculator and you will be under constant time pressure to complete each question fairly quickly, so simply running through every possible numerical combination seems like a fool’s errand. There may be a time when the brute force approach works, but it is like trying to break into someone’s e-mail by trying 00000001, 00000002, 00000003, etc until you find the correct password. You’d probably have more success with a logical approach (such as guessing birthdays or other important dates) than with trying every possible permutation until the lock opens.

Approaching the problem in a logical and methodical way should be your goal for both quant and verbal questions. The approach as such may vary a little, but pattern recognition and extrapolation are two skills that will come up over and over again. If you’ve ever asked a 5-year-old what 2 + 2 was, they generally answer 4. If you ask them what 1,002 + 1,002 was, you’d usually get a lot of blank stares and puzzled looks. (My attempts to explain that they are essentially the same question have led to more crying fits than I’d care to admit). The GMAT uses the same elements of misdirection to bait you into thinking this particular problem is one that you can’t solve.

Let’s look at a quant problem to get an idea of what we’re looking to do on these questions:

How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?

(A) 20

(B) 31

(C) 42

(D) 53

(E) 64

This is the type of question that most people can get with unlimited time. You can simply go through every possible number from 1 to 249 and see if each number meets the criteria. Apart from going cross-eyed halfway through, you will also spend an atrocious amount of time on a question clearly designed to reward you for using logic. Let’s look at this question logically and see what we can determine.

Firstly, it only cares about positive integers, so we can disregard zero. This is helpful because a lot of questions hinge on whether or not zero is included, but that won’t matter in this instance. Furthermore, only integers matter, and we’re looking for multiples of 4 but not 6. Your initial pass on a question like this might look might concentrate on the multiples of 4 and you might write (part of) the following sequence down:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100…

After writing a couple of dozen numbers, you may try to figure out the pattern and extrapolate from there. Numbers divisible by 6 are to be eliminated, so you could rewrite this sequence:

4, 8, 16, 20, 28, 32, 40, 44, 52, 56, 64, 68, 76, 80, 88, 92, 100…

Even with this, we have a long sequence of numbers, some of which are crossed off, and less than halfway through the entire sequence. Perhaps approaching the question from a more strategic approach would yield dividends:

The number must be divisible by 4 but not by 6. Calculating the LCM gives us 12, which means that every 12th number will be divisible by both of these numbers. We want the integers to be divisible by four, but not by six, so 12 is out. Along the way, we stop by 4 and 8, both of which are divisible by four but not by six. So every 12 numbers, our count goes up by two, and we start the pattern again. 1-12 will give two numbers that work. 13-24 will give two more numbers that work. 25-36 gives two more, 37-48 gives two more and 49-60 gives two more as well. Thus, through 60 numbers, we have 10 elements that are divisible by 4 and not 6.

From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. The numbers 244 and 248 will come and complete the list that’s (naughty or nice) under 250. Answer choice C is correct here.

There are other ways to get the right answer, but the fastest ones all hinge on pattern recognition. Figuring out that every 12 numbers gives two more answers can take us from 1 to 240 in one shot (20 sequences x 2). Alternatively, once finding 4 elements at 24, you can probably easily envision multiplying the total by 10 and getting to 240 straight away (like warping over worlds in Super Mario Bros).

Timing is one of the key elements being tested on the GMAT, and one of the goals of the exam is to reward those who have good time management skills. Given 10 minutes, almost everyone would get the correct answer to this question, but the exam wants to determine who can get it right in a fraction of that time. On the GMAT, as in business, timing is everything.

One important thing to remember is that you won’t have a calculator on the exam, so blindly executing mathematical equations will be an exercise in futility. If the numbers seem large, the first thing to do is to determine whether the large numbers are required or just there to intimidate you. The difference between 15^2 and 15^22 is staggering, and yet most GMAT questions could use these two numbers interchangeably (think unit digit or factors).

Once you determine whether the bloated numbers truly matter, you need to ascertain how much actual work is required. If the question is asking you for something fairly specific, then you might need to actually compute the math, but if it’s a general or approximate number, you can often eyeball it (like proofreading at Arthur Andersen). Even if you end up having to execute calculations, you can usually estimate the correct answer and then scan the answer choices. Even in data sufficiency, determining how precise the calculations need to be can save you a lot of time and aggravation.

Let’s take a look at a question that can be somewhat daunting because of the numbers involved, but is rather simple if we correctly determine what needs to be done:

*If 1,500 is the multiple of 100 that is closest to X and 2,500 is the multiple of 100 closest to Y, then which multiple of 100 is closest to X + Y?*

* (1) X < 1,500 *

*(2) Y < 2,500*

*(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 but neither statement is sufficient alone.*

*(D) **Each statement alone is sufficient to answer the question.*

*(E) **Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.*

The first step here is to try and understand what the question is asking. It can be a little confusing so you might have to read it more than once to correctly paraphrase it. Essentially some number X exists and some number Y exists, and the question is asking us what X + Y would be. The only information we get about X is that 1,500 is the closest multiple of 100 to it, meaning that X essentially lies somewhere between 1,450 and 1,550. Any other number would lead to a different number being the closest multiple of 100 to it. Number Y is similar, but offset by 1,000. It must lie between 2,450 and 2,550. At this point we may note that the problem would be exactly the same with 100 and 200 instead of 1,500 and 2,500, so the magnitude of the numbers is simply meant to daunt the reader.

Without even looking at the two statements, let’s see what we can determine from this problem: Essentially if we add X and Y together, the smallest amount we could get is (1,450 + 2,450 =) 3,900. The largest number we could get is (1,550 + 2,550 =) 4,100. The sum can be anywhere from 3,900 to 4,100, and therefore the closest multiple of 100 could be 3,900, 4,000 or 4,100, depending on the exact values of X and Y. This tells us that we have insufficient information through zero statements, which isn’t particularly surprising, but it also sets the limits on what we need to know. There aren’t dozens of options; we’ve already narrowed the field down to three possibilities.

(1) X < 1,500

Looking at statement 1, we can narrow down the scope of value X. Instead of 1,450 ≤ X ≤ 1,550, we can now limit it to 1,450 ≤ X < 1,500. This reduces the maximum value of X + Y from 4,100 to under 4,050. This statement alone has eliminated 4,100 as an option for the closest multiple of 100, but it still leaves two possibilities: 3,900 and 4,000. Statement 1 is thus insufficient.

(2) Y < 2,500

Looking at statement 2 on its own, we now have an upper bound for Y, but not for X. This will end up exactly as the first statement did, as we can now limit the value of Y as 2,450 ≤ Y < 2,500. This is fairly clearly the same situation as statement 1, and we shouldn’t spend much time on it because we’ll clearly have to combine these statements next to see if that’s sufficient.

(1) X < 1,500

(2) Y < 2,500

Combining the two statements, we can see that the value of X is: 1,450 ≤ X < 1,500 and the value of Y is 2,450 ≤ Y < 2,500. If we tried to solve for X + Y, the value could be anywhere between 3,900 and 4,000 (exclusively), so 3,900 ≤ X+Y < 4,000. This still leaves us in limbo between two possible values. To illustrate, let’s pick X to be 1,460 and Y to be 2,460. Both satisfy all the given conditions and give a sum of 3,920, which is closest to 3,900. If we then picked X to be 1,490 and Y to be 2,490, we’d get a sum of 3,980. The second situation clearly gives 4,000 as the closest multiple. If we can solve the equation using valid arguments and yield two separate answers, we have to pick answer choice E.

These types of questions can be daunting because of the big numbers and the ambiguous wording, but the underlying material on these questions will never be something that can’t be solved in a matter of minutes. The difficulty often lies in determining how much work we really need to do to solve the question at hand. The old adage is that you get A for effort, but that’s applicable when you tried earnestly and failed. On the GMAT, you want to put in as much effort as is needed, but the only A you want to get is for Awesome GMAT Score (admittedly an AGMATS acronym).