Students routinely report that they end up in this exact situation multiple times on test day, particularly on Critical Reasoning questions in the verbal section. Sometimes, you can predict the correct answer before perusing the answer choices, and avoid this dilemma. However, inference questions frequently ask for the best implication of the sentence, and many correct possibilities could exist. This leads to considering two answer choices as accurate, when in fact only one of them is correct.

As a simple example, a question could indicate that Ron is taller than Tom, and then ask for inferences based on this conclusion. Valid inferences that can be drawn from this situation include “Tom is shorter than Ron”, “Ron and Tom are not the same height”, and even (my personal favorite) “Ron is taller than Tom”. Indeed the exact same idea could be inferred from the conclusion because it must logically be true. More generally, multiple conclusions can all be inferred from the same statement, from the mundane to the insightful.

The one element that must always be considered is that any statement that can be inferred must be true in all situations. Oftentimes when you’re stuck selecting between two choices, one must actually be true whereas the other simply seems to be true. Our brains are trained to complete incomplete data, such as filling in missing letters in words and assuming relevant context (this is a perfet exmple). The GMAT test takers know this about human nature, so we must be careful not to fall into their clever traps and consider fringe corner situations when selecting between two tempting choices.

Let’s look at an example and see how the test makers exploit subtle differences in the answer choices:

*SwiftCo recently remodeled its offices to comply with the Americans with Disabilities Act (ADA), which requires that certain businesses make their properties accessible to those with disabilities. Contractors built ramps where stairs had been, increased the number of handicapped parking spaces in the parking lot, lowered door knobs and cabinet handles, and installed adaptive computer equipment.*

*Which of the following is the most likely inference based on the statements above?*

*(A) **SwiftCo is now in compliance with ADA requirements.*

*(B) **SwiftCo has at least one employee or customer who uses a wheelchair.*

*(C) **Prior to the renovation, some doors and cabinets may have been out of reach for some employees.*

*(D) **The costs of renovation were less than what SwiftCo would have been liable for had it been sued for ADA violations.*

*(E) **Businesses without adaptive computer equipment are in violation of the ADA.*

The situation (not the abs guy from Jersey Shore) above describes a recent remodel to the SwiftCo offices in order for them to comply with ADA regulations. The changes are described in some detail, from ramps to parking spots to door knobs. The question then asks us about which statement below is the most likely inference, which really means which of these must be true whereas the other four don’t have to be. Let’s do an initial pass to eliminate obvious filler.

Answer choice A “SwiftCo is now in compliance with ADA requirements“ seems perfect. The changes were made due to ADA standards, so A seems like a great choice. Let’s keep going.

Answer choice B “SwiftCo has at least one employee or customer who uses a wheelchair” makes some semblance of sense, because otherwise why install the ramps? However this clearly doesn’t have to be true, SwiftCo can simply be acting proactively in order to comply with standards. Answer choice B does not have to be true, and can thus be rapidly eliminated.

Answer choice C “Prior to the renovation, some doors and cabinets may have been out of reach for some employees” seems like another great choice. After all, why remodel if everything was already handy. This could easily be correct as well. Let’s keep going.

Answer choice D “The costs of renovation were less than what SwiftCo would have been liable for had it been used for ADA violations” makes a completely unsupported claim. (As Harvey Specter would say: “Objection. Conjecture”.) We can quickly eliminate this unconfirmed option as it does not have to be true.

Answer choice E “Businesses without adaptive computer equipment are in violation of the ADA” makes a similar claim to answer choice D, but at least has a little bit more logic behind it. If the company is installing adaptive equipment, it might be in order to comply with ADA regulations; however it might also be another proactive practice put in place by management of their own volition. Answer choice E doesn’t have to be true, and thus can be eliminated.

And thus we’re left with two answer choices that both seem reasonable. And yet there can be only one (so says Connor MacLeod). How do we select between answers A and C? Quite simply, we must look at every possible scenario and see if each option must still hold. This can be an arduous process, but sometimes the evaluation of discarded answer choices helps to guide our approach.

In evaluating answer choice E, the issue of whether or not these changes were exactly aligned with ADA requirements came up. It’s entirely possible that adaptive computer equipment is not required by ADA guidelines; however it’s also possible that it is required. We simply don’t have enough information to make that decision with the information given. That same logic, taken in a broader context, hints that the changes made may or may not align SwiftCo with ADA regulations. Therefore, although answer choice A could be true, it does not necessarily have to be. Perhaps ADA regulations call for other changes that weren’t effectuated for whatever reason (budget, space, zombies).

Comparing with answer choice C, some doors and cabinets may have been out of reach for some employees. The phrase does not even give 100% certainty that the handles were out of reach, it merely states that it was a possibility. If the handles were lowered, it’s likely because some people couldn’t reach them, but it could also have been a practical improvement. No matter the situation, answer choice C must therefore be true.

Often when pitting two choices against each other, students report that they couldn’t find any differences and essentially flipped a coin. (Always pick Heads!) There will always be a difference between two answer choices, and the trick is to determine in which situations the two options actually differ. One will always work, whereas the other one will have one or two corner cases in which it doesn’t hold. If you master the art of correctly separating the last two options, your coin flip becomes a much more attractive proposition. Heads I win. Tails the GMAT loses.

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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.*

What do I mean by vague? I do not mean that two possible answers could both be the correct answer to the query. Such divergence would be unfair in a multiple choice exam where only one answer can be defensible. What happens on the exam is that a question is asked, but deciphering what that actually means is a task unto itself.

Let’s look at a simple example. If a question asks: “X is twice as big as Y. Y is 5. What is X?”, then it would be considered painfully simple. Y is known to be 5, X is double that, so the answer is 10 (don’t forget to carry the 1). If the exact same question were phrased as “John has two pineapples for every pineapple that Mary has. Mary counted the number of pineapples she had, and the number was the smallest prime factor of 35. How many pineapples does John have?” This question essentially asks for the same result, but the wording is so convoluted that many people get lost in it and don’t reach the correct answer.

While you likely won’t get a question like the above example (unless you’re scoring in the low 200s), every convoluted question can be broken down to a similar simple problem. The simplification won’t always be easy, but the tricks utilized on the GMAT to make questions long-winded repeat over and over again. Hopefully, if you’ve seen a few of them during your preparation, you’re more likely to know how to translate the GMATese™ (Patent Pending) and get the right answer on test day.

Let’s look at a typical vague question on the GMAT:

*A group of candidates for two analyst positions consists of six people. If one-third of the candidates are disqualified and three new candidates are recruited to replace them, the number of ways in which the two job offers can be allocated will:*

*(A) **Drop by 40%*

*(B) **Remain unchanged*

*(C) **Increase by 20%*

*(D) **Increase by 40%*

*(E) **Increase by 60%*

After reading such a question, you may still not be sure what to do, but you can start piecing together the issue at hand. There are six people interviewing for two jobs, but then some will drop out and others will join, and the overall impact must be gauged. The answer choices seem to offer various increases and decreases, so the answer must be in terms of the adjustment of job offer possibilities. This makes the question seem like a combinatorics or probability question.

Looking at the information provided, we have six applicants for two positions, and then one-third of them are disqualified. This leaves us with four finalists for the two jobs (like musical chairs), but before a decision is rendered, three more applicants join. There are now seven candidates for the two jobs, yielding a net change of one new contender. From 6 to 7 people, the change would be 1/6 of the old total, or 16.7%. This is closest to answer choice C, but there is no direct match among the answer choices. Since the GMAT doesn’t provide horseshoe answer choices (unless approximation is specified), this is our first hint that we may need to dig deeper in our approach.

The questions specifically asks about “*the number of ways in which the two job offers can be allocated”, *which should hopefully make you realize that the question is ultimately about permutations. In the initial setup, two positions are available for six candidates, meaning we can calculate the number of possible outcomes.

The only decision we have to make is about the order mattering, and since it’s not indicated anywhere that the jobs are identical, it’s reasonable to assume we can differentiate between job 1 and job 2. Let’s say that the first job is a senior position and the second is a junior position, how many ways can we fill these openings? Anyone can take the first position, so that gives us 6 possibilities, and then anyone of the remaining choices can fill the second position, yielding another 5 possibilities. Since any of these can be combined, we get 6*5 or 30 choices. Using the permutation formula of N!/(N-K)! yields 6! /4! which is still 6*5 or 30, confirming our answer.

If there were 30 possibilities at first, the addition of a new candidate will undoubtedly increase the number of possibilities, so we can consider answer choices A and B eliminated. After the increase, we can essentially make the same calculations for 7 candidates and 2 jobs, giving us 7*6 or 42 choices. We used to have 30 choices and now we have 42, so that works out to 12 new choices out of the original 30, equivalent to a 40% increase. Answer choice D is a 40% increase, and thus exactly the correct answer.

Some of you may be asking about the assumption I made about order mattering a few paragraphs back. “Ron, Ron”, you ask, “what happens if we assume that the order doesn’t matter?” Let’s run the calculations to see. If the order doesn’t matter and we’re dealing with a combination, then we have 6 candidates for 2 positions, we will get N! / K! (N-K)! which is 6! / 2! * 4! Simplifying to 6*5 / 2 gives us 15 options instead of the previous 30. Really, these are the same options but now we divide by two because the order no longer matters (i.e. AB and BA are equivalent). The updated scenario will have 7! / 2! * 5!, which becomes 42 / 2 or 21. This is exactly half the previous number again. The delta from 15 to 21 is 6, again 40% of the initial sum of 15. Since we’re dealing with percentages, both combinations and permutations will be completely equivalent. (Ain’t math grand?)

Regardless of minor assumptions made while solving this problem, the solution will always be the same. Indeed, the hardest part of solving the problem is often determining what is being asked. Remember that there can only be one answer to the problem, and that the answer choices can help steer you in the right direction. If you know what you’re looking for, the questions on the GMAT may be somewhat vague, but your goal will be crystal clear.

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The GMAT was first administered in 1953, and roughly 250,000 students take this exam on a yearly basis. Every year, I see students studying for the exam, hoping that a good grade gets them accepted to the business school of their choice. However, I believe one person who would have fared well on the test died about 40 years before the first exam was even introduced. I’m referring to noted American author Mark Twain.

Mark Twain is often referred to as the father of American literature, but his off colour remarks made him something of a celebrity in the 19^{th} Century. He was known for quotes that could be construed as inconsiderate, but often were just humorous observations on everyday minutiae (like a historical Seinfeld). As a renowned author, he undoubtedly could have excelled at the verbal section of the GMAT by noticing little details that others could overlook.

As this blog is nothing if not introspective, let’s look at a sentence correction problem about Mark Twain, and solve it in the way Twain likely would (Inception).

*A letter by Mark Twain, written in the same year as The Adventures of Huckleberry Finn were published, reveals that Twain provided financial assistance to one of the first Black students at Yale Law School.*

*(A) **A letter by Mark Twain, written in the same year as The Adventures of Huckleberry Finn were published, *

*(B) **A letter by Mark Twain, written in the same year of publication as The Adventures of Huckleberry Finn,*

*(C) **A letter by Mark Twain, written in the same year that The Adventures of Huckleberry Finn was published,*

*(D) **Mark Twain wrote a letter in the same year as he published The Adventures of Huckleberry Finn that*

(E) *Mark Twain wrote a letter in the same year of publication as The Adventures of Huckleberry Finn that*

An astute observer such as Mark Twain would first notice that there is a clear 3-2 split between answer choices that begin with “A letter by Mark Twain” and “Mark Twain wrote a letter…” It is possible that either turn of phrase could be correct, but it is more likely that we can eliminate one selection entirely because it does not flow properly with the rest of the sentence.

The original sentence (answer choice A) postulates that a letter by Mark Twain reveals that he provided financial assistance to an aspiring young law student many years ago. This phrase makes logical sense and does not have to be automatically discarded. The other options begin with “Mark Twain wrote a letter that reveals that Twain provided financial assistance…” Even without the redundancy of “that reveals that”, the timeline of this sentence does not work properly. If Mark Twain wrote a letter in the past, then the letter would have “revealed” the information, and would have needed to have been conjugated in the past. An author like Twain would eliminate answers D and E as the timeline construction does not make sense.

With only three options remaining, Twain would examine the differences between answer choices A, B and C more closely. The only real difference between answer choices A and C is the verb agreement of the publication of the Adventures of Huckleberry Finn. Answer choice proposes that the verb be plural, while answer choice C contains the singular conjugation of the verb. While “The Adventures of Huckleberry Finn” sounds plural, it is actually the title of a single book and therefore must be treated as a singular noun. Answer choice A can thus be eliminated because of the agreement error.

Having narrowed the quest down to only two choices, Twain would likely contrast the two choices again and note the construction of answer choice B is faulty. If we follow the logic: “*A letter by Mark Twain, written in the same year of publication as Huck Finn…”* doesn’t make any sense. Grammatically, the letter is supposed to have been written in the same year that the novel was published, yet the grammar indicates that both the letter and novel were published in the same year. This change in meaning eliminates answer choice B, and leaves only answer choice C as the correct option.

Eliminating incorrect answer choices is the name of the game in Sentence Correction, and a shrewd reader can easily differentiate between turns of phrase that are acceptable and garbled prose that doesn’t mean anything. Remember that only one answer choice can be correct, so you must eliminate incorrect answer choices by any means you have available to you. It’s fine to think of yourself as a 19^{th} Century author and begin to decimate the given answer choices. Just because most people don’t think of themselves as Cosplayers during the GMAT (they just can’t pull off the elaborate costumes), that doesn’t mean you can’t use your imagination to your advantage. To quote Twain: “Whenever you find yourself on the side of the majority, it is time to pause and reflect”.

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From the time we’re in elementary school, we’re encouraged to use our calculators to solve even the most mundane equations. If John is buying six dozen eggs, how many total eggs is John buying? Many people instinctively reach for their calculators, even if they can do the simple multiplication in their heads. Calculators provide safety and accuracy. The little machine says that the answer is 72; I won’t even bother double checking the result manually because I know the machine won’t make a mistake. This is even more prevalent as the math involved gets harder (a dozen dozen eggs?). Indeed the lure of the calculator is very strong.

Why does the GMAT not allow for calculators on the exam? Quite simply, the exam is trying to test how you think, not how quickly you can type on a calculator. This allows for questions to include relatively simple math that you must solve manually, or for rather difficult math that you must understand in order to reach a conclusion. Both types of questions show up on the exam, but the answer choices always provide some sort of hint as to what to do, since the correct answer must be among the five choices given.

Let’s look at two simple interest rate questions to highlight the methods we can free ourselves of our calculator addiction:

*Marcus deposited $8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcus’ account one year after the account was opened?*

*(A) **8,200*

*(B) **8,205*

*(C) **8,400*

*(D) **8,405*

*(E) **8,500*

Many students (especially those in finance) immediately recognize this as a compound interest problem, which can be solved effortlessly with a financial calculator. You only have to plug in the term, the interest rate, the principal and the rate of compounding, and the calculator will spit out the correct output in a matter of seconds. However, the underlying concept is what the GMAT is really testing. The authors of this question want to ensure you comprehend how to make the calculations, so the question is asking about only one year.

In this case, we can easily calculate the amount without a calculator. We have 8,000$ making 5% annually, which translates to 400$ in one year. Thus, if the interest were compounded annually, the answer would be 8,400$. If we don’t notice that the interest is compounded more frequently than that (or we don’t understand what that entails), then we might pick answer choice C and move on. However, that would be incorrect because the question indicates that the interest is compounded twice a year.

If the interest is compounded twice a year, that means that after 6 months you make 2.5% of the 8,000$, or half of the 400$ we’d previously calculated. If you’re trying to calculate 2.5%, it’s easiest to take 10% and then divide it by four. Multiplying by fractions can be tedious without a calculator, but GMAT questions are set up in such a way that the answers are almost always integers. You just have to determine the best way of getting to that integer without getting bogged down in tedious math.

Whichever method you used, you should have 8,200$ after 6 months. After another 6 months, you need to calculate another 2.5% on 8,200$. The simplest way to do this is to recognize that the 8,000$ will still yield 200$, and only the extra 200$ must be adjusted for. Since we need ¼ of 10%, that’s ¼ of 20$ or exactly 5$. The interest accrued in the second semester will be 205$ instead of simply $200 (#winning), making the total for the year 405$. The correct selection is thus answer choice D.

However, we don’t even need to get this precise on most GMAT questions. Look at the answer choices again. Once we’ve determined that we need slightly more than 400$ in interest because of the compounding, the only answer choice that makes any sense is D. Oftentimes the simple fact that the answer must be slightly higher or lower than a known benchmark eliminates all answer choices except for one. The complete calculations can be accomplished, but a rough estimate will work in 99% of cases.

Let’s look at a similar question where the estimation is our best approach:

*Michelle deposited a certain sum of money in a savings account on July 1st, 2012. She earns an 8% annual interest compounded semi-annually. The sum of money in the account on January 1st, 2015 will be approximately what percent of the initial deposit?*

*(A) **117%*

*(B) **120%*

*(C) **121%*

*(D) **135%*

*(E) **140%*

In this case estimation is the best approach because the answer choices are far apart. If Michelle is earning 8% per year compounded semi-annually, then every six months she’s making about 4%, which over 30 months is 20%. Answer choice B is thus close but ultimately too low for the compounding interest. It must be ever so slightly higher than that, which leads us inexorably to answer choice C. We need a little more than 120%, but there’s no way we can get to 135%. The answer must be C, and we don’t really need to do any verification to know that this is the correct answer (you can do the math and get to 121.67% if you’d like).

While the calculator is an ever-present tool in the real world, the GMAT remains a test designed to test how you think. The shortcuts and instruments you use in everyday life should only serve to accelerate your calculations, not replace the thought processes that allow you make calculations. Remember that if everything you do can be replaced by a calculator (or spreadsheet or abacus), then sooner or later you might be too.

When looking over Sentence Correction questions, there are common errors that appear over and over as potential gaffes that must be avoided in the correct answer. One such error is that of the false comparison, where the author erroneously compares one thing to another of a different type. Consider the frequently misused example of “The Yankees’ record is more impressive than the Mets.” Without adding a possessive determiner (Mets‘) at the end of the sentence, we are comparing the Yankees’ record with the actual Mets team. This is clearly an illogical comparison, yet one that often goes unnoticed.

Some questions will contain more than a simple comparison issue, and the other rules of English grammar we know must also be followed, but comparison issues tend to disproportionally mess students up. These errors frequently occur in daily life without anyone batting an eyelash (well, except for those studying for the GMAT), so they’re often difficult to spot.

Let’s look at an example that highlights this issue:

*Unlike the terms served by Grover Cleveland, separated by four years, all former two-term U.S. Presidents have served consecutive terms.*

*(A) **Unlike the terms served by Grover Cleveland, separated by four years*

*(B) **Besides the terms of Grover Cleveland that were separated by four years*

*(C) **Except for Grover Cleveland, whose terms were separated by four years*

*(D) **Aside from the terms of Grover Cleveland that were separated by four years*

(E) *Other than the separated terms of Grover Cleveland, of four years*

Many amateur historians will stop to consider the accuracy of the subject matter (feel free to check “the Google”), but more astute GMAT students will quickly recognize that the original sentence contains a comparison trigger word. The word “unlike” typically signals that we’ll be comparing two or more elements; however these elements may or may not be congruent. If they are not comparable, we’ll be dealing with a glaring comparison error. This may not be the only error we have to sort through, but it’s undeniably a good place to begin our analysis.

The sentence begins by comparing the terms of the 22^{nd} (and 24^{th}) U.S. president to the other 11 presidents who have served two presidential terms. This connection should immediately seem incorrect, as presidential terms and people are not interchangeable. The underlined portion will thus need to be changed as the second half of the comparison is not underlined and therefore must remain untouched. Answer choice A can be eliminated because of this comparison mistake.

Looking through the other choices, answer choice B changes a couple of words in the answer choice, but still starts by comparing terms to humans. It can therefore be eliminated. Answer choice C changes the wording to begin with “Except for Grover Cleveland, whose terms…”, which changes the comparison to one person versus other people. This comparison is logical and acceptable, and the rest of the sentence seems fine as well. We can eliminate answer choices A and B so far, but not answer choice C. Let’s look at the two remaining choices before we look for another error.

Answer choice D again tries to compare terms to a person, which can easily be eliminated. Answer choice E makes the same mistake, and this sentence makes more mistakes as we read through all of it, however one strike is all you get on the GMAT. Only answer choice C correctly compares the 24^{th} (and 22^{nd}) U.S. president to the other presidents. Answer choices A, B, D and E are all eliminated because of the same comparison error, and choice C must be the correct answer.

Sentence Correction on the GMAT is full of questions like this, where one issue will get you to the correct answer, but if you don’t see it, you’ll spend time dissecting slight meaning differences between synonyms. If you don’t recognize the comparison error, you might think that this question is asking you to choose between “Aside” and “Unlike” in a sentence, which is a fool’s errand. Recognizing the common errors that pop up on the GMAT helps both your success rate and your pace, helping build confidence. Best of all, it ensures you’re comparing apples with apples.

Suddenly the chances of scoring in a top percentile don’t seem so bad.

If it comes to this … at least we won’t panic.

I knew 10 easy questions in a row seemed too good to be true…

So *that’s* where they’re hiding it.

What can we infer here? Not all, but at least Some.

And, the GMAT is a better choice than the LSAT, perhaps. Better take plenty of practice tests.

And, thanks to GMAC’s new score-cancellation policy…. You mean I can now cancel my score *after* seeing it?

Those who struggle with the GMAT often fall into two camps – those who take it too seriously and those who don’t take it seriously enough – each a kind of evil. If this sounds like you, take another tip from Mr. Wright: “if you must choose between two evils, pick the one you’ve never tried before.”

So remember these bits of wit, as unconventional as they seem, when studying for your GMAT. Though they sound like cynical one-liners and wry observations, ironically they speak to a set of truths. Truths that can work in your favor come game day. Not that you should take them too seriously.

Planning to take the GMAT soon? We have online GMAT prep courses starting all the time! And, be sure to find us on Facebook and Google+, and follow us on Twitter to better learn how to Think Like the Testmaker!

*Joseph Dise has been teaching GMAT preparation for Veritas Prep for the last 6 years in Paris, New Brunswick, and New York City.*

“How could this have happened? I was doing so well!”, you think. “What do I do now?”

A bad practice test can happen to anyone. In isolation, it’s certainly not the end of the world, but you should use the result to diagnose what went wrong and how to fix it moving forward. There are several potential causes worth considering. Let’s look at a few:

**1. Mental/Physical**

In many respects, the GMAT is as much a psychological exam as a content exam. Your mental state going into the test can set you up for success or failure.

Were you fatigued or stressed before the exam started? If so, your ability to pick up on subtle clues and notice testmaker tricks and traps was likely not at its usual level. Even if you felt fine to start the test, you may have “hit the wall” midway through the test. Many students have performed normally through the first part of the test, only to run out of gas towards the end of the quant section or in the verbal section.

If this is you, consider how you can improve your pre-test condition. Are you sleeping and eating well? Are work and other responsibilities taking a toll? Obviously, quitting your job to study for the GMAT is not a winning proposition, but recognize that there may be situations in which taking a practice test is counterproductive. If you don’t feel great when you’re about to start the test, push it back by a day or two.

**2. Technical**

GMAT writers are masterful at asking the same question in multiple ways. You may know how to handle a question when asked one way, but when the test asks you to solve in a different way, you’re not as comfortable.

Thanks to the adaptive nature of the exam, you can see a practice test where specific question types (such as exponents or weighted average) are asked in a way that fits what you’re good at, and you do well on them. Conversely, you may see the same concepts asked in a way that exploits your conceptual weaknesses, and you struggle more than expected.

If this is you, consider what gave you trouble. If you notice that your understanding of triangles or ratios isn’t as thorough as you thought, you now know what to address to improve going forward. Having a strong grasp of multiple approaches will make you more prepared to handle a question type, regardless of how it is set up.

**3. Tactical**

Even if your conceptual knowledge is strong, it’s still possible to run into issues with test strategy. Allow stubbornness to creep in on a few early questions, and your pacing may be off for the rest of the section. If you get away from your standard approach for a specific question type (such as Data Sufficiency or Sentence Correction), you may open yourself up to errors you wouldn’t make on homework questions.

If this is you, review your overall approach to the exam. How are you keeping track of pacing? If this is a consistent struggle, find a way to make sure you stay on track. Can you get better at letting go of questions that got away from you? Work on recognizing when to make a guess and move on to save time for questions you can get right. Are you finding ways to answer questions more easily or quickly? When you review practice problems, look for clues in the question and answers that could’ve led to a more efficient solution.

A bad result is a perfect opportunity for self reflection. You have time to come up with a plan of attack, and with this new information you can tailor your approach to the areas that need improvement. After all, it’s much better to have your weaknesses exposed by a practice test than the real thing!

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*By Bill Robinson*

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.

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.

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.