Using Algebra vs. Logic on GMAT Quant Questions

GMAT QuantIn pretty much every class I teach, at some point I’ll get the algebra vs. strategy question. Which is better? How do you know? I sympathize with the students’ confusion, as we’ll use the two approaches in different scenarios, but there doesn’t seem to be any magic formula to determine which is preferable. In many instances, both approaches will work fine, and the choice will mostly be a matter of taste and comfort for the test-taker.

In other cases, the question seems to have been specifically designed to thwart an algebraic approach. While there’s no official litmus test, there are some predictable structural clues that will often indicate that algebra is going to be nothing short of hemorrhage-inducing.

Here’s my personal heuristic; if an algebraic scenario involves hideously complex quadratic equations, I avoid the algebra. If, on the other hand, algebra leaves me with one or two linear equations to solve, it will almost certainly be a viable option. You might not recognize which category the question falls under until you’ve done a bit of leg-work. That’s fine. The key is not to get too invested in one approach and to have the patience and flexibility to alter your strategy midstream, if necessary.

Let’s look at some scenarios with unusually complex algebra. Here’s a GMATPrep® question:

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800

Simple enough. Let’s say the sides of this rectangular park are a and b. We know that the perimeter is 2a + 2b, so 2a + 2b = 560. Let’s simplify that to a + b = 280.

The diagonal of the park will split the rectangle into two right triangles with sides a and b and a hypotenuse of 200. We can use the Pythagorean theorem here to get: a^2 +b^2 = 200^2.

So now I’ve got two equations. All I have to do is solve the first and substitute into the second. If we solve the first for a, we get a = 280- b. Substitute that into the second to get: (280 – b)^2 + b^2 = 200^2. And then… we enter a world of algebraic pain. We’re probably a minute in at this point, and rather than flail away at that awful quadratic for several minutes, it’s better to take a breath, cleanse the mental palate, and try another approach that can get us to an answer in a minute or so.

Anytime we see a right triangle question on the GMAT, it’s worthwhile to consider the possibility that we’re dealing with one of our classic Pythagorean triples. If I see root 2? Probably dealing with a 45:45:90. If we see a root 3? Probably dealing with a 30:60:90. Here, I see that the hypotenuse is a multiple of 5, so let’s test to see if this is, in fact, a 3x:4x:5x triangle. If it is, then a + b should be 280.

Because 200 is the hypotenuse it corresponds to the 5x. 5x = 200 à x = 40. If x = 40, then 3x = 3*40 = 120 and 4x = 4*40 = 160. If the other two sides of the triangle are 120 and 160, they’ll sum to 280, which is consistent with the equation we assembled earlier.

And we’re basically done. If the sides are 120 and 160, we can just multiply to get 120*160 = 19,200. (And note that as soon as we see that ‘2’ is the first non-zero digit, we know what the answer has to be.)

Here’s one more from the Official Guide:

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

  1. $1
  2. $2
  3. $3
  4. $4
  5. $12

First the algebraic setup. If we want T towels that we buy for D dollars each, and we’re spending $120, then we’ll have T*D = 120.

If the price were increased by $1, the new price would be D+1, and if we could buy 10 fewer towels, we could then afford T -10 towels, giving us (T-10)(D+1) = 120.

We could solve the first equation to get T = 120/D. Substituting into the second would give us (120/D – 10)(D + 1) = 120. Another painful quadratic. Cue hemorrhage.

So let’s work with the answers instead. Start with D. If the current price were $4, we could buy 30 towels for $120. If the price were increased by $1, the new price would be $5, and we could buy 120/5 = 24 towels. But we want there to be 10 fewer towels, not 6 fewer towels so D is out.

So let’s try B. If the initial price had been $2, we could have bought 60 towels. If the price had been $1 more, the price would have been $3, and we would have been able to buy 40 towels. Again, no good, we want it to be the case that we can buy 10 fewer towels, not 20 fewer towels.

Well, if $4 yields a gap that’s too narrow (difference of 6 towels), and $2 yields a gap that’s too large (difference of 20 towels), the answer will have to fall between them. Without even testing, I know it’s C, $3.

This is all to say that it’s a good idea to go into the test knowing that your first approach won’t always work. Be flexible. Sometimes the algebra will be clean and elegant. Sometimes a strategy is better. If the algebra yields a complex quadratic, there’s an easier way to solve. You just have to stay composed enough to find it.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council.

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

By David Goldstein, a Veritas Prep GMAT instructor based in Boston.

How to Attack GMAT Sentence Correction Questions Like a Boss

Many people think that finishing the GMAT verbal section on time hinges on quickly solving Sentence Correction problems. This is because these questions tend to have the shortest stimuli of any question type. Even if you’re a speed reader (hopefully you never ordered Mega Reading by Kevin Trudeau), it will still take a minute or so to sift through a passage that’s a few hundred words long. Sentence Correction problems sometimes have stimuli that are two or three lines, and therefore are prime candidates for quick dispatching.

However, sometimes you encounter Sentence Correction passages that are as long as paragraphs. Your job is the same no matter the length of the text, but Sentence Correction problems require you to evaluate every decision point among the answer choices. The longer the sentence, the more decision points you may have to consider. The number of false decision points also tends to increase as the sentence length increases. False decision points are differences between answer choices in which both options are acceptable, so making a choice based on such a decision point could erroneously eliminate a valid answer choice. Indeed, picking between an alternative and a substitute is an exercise in futility.

Another issue that comes up is mental fatigue. Conventional grammatical wisdom postulates that sentences longer than 20-25 words begin to lose their effectiveness, as the human brain struggles to process all the information. Run-on sentences can cause readers to disengage as they find themselves apathetic to the point that the author is trying to make. Often students report a lack of interest on longer passages, and an increased urge to simply select an answer choice (sometimes at random) to move on to a different question.

Let’s look at an example, which clocks in at an impressive 51 words.

The first trenches that were cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence for centrally administered complex societies in northern regions of the Middle East that are arising simultaneously with but independently of the more celebrated city-states of southern Mesopotamia, in what is now southern Iraq.

(A)   that were cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence for centrally administered complex societies in northern regions of the Middle East that are arising simultaneously with but

(B)   that were cut into a 500-acre site at Tell Hamoukar, Syria, yields strong evidence that centrally administered complex societies in northern regions of the Middle East were arising simultaneously with but also

(C)   having been cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of the Middle East were arising simultaneously but

(D)   cut into a 500-acre site at Tell Hamoukar, Syria, yields strong evidence of centrally administered complex societies in northern regions of the Middle East arising simultaneously but also

(E)    cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of the Middle East arose simultaneously with but

The first thing you might notice is that, not only is this sentence way too long, most of it is underlined. That means it will take a fair amount of time just to peruse the answer choices. Our best strategy will probably not be to read through the five similar answer choices without any specific goal.

With run-on sentences, you want to be methodical and review each decision point as it comes up. As noted before, some may be false decision points and you cannot eliminate any choice. However, some words are low hanging fruit, such as verbs or pronouns, which have to be in specific forms (i.e. singular vs. plural). Connectors to and from the underlined portion are often significant as well, since they serve as springboards from one section to the next.

Looking at the original sentence (answer choice A) and going through the words, we’re looking for verbs and pronouns that can help guide our decisions. The first verb encountered is “were cut”, but the verb cut is tricky because it has the same form in the past, the present and the future. Answer choice C’s “having been cut” seems unnecessarily wordy, but that is not necessarily enough to eliminate it outright, so we’ll keep it with an asterisk and continue looking for other verbs.

The next verb encountered is “have yielded”, and a cursory comparison of the other answer choices reveals a 3-2 split between “have yielded” and “yields”. The subject of the verb is “The first trenches”, which is plural. The verb formulation of “yields” only works if the subject is singular, and thus we can eliminate these answer choices with 100% certainty as they contain agreement errors. Answer choices B and D can both be eliminated.

Continuing on, the second verb we encounter is “are arising”. Everything else about specific locations, sizes of land and other minutiae can be ignored using the slash-and-burn technique. We’re on a mission to compare specific terms that can help illuminate errors in various answer choices. Answer choice C has “were arising” and answer choice E has “arose”. The subject of the verb is “societies”, and therefore any of the three could be correct from an agreement standpoint. However, the timelines vary from present to past continuous to simple past, and the rest of the sentence began with the past-tense verb “have yielded”, meaning that the present tense would be erroneous. Answer choice A can be eliminated because of a timeline error.

At this point, only answer choices C and E remain. The verbs are not identical in the two options, but either one could conceivably make sense, so we must look for other differences in order to differentiate between the two. Looking through the answer choices, there are no pronouns to compare, but the first and last words are not the same. These connectors often cause answer choices to be eliminated because they make sense with the underlined portion but they do not fit nicely into the rest of the sentence (like merging onto the highway on a horse and buggy).

Answer choice C is already on our radar because of the wordy verb choice, but let’s examine how it fits back into the sentence at the end. The societies “were arising simultaneously…” is missing the word “with” in order to make grammatical sense. You arise simultaneously with something else. The original sentence had this word, but answer choice C omits the key words, and it’s difficult to see because the text is so verbose. This incorrect construction dooms answer choice C. Only answer E remains as the correct choice.

As with any Sentence Correction question, process of elimination is the name of the game. However, when the sentences get very long, very technical, or otherwise disengaging, you have to go through the text in a methodical manner. The best words to compare are the verbs, the pronouns and the connectors to and from the underlined portion. If you have a sound strategy, you’ll be able to execute the run on sentence correction.

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

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

How to Make the GMAT Quant Section Easier on Test Day

QuestioningIn my decade of teaching the GMAT, perhaps no single group has found the quant section on the test more exasperating than math nerds. Yep, math nerds. Engineers, financial analysts, Physics majors, etc.

This may seem somewhat paradoxical, but the quant section on the GMAT isn’t testing your math ability. The skills that allowed the quantitatively-inclined to ace their tests in high school and college not only have limited value on the GMAT, but actually undermine test-takers, prompting them to grind through calculations when the question is really about how to avoid those very calculations.

Take this * GMATPrep® question, for example.

Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $165,000.

II. At least one of the homes was sold for more than $130,0000 and less than $150,000

III. At least one of the homes was sold for less than $130,000.

A. I only

B. II only

C. III only

D. I and II

E. I and III

Perhaps you were tempted to do it algebraically. Maybe you thought you had to evaluate every scenario independently. If that was the case, you’re in good company. Most of the students I’ve taught over the years have had the same instinctive response. But we need to keep reminding ourselves about the aforementioned axiom: the GMAT isn’t testing math ability. It’s testing fluid thinking ability under pressure. So let’s take a deep breath and think about this for a moment.

How can I make this easier? What if I could construct a very simple scenario that violates two of the three statements?

The simplest possible scenario I can think of involves a set where the first 14 terms are equal to 130,000 exactly. (Clearly, in this case, the middle term, or median will be 130,000.) Then the last member will have to be enormous in order to increase the average to 150,000.  (If you were so inclined, you could do 14*130,000 + x = 15*150,000 and solve for x. x would be 430,000. But there’s no need to actually do this. It’s enough to see that x will be way more than 165,000.)

Well, this set {130, 130, 130, …430} proves that we don’t HAVE to have anything below 130,000. Kill Statement III. And it also proves that we don’t HAVE to have anything between 130,000 and 150,000. Kill II. We’re done. Only I has to be true, and there’s no need to test another scenario, because we’ve already logically disproved the other statements. The answer must be A, I only. All we needed was one simple scenario.

Now let’s look at a second GMATPrep® problem that, on the surface, appears to have absolutely nothing to do with the previous one.

Which of the following lists the number of points at which a circle can intersect a triangle?

1) 2 and 6 only

2) 2,4 and 6 only

3) 1,2,3 and 6 only

4) 1,2,3,4 and 6 only

5) 1,2,3,4,5 and 6

Again, the default response is to just start grinding through scenarios with the hope that, eventually, you’ll hit all of them. But that’s not a very efficient approach. Let’s slow down and think strategically. How can we save time? Well, look at the statements. Notice that there’s plenty of overlap, but only choice E has ‘5’ as a possibility. So if we can draw a triangle that intersects a circle at 5 points, I’ll know that’s the answer.

So, I’ll draw a circle:

Now I’ll draw 5 points on the circle, and try to draw a triangle through those points.

Looks like I can do it. I’m done. E is the answer.

(Interesting Parenthetical Note: if you were the question writer and were trying to concoct a question/answer that would that would be most difficult and time consuming for a test-taker, wouldn’t you have the correct answer contain the greatest number of possibilities? That’s another clue that E is where we want to start.)

The big takeaway here is that it’s good if we can keep reminding ourselves that the GMAT isn’t interested in our raw computational ability.  What the GMAT is interested in is our ability to make good decisions under pressure. So when you see a tough question, slow down. Look at the answers. Then think of the simplest possible scenarios that will allow you to test those answers in the fewest number of steps.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council.

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

By David Goldstein, a Veritas Prep GMAT instructor based in Boston.

WTF! Leverage Your Assets on These GMAT Questions

When preparing to take the GMAT, you often solve hundreds or even thousands of practice problems. As you solve more and more of them, you start to realize that almost every question is testing something specific. There’s a geometry question about right angle triangles that’s really all about Pythagoras’ theorem, and an algebra problem that is easy to solve if you expand the difference of squares. However, there are some questions that make you scratch your head and wonder: “What in the world?” Some questions make you think you missed a section of material that you need to review (are there triple integrals on the GMAT?), or at the very least that you don’t know the correct strategic approach. I will euphemistically call these “WTF” questions, which of course stands for “Want To Finish”.

On questions where the entire goal of the question remains a mystery even as you try and come to a conclusion, the best strategy is to leverage all the information provided to you. As an example, if the question asks you about a specific property of an odd number, then try plugging in a few odd numbers to see what’s going on. You can then plug in a few even numbers to contrast the two; this often sheds some light on why only odd figures were selected in the premise. Exploiting seemingly inconsequential hints like these might be the difference between getting the right answer and wasting copious amounts of time on a single question, so look for hints in the set up.

Another important thing to remember is that you are just looking for a single answer choice. On the GMAT, there are no part marks for development, and a single incorrect calculation can sink an otherwise flawless algorithm. So you’re going for the correct answer more than a perfect understanding of what the question is testing. Understanding the question generally leads to a correct answer, but stumbling on the correct choice is worth exactly the same number of points on the GMAT (The Maxwell Smart approach). This also means that eliminating incorrect answer choices is valuable, as worst case you can take an educated guess that’s 50/50 instead of one out of five.

Let’s look at one of these WTF (Want To Finish) questions and see if we can figure out a solution:

If x and y are both prime, is x*y = 323?
(1) x is the first prime number after 18
(2) y is the last prime number before 180

(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.

So the first thing that came to my mind is “Wow, that’s random”. The premise seems so arbitrary that it makes many approaches seem irrelevant. Even knowing that the two numbers are prime, we cannot quickly determine whether they must multiply to 323 without some more analysis and manipulation. Luckily, this is a Data Sufficiency question, so we have two additional statements that can help guide our analysis.

It’s important to note that in Data Sufficiency, we are trying to determine whether we can say with certainty that the two numbers multiply together to 323. This also means that if we can determine with certainty that the two numbers cannot multiply to 323, we have sufficient data. The uncertainty arises when we don’t know either way (i.e. maybe), so that provides a good framework for our analysis.

The first statement gives us a big hint, telling us that x is the first prime number after 18. This very quickly implies that x must be 19. We now have a hint as to why the number 323 was chosen (perhaps the author drove a Mazda in the ‘90s). If 323 is not a multiple of 19, then statement 1 will provide definitive evidence that x*y cannot possibly equal 323. Short of using a calculator, we can find multiples of 19 that are nearby and iterate manually until we find the correct answer. 19 x 20 would be easy to calculate as we can consider it as 19 x 2 x 10, or 38 x 10, or 380. From there, we can drop 19s until we get in the correct range.
380 – 19 is 361
361 – 19 is 342
342 – 19 is 323

You might be able to get there faster than by using this strategy, but after a few seconds of calculations, you can determine that 19 * 17 yields exactly 323. The question indicated that x and y would both be prime numbers, and 17 is indeed a prime number, so the possibility exists. However, it’s important to note that we know nothing (John Snow) about the value of y, other than it is a prime number. It could just as easily be 2, or 7, or 30203 (yes that’s a prime; I like palindromes). Since y could have any prime value, there’s insufficient evidence to determine that the product of x and y must be 323. Statement 1 is insufficient, and we can eliminate answer choices A and D.

Statement 2 indicates that y is the last prime number before 180, but it is important to remember that we must evaluate this statement alone. We now have no information about the value of x, other than it is a prime number. Statement 2 gives us a specific value of y, even if we’re not exactly sure what it is. We could do a little math and check to see if 179 (the number right before 180) is a prime, and in this case it is. The verification process is somewhat tedious, you have to check to see if it’s divisible by any prime number smaller than the square root of the number, so once you check 2, 3, 5, 7, 11 and 13, you’re confident than 179 is a prime number.

Knowing only that x is a prime number, we must now try and determine whether 179 and any prime could yield a product of 323, and the answer is very quickly no. The smallest prime number is 2, and 179 * 2 is already 358. You can also visually determine that 179 is more than half of 323, so there’s no need to even formally calculate the result. This statement on its own guarantees that x * y can never be 323, and thus is sufficient information to answer the question. The correct selection is answer choice B, as this statement alone is sufficient.

It is important to point out that these statements, taken together, give very clear numbers for both x and y. When this happens, you know that you can combine the statements and get only one value. That value may or may not be 323 (in this case it’s really, really not), but either way it provides sufficient information to definitively answer the question. However, it is almost always going to be the wrong answer, as it simply provides too much information. There’s no mystery or intrigue left, everything is laid out on the sheet in front of you. In business, as in life, if something seems too good to be true, it usually is.

Indeed, this question is essentially testing to see whether you’ll overpay for information on Data Sufficiency. However, at first blush, it just seems like an arbitrary collection of numbers with a question attached. When faced with similar head-scratchers, keep in mind that the statements (and/or answer choices) will provide hints. Trying to factor out 323 without any hints is a challenging endeavour, so look for hints and exploit them as much as possible. Hopefully, on test day, the only head scratching you’ll do is wondering which school you’ll go to with your outstanding score.

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

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

Should You Purchase The New Enhanced Score Report?

GMACFor anyone who has ever underperformed their goals on the GMAT, the first question they’ve asked is usually “where did it all go wrong?”. And for those who have asked that question since October 1, 2013, or will ask it soon, there may be an answer waiting for you.

The GMAT Enhanced Score Report is here.

This new add-on report, which costs $24.95 USD, will provide you with diagnostic feedback from your official GMAT exam, including such information as:

-Performance (percentile ranking) by question type, with question types including Data Sufficiency vs. Problem Solving; Arithmetic vs. Algebra/Geometry; Critical Reasoning vs. Sentence Correction vs. Reading Comprehension

-Time management by question type, broken down by the same categories above

-Time management by correct vs. incorrect answers for Integrated Reasoning

-Percent of Integrated Reasoning questions answered correctly

So those are the features, but the question remains…is this worth $25? And the answer is a little less concrete than you might like: it depends. Why?

*The report won’t give you question-by-question feedback, so you’ll never know if you got that crazy coordinate geometry problem at #17 right or wrong, and you won’t know which individual problems you spent way too much time on. You’ll get much more aggregate data, which may or may not help.

*If your performance was pretty similar to that of your practice tests – which ought to be the case for most examinees who have taken several practice tests – the report should likely match your expectations. If you’ve prepared well for the test, there shouldn’t be many surprises in that report.

*However, some users will see some VERY enlightening information. Say, for example, you were quite strong on Critical Reasoning and Reading Comprehension (~80th percentile each) but significantly less adept on Sentence Correction (

So who will benefit from the report? Those who have some outliers or anomalies in their performance. If you were 60th percentile on quant, and a combination of 55th, 62nd, 63rd, and 59th on DS, PS, Arith, Alg/Geo, you’re not going to learn very much from that report. But if one area is significantly higher or significantly lower than the others, you’ll learn something.

And so what’s the advice?

-If you’re going to retake the exam, the Enhanced Score Report is essentially a 10% increase on your next registration fee, and has the potential to be pretty enlightening. Especially if you’re likely to spend $25 over the next month on Starbucks or Amazon impulse purchases or anything else extraneous, it’s a good idea to put that $25 toward the score report. You might not learn anything, but the chance that you’ll learn something is substantial enough that you should leave no stone unturned.

-But if you have $25 left in your GMAT budget and the choice is between the Enhanced Score Report or a tool like the GMAT Question Pack or one of the Official Guide supplements, choose the extra practice. If you’ve prepared thoroughly there shouldn’t be too many surprises on that report, and whatever you’d learn you’d have to improve by practicing anyway.

So in sum, GMAT retakers should probably pony up the $25 because the more you know about your performance, the higher the likelihood that you can improve it. Almost all Veritas Prep instructors agree – we want to see those reports from our students! But don’t be surprised if the report only confirms what you suspected. The Enhanced Score Report is a tool to guide your hard work, not a substitute for the effort required to improve.

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

By Brian Galvin

What You Need to Know about Assumption Questions in GMAT Critical Reasoning

When it comes to Critical Reasoning on the GMAT, one question that continues to frustrate people is the assumption question. Quite simply, the question is asking you which answer choice is required to support the conclusion that has been drawn in the passage. To successfully navigate these questions, you should use the Assumption Negation Technique, which requires a negation of the answer choice to determine whether or not it was actually required. More than that, though, the correct answer choice must be within the scope of the question. An answer choice that goes too far will not be the correct answer to the question.

As an example, think about a passage that deals with the Super Bowl. It’s very possible that the passage will discuss how good the Seahawks’ defense is, or how good Tom Brady is as a quarterback. The conclusion could then be something like how the Patriots will likely win (disclaimer: this was written before the Super Bowl). If a question was asked about what assumption is needed to reach the conclusion, the correct answer choice must be about Tom Brady or the Seahawks’ defense, given that’s what was discussed as evidence. If an answer choice discusses the catching ability of Rob Gronkowski or the Patriots’ (alleged) (systemic) pattern of cheating, then it is going outside the scope of the question and cannot be the correct selection.

It is important to note that strengthen and weaken questions may sometimes provide new information, so you should be on the lookout for things that weren’t written verbatim in the text. Nonetheless, for assumption questions, it’s easy to select an answer choice that provides new information but goes outside the scope of what was discussed. A choice that has no basis in the passage is usually a clear indicator of a trap answer.

Let’s look at an example to demonstrate scope in assumption questions:

It is a mistake to give post office employees individual discretion as to when to inspect or open suspicious packages. If individual employees are allowed to open “suspicious” packages without first following a strict protocol, it is only a matter of time before all packages will arrive having already been opened due to some postal employee’s idle curiosity.

The conclusion above is based on which of the following assumptions?

(A)   Postal service managers are the only people with the authority to open suspicious packages.

(B)   Suspicious packages are indistinguishable from all other kinds of packages.

(C)   The efficiency of the postal service will be greatly reduced if more packages are inspected.

(D)   There is currently no protocol in place for the inspection of suspicious packages.

(E)    Postal employees desire to open packages out of curiosity.

This question is asking about which assumption is required for the conclusion, which warns that all parcels will eventually be opened by overzealous mail carriers. While it’s somewhat understandable to be concerned about the privacy of your mail, the author’s fears may be unfounded (I’m more concerned about the NSA). The evidence provided in the passage is about when packages are allowed to be opened and verified. The passage mentions that only suspicious packages are allowed to be opened, but there are protocols in place that dictate when this verification can occur.

For assumption questions, the best strategy is to employ the Assumption Negation Technique and negate each answer choice to see if the conclusion falls down without the negated assumption. This approach is similar to the strategy of knocking down beams in a home to see which one was load-bearing. (Not something I’d recommend). If the conclusion falls down without this assumption, then it was absolutely required. If it changes nothing, then it was purely decorative and can be ignored.

Beginning with answer choice A, let’s negate them and see if the author’s paranoia is still defensible. The negation will be underlined to differentiate the negated form from the original assumption:

(A)   Postal service managers are not the only people with the authority to open suspicious packages.

If this were true, then there might be even more people who could open errant parcels. This makes the author’s argument more likely to be true, as seemingly random people could have authority to open packages. If nothing else, it certainly doesn’t lessen the chances of the author’s prediction coming to be, so this assumption is not required.

(B)   Suspicious packages are not indistinguishable from all other kinds of packages.

This double negation is saying that suspicious packages are easy to distinguish from other kinds of packages. If this were true, the employees would be able to tell which packages were suspicious, but they would nonetheless have the authority to open any package. Therefore, the fact that they can ascertain in most instances what constitutes a “suspicious” package would not necessarily stop them opening other packages. The passage is arguing that postal workers would open everything if given unilateral power, whether the package was deemed suspicious or not. This answer choice is probably the closest incorrect choice, but the scope alerts us to the superfluous nature of this assumption.

(C)   The efficiency of the postal service will not be greatly reduced if more packages are inspected.

This answer choice is discussing how the efficiency of the postal office (which many people think is an oxymoron) would not be affected by increasing the number of inspected packages. While this may quell the fears of some people who assume that more inspections would slow down the service, the author’s argument is primarily concerned with the privacy aspect of the inspections. This answer choice is thus out of scope, as the efficiency of the post office was (somehow) never in question.

(D)   There is currently no a protocol in place for the inspection of suspicious packages.

This answer choice, negated, indicates that there is already a protocol in place for suspicious packages. If this were true, it would actually strengthen the argument, as there would be no reason to give postal workers additional power to open packages. The system would indeed be working fine the way it is, and this argument only demonstrates the author’s point, it does not weaken it.

(E)    Postal employees do not desire to open packages out of curiosity.

This answer choice, by process of elimination, must be the correct choice. However, let’s confirm that it makes sense. If postal employees did not want to open packages out of (idle) curiosity, then the author’s entire argument would fall apart. Indeed, the entire argument relies on the fact that the postal employees will open every package they possibly can. If we could ensure that this was not the case (say with a hypnotic suggestion or some Borg nanoprobes), then the whole argument would become moot. Answer choice E is an assumption required by the conclusion, because without it, the argument falls apart.

On questions such as these, it’s entirely possible to get reeled in by an enticing answer choice. Remember to use the Assumption Negation Technique to verify whether an assumption is actually necessary or whether it just sounds important. The incorrect answer choices provided are designed to tempt you, so keep an eye on the evidence provided in the passage as well. If the answer sounds good, but isn’t based on the evidence provided, then much like the guy at my gym with halitosis, it is out of scope.

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

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

Why You Felt Good on the GMAT Quant Section but Didn’t Score Well

This is a problem that I have seen many times before. It leaves students bewildered because all of the signs that would lead them to expect a lower score are absent. They did not run out of time, they did not have to guess at lots of questions, and they did not feel overwhelmed. Even I have suffered from this a bit, my lowest Quant score came on the exam where I felt most comfortable – and my highest score on Quant came on the exam that felt the worst.

How is it that you can confidentially answer question after question while obviously missing quite a few questions that felt “easy?”

One culprit is the subtlety of the official GMAT questions overall. No other questions do as good a job of luring you into confidently choosing the wrong answer. This can happen on problem solving, but today I would like to focus on Data Sufficiency.

I sometimes refer to Data Sufficiency as “the Silent Killer” because the very structure of the Data Sufficiency question invites you to choose the wrong answer. This is because you do not know that you have forgotten to consider something. There are no values in the answer choices to help you see what you might have overlooked. That is why the person choosing the incorrect answer is often more confident than is the one who got the question right.

As you can see it is often difficult to gauge how you are doing on Data Sufficiency. And because the Quantitative section adapts as a whole, missing these data sufficiency questions results in the computer selecting lower-level questions in problem solving. So the problem solving questions may have seemed easier because they actually were at a lower level.

This is a pattern that I have seen repeated many times on practice exams. Students miss mid-level data sufficiency questions in the first part of the exam. This results in lower level questions being offered, and the student keeps missing just enough problems (of both Data Sufficiency and Problem Solving) to keep the difficulty level from increasing.

The result? A quant section that felt comfortable because most of the questions were below the level that would really challenge the student. This may be what happened to you.

How to avoid this fate:

With Data Sufficiency questions there are no answer choices to provide a check on your assumptions or calculations. You must be your own editor and look for mistakes before you confirm your answer. Fortunately, there are several things you can do:

  1. Think with your pen. Do not presume that you will remember what the question is asking, the facts you are given, or the hidden facts that are implied by the question stem. Note these things on your scratch paper so that you do not forget them. It may seem unnecessary to write “x is integer” or “must be positive” but just think of how dangerous it would be to forget this information!

  1. Do your work early. Rewording the question is a great way to make data sufficiency more fool-proof. For example, it is much easier to comprehend the question “Is x a multiple of 4” than it is to wrestle with the questions “Is x/2 a multiple of 2?” Think about what the question is really asking and re-word it when you can.

  1. Catch mistakes before you submit. Always keep in mind the most common number properties, “positive/ negative” “integer/ non-integer” and “the numbers 0 and 1.” The test makers can really hide these number properties so that even experts could overlook them, so just run through these three number properties on every problem and you will catch lots of your mistakes before you submit.

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

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

Use This Strategy for Fractions and Save Time on GMAT Test Day

One of the most uncomfortable aspects of the GMAT is that you are not allowed to use a calculator for the quantitative section. This is uncomfortable because, throughout your everyday life, you are never more than about 5 feet from a calculator (yes, even in Death Valley). Almost everyone has a cell phone, a laptop, a desktop or a GMAT guru nearby to compute difficult calculations for them. Even high school students are generally allowed their calculators on test day. However, the lack of a calculator allows the GMAT to test your reasoning skills and time management skills much more easily than if you had access to electronic help.

As an example, remember open-book tests. These tests always seemed easier when they were discussed in theory than when they were attempted in practice. An open book test must necessarily test you on more obscure and convoluted material, otherwise the test becomes too easy and everyone gets 100. Closed-book tests, by contrast, can concentrate on the core material and gauge how much preparation each student has put in. Adding more tools only serves to make the test more difficult in order to overcome these enhancements.

With a calculator, asking you to calculate the square root of an 8 digit number or the 9th power of an integer is trivial if you only have to plug in some numbers. However, if you need to actually reason out a strategic approach in your head, you have accomplished more than a thousand brute force calculations would. On the GMAT, the mathematics behind a question will always be doable without a calculator, but the strategy chosen and the way you set up the equations will generally be the difference between the correct answer in two minutes and a guess in four.

Let’s look at a question where the math isn’t too difficult, but can get tedious:

Alice, Benjamin and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8 and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?

(A)   3 / 140

(B)   1 / 28

(C)   3 / 56

(D)   3 / 35

(E)    7 / 40

This is a probability question, and therefore we must calculate the chances of any one event occurring. However, the question is asking about several possibilities, specifically any occurrence where two players win and the third loses (think of any romantic comedy). This means that we have to calculate several outcomes and manually add these probabilities. This is entirely feasible, but it can be somewhat tedious. Let’s look at the best way to avoid getting bogged down in the math:

Firstly, the three players’ are suitably abbreviated as A, B and C (convenient, GMAT, convenient). We therefore want to find the probability that A and B occur, but that C does not occur (denoted as A, B, ⌐C). This represents one of our desired outcomes. However, this is not the only possibility, as any situation where two occur and the other doesn’t is acceptable as well. Thus we can have A and C but not B (A, ⌐B, C), or B and C but not A (⌐A, B, C). The sum of these three outcomes is the desired fraction, so only some math remains.

Let’s do them in order. For (A, B, ⌐C), we take the probability of A, multiplied by the probability of B, and then multiplied by the probability of 1-C. If the chances of C are 2 / 7, then the probability of them not occurring must be the compliment of this, which is 5 / 7. The calculation is thus:

1 / 5 * 3 / 8 * 5 / 7.

In a multiplication, we only care about multiplying the numerators together, and then multiplying the denominators together. There is no need to put these elements on common denominators. The math gives us:

(1* 3 * 5) / (5 * 8 * 7). This is 15 / 280.

There is a strong temptation to cancel out the 5 on the numerator and on the denominator to make the calculation easier, but you should avoid such temptation on questions such as these. Why? (I’m glad you asked). If you simplified this equation, you would get the equivalent fraction of 3 / 56, which is easier to calculate, but since we still have to execute two more multiplications, we will end up adding fractions that have different denominators. This is not a pleasant experience without a calculator, and likely will cause us to revert to our common denominator for all three fractions, which is 5 * 8 * 7 or 280. Additionally, now that we’ve calculated it once, we don’t need to worry about the denominator for the following fractions, it will always be the same. Let’s continue and hopefully this strategy will become apparent.

The next fraction is (A, ⌐B, C), which is equivalent to

1 / 5 * 5 / 8 * 2 / 7. Note that ⌐B is (1 – 3/8)

Executing this calculation yields a result of 10 / 280.

Finally, we need (⌐A, B, C), which is equivalent to

4 / 5 * 3 / 8 * 2 / 7. Note that ⌐A is (1 – 1/5)

Executing this last fraction gives us 24 / 280.

Once we have these three fractions, we must add them together in order to get the probability of any one of them occurring (“or” probability, as opposed to “and” probability”). This is simple because they’re all on the same denominator, so we get 15 / 280 + 10 / 280 + 24 / 280 which is 49 / 280.

Now that we have this number, we can try to simplify it. 49 is a perfect square that is only divisible by 1, 7 and 49, whereas 280 has many factors, but one of them fairly clearly is 7. We can thus divide both terms by 7, and get 7 / 40. Since the numerator is a prime number, there is no additional simplification possible. 7 / 40 is answer choice E, and it is the correct pick on this question.

Had we simplified each probability as much as possible, we would have ended up with 3 / 56, 2 / 56 and 3 / 35. While the addition would not be impossible, it would become much more difficult. In fact, to correctly add these numbers together, you’d have to put them on their least common multiple, which would be 280 again. There is usually no point in simplifying fractions in questions like this because they must usually be recombined at the end. Save time and don’t convert once only to convert back.

The math on this question is not difficult, but having to add together multiple fractions and simplifying expressions can be quite time-consuming. With a calculator, you could simply add the decimals together, regardless of their fractional equivalents. However, the GMAT doesn’t allow you that shortcut on test day (unless you approximate in your head), so you must find a better tactic. The difference between solving all the questions and running out of time on the math section is often the approach you take on each question. Keep up a consistent strategy and you’ll solve a large fraction of the questions you face on test day.

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

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

Ariana Grande’s Real Problem with the GMAT

As a GMAT aficionado, I often find GMAT themes in everyday things. This is what happened last week when I was listening to the radio and Ariana Grande’s “Problem” started playing. I’d heard the song before, and despite its catchy melody, there is a glaring grammatical error in the chorus. This may not be that surprising: songs in general are dubious sources of grammar to begin with, and R&B songs often take additional liberties with their lyrics (Timbaland’s “The Way I Are” jumps to mind). However this error is the kind a lot of people make in their daily speech, so I figured I’d use it as an opportunity to improve our grammatical skills beyond what we hear on the radio.

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

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

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

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

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

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

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

A)     in 20% fewer teachers and 10% less

B)      in 20% fewer teachers and 10% fewer

C)      in 20% less teachers and 10% less

D)     with 20% fewer teachers and 10% fewer

E)      with 20% less teachers and 10% less

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

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

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

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

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

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

Calculating Perfect Squares on the GMAT

The GMAT is an exam that evaluates how you think. The test is designed to measure your reasoning skills and gauge how successful you will be in business school. This means that the test is not simply trying to ascertain how much you already know. This is similar to the mantra of “Give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime”. If you happen to already know that 144 is 12^2, then any question that asks about this specific number becomes much easier. However, if the exam starts asking about 13^2 or 14^2, and you only know 12^2, then you must find some method to take your knowledge and apply it to new and unscripted problems.

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

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

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

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

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

225, or 15^2, is the first perfect square that begins with two 2s. What is the sum of the digits of the next perfect square to begin with two 2s.
(A) 7
(B) 9
(C) 13
(D) 16
(E) 21

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

First things first, the next perfect square cannot possibly be 22x. The next perfect square after 15^2 is 16^2, which is 256 (you can get here any way you like). This means that the next perfect square has to be 22xx. This gives us an order of magnitude to shoot for. Until we have a better idea on which numbers to hone in on, let’s use easy numbers to get a sense of where we’re going:
20^2 = 400
30^2 = 900
40^2 = 1,600
50^2 = 2,500

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

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

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

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

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

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

Warning: Don’t Fall Into the C Trap on Data Sufficiency Questions

Studying for the GMAT can take over your life. I’m sure many of you are nodding your heads as you read this. If you’re not, you probably haven’t gotten there yet. I sincerely hope that you never do, but it is an almost unavoidable part of studying for this test. Eventually, you start correcting artists in songs (I got one less problem without you… more like one fewer problem) and wondering if your table number is a prime number (how about table 51… oops that’s divisible by 3). The first time you catch yourself using a GMAT specific term, you know you’re really deep in studying for this exam.

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

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

Let’s look at question that highlights this issue:

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

(1) No cats were adopted on Tuesday.

(2) 4 dogs were adopted on Tuesday.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How to Use Your Time Wisely on Reading Comprehension GMAT Questions

On the verbal section of the GMAT, students invariably spend more time on Reading Comprehension questions than on either Sentence Correction or Critical Reasoning problems. In fact, I’ve seen score reports where people spent more time on Reading Comprehension than on the other two question types combined! Students spend a lot of time on these passages because they are consistently packed with pointless information, run-on sentences and dense technical jargon. Attempting to untangle these passages can lead to a lot of frustration for test takers (Fortunately, there’s an app for that).

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

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

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

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

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

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

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

According to the passage, which of the following contributed to the inability of the workers at Lowell to have their demands met?
(A) The very young age of some of the workers made political organization impractical.
(B) Social attitudes of the time pressured women into not making demands.
(C) The Lowell Female Labor Reform Association was not organized until 1844.
(D) Their families depended on the workers to send some of their wages home.
(E) The people who were most sympathetic to the workers lived outside of New England.

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

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

Rereading this paragraph, we go through a description of what prompted the strike and then how many people participated. Directly following this is the line: “However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families”. This was their downfall: they needed money to support themselves and their loved ones (unsurprisingly the downfall of most strikes). The wording used may be somewhat obtuse, but the context makes it quite clear that the issue was money. Going through the answer choices, D is the only option that is remotely close to what we want, and is therefore the correct answer.

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

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

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

Why Does the GMAT Test Geometry?

One topic that always makes me think on the GMAT is geometry. It’s not that geometry is particularly hard, or even particularly easy, but rather that it’s particularly irrelevant! Having done an MBA in the past few years, I can virtually guarantee you that you will never have to calculate the area of a rhombus or the volume of a cone during your graduate studies. It’s possible that you have to calculate various geometric shapes in your career after graduating (say you run an ice cream shop!), but during your education the entire discipline seems somewhat superfluous.

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

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

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

If the radius of a circle that centers at the origin is 5, how many points on the circle have integer coordinates?
(A) 4
(B) 8
(C) 12
(D) 15
(E) 20

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

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

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

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

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

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

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

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

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

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

A Closer Look at Parallel Structure on GMAT Sentence Correction Questions

The holiday season is upon us in North America, as many families unite for Thanksgiving, some decadent shopping, and the imminent Christmas season. While Thanksgiving and Christmas are independently two of the biggest holidays of the year, the fact that they always come together and are so habitually linked makes me think of the GMAT (yes a lot of things make me think of the GMAT, it’s what I do). Just as the thought of Christmas makes a lot of people think of Black Friday deals and line ups at their local stores, some elements on the GMAT are as inextricably linked together.

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

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

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

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

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

(A) act as a buffer, so that it absorbs
(B) act like a buffer, so as to absorb
(C) act as a buffer, absorbing
(D) acting as a buffer, absorbing
(E) acting like a buffer, absorb

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

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

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

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

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

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

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

How to Manage Unmanageable Numbers on the GMAT

When going through the quantitative section of the GMAT, you will often be confronted by numbers that are, shall we say, unwieldy (some people refer to them as “insane”). It is common on the exam to see numbers like 11!, 15^8, or even 230,050,672. Regardless of the form of the number, the common mistake that many novice test takers make is the same: They try to actually solve the number.

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

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

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

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

For integers x, y and z, if ((2^x)^(y))^(z) = 131,072, which of the following must be true:
(A) The product xyz is even
(B) The product xyz is odd
(C) The product xy is even
(D) The product yz is prime
(E) The product yz is positive

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

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

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

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

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512

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

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

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

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

10 of Your Pressing GMAT Questions Answered by a Veritas Prep Expert

The following interview comes from Top GMAT Prep Courses. Top GMAT Prep Courses recently had the opportunity to conduct a Q&A session with Chris Kane, one of Veritas Prep’s most seasoned GMAT instructors, to inquire about the GMAT and get his take on 10 great questions that many MBA candidates would like to ask with regards to GMAT prep courses and useful tips on how to be successful at achieving their desired GMAT score.

What motivates you to be a GMAT instructor?

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

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

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

Click here for Chris’ other two points of advice.

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

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

Read the rest of the interview here!

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

Choosing from 2 Answer Choices in GMAT Critical Reasoning

In life, you are often given binary choices. This is true even if the word binary isn’t something you recognize right away. Binary comes from the Latin “bini”, which means two together, and is used to regroup decisions in which you have exactly two choices. On forms, you might see categories such as “smoker” or “non-smoker”, and you are prompted to answer exactly one of the options. At a restaurant, you might get asked “Soup or salad?” (super salad??), and you are expected to make a decision as to which appetizer you want. Very frequently, these two choices cover the entirety of your options. There is no third option to select.

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

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

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

Let’s look at an example:

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

Which one of the following can be properly inferred from the passage above?
(A) All bad writers can become better writers
(B) All great writers had to be taught to become better writers.
(C) Some bad writers can never become great writers.
(D) Some bad writers can become great writers.
(E) Some great writers can be taught to be even better writers.

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

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

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

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

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

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

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

1 Simple Way to Solve Puzzling GMAT Questions

If you’ve ever built a puzzle, you probably know that you can’t expect to start at a certain point and build the entire puzzle without moving around. You may find two or three pieces that fit together nicely, but then you find three pieces that fit together nicely somewhere else, and then work to connect these disparate sections.

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

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

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

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

In the sequence a1, a2, a3, an, an is determined for all values n > 2 by taking the average of all terms a1 through an-1. If a1 = 1 and a3 = 5, then what is the value of a20?
(A) 1
(B) 4.5
(C) 5
(D) 6
(E) 9

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

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

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

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

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

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

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

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

Think Inside the Box on Tricky GMAT Questions

When dealing with questions that ask us to compartmentalize information, there are two major sorting methods that we can use on the GMAT. The first, and perhaps more familiar concept, is the Venn diagram. This categorization is very useful for situations where information overlaps, as it allows a visual representation of multiple categories at once. However, if the information provided has no possible overlap, such as indicating whether something is made of gold or silver, or if they’re male or female (Bruce Jenner notwithstanding), the preferred method of organization is the matrix box.

The advantage of the matrix box is that it highlights the innate relationships that must be true, but that are not always easy to keep track of. For instance, if a box contains 100 paperclips, some of which are metallic and some of which are plastic, then if we find 40 paperclips made of metal, there must necessarily be 60 that are made of plastic. The binary nature of the information guarantees that all the elements will fall into one of the predetermined categories, so knowing about one gives you information about the other.

The matrix box allows you to catalogue information before it becomes overwhelming. Anyone who’s studied the GMAT for any length of time (five minutes is usually enough) knows that the exam is designed to be tricky. As such, questions always give you enough information to solve the problem, but rarely give you the information in a convenient manner. Setting up a proper matrix box essentially sets you up to solve the problem automatically, as long as you know what to do with the data provided.

Let’s look at an example and what clues us into the fact that we should use a matrix box.

Of 200 students taking the GMAT, all of them have college degrees, 120 have been out of college for at least 3 years, 70 have business degrees, and 60 have been out of college for less than 3 years and do not have business degrees. How many of them have been out of college for at least 3 years and have business degrees.

A) 40
B) 50
C) 60
D) 70
E) 80

The principle determinant on whether we should use Venn diagrams or matrix boxes is whether the data has any overlap. In this example, it’s very hard to believe that a student could both have a business degree and not have a business degree, so it looks like the information can’t overlap and a matrix box approach should be used. Before we set up the matrix box, it’s important to know that the axes are arbitrary and you could put the data on either axis and end up with essentially the same box. We can thus proceed with whichever method we prefer. The box may look like what we have below:

Business Degree

No Business Degree

Total

At least 3 years

Less than 3 years

Total

Without filling out any information, it’s important to note that the “Total” column and row will be the most important parts. They allow us to determine missing information using simple subtraction. If we have the total figures, as little as one piece of information in the inside squares would be enough to solve every missing square (like the world’s simplest Sudoku). Let’s populate the total numbers provided in the question:

Business Degree

No Business Degree

Total

At least 3 years

120

Less than 3 years

Total

70

200

With these three pieces of information, we can fill out the remaining “Total” squares by simply subtracting the given totals.

Business Degree

No Business Degree

Total

At least 3 years

120

Less than 3 years

80

Total

70

130

200

Now all we would need to reach the correct answer is one piece of information: any of the remaining four squares. Luckily the question stem will always provide at least one of these, as the problem is unsolvable otherwise. Problems may be tricky and convoluted on the GMAT, but they will never be impossible. Looking back at the question, there are 60 students who have been out of college for less than 3 years and do not have business degrees. Plugging in this value we get:

Business Degree

No Business Degree

Total

At least 3 years

120

Less than 3 years

60

80

Total

70

130

200

Using a little bit of basic math we can turn this into:

Business Degree

No Business Degree

Total

At least 3 years

70

120

Less than 3 years

20

60

80

Total

70

130

200

And finally the completed:

Business Degree

No Business Degree

Total

At least 3 years

50

70

120

Less than 3 years

20

60

80

Total

70

130

200

The question was asking for how many students have been out of college for at least 3 years and have business degrees, but using this method we could solve any potential question (Other than “What is the meaning of life”?). Since the number of students with business degrees who have been out of college three years or more is 50, the correct answer will be answer choice B.

In matrix box problems, setting up the question is more than half the battle. Correctly setting up the parameters will ensure that the rest of the problem gets solved almost automatically, and all you have to do is avoid silly arithmetic mistakes or getting ahead of yourself too quickly. Remember that if the information doesn’t overlap, it will likely make for a good matrix box problem. On these types of questions, don’t be afraid to think inside the box.

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

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

Should I Cancel My GMAT Score? (Hint: Probably Not)

Last year, I wrote an article for this blog discussing the pros and cons (and pros and cons and pros) of cancelling your GMAT score. At the time, you had to sit through an entire 3+ hour exam, go through every question asked and then be offered the possibility of cancelling your score without ever knowing what your grade would have been.

Needless to say, many people opted to cancel their scores out of fear that a disappointing result would reflect badly on them and hinder their chances of being accepted into the school of their choice. The overall takeaway of my article was that most people felt that they did badly on the GMAT, and therefore tended to cancel their scores more often than they should have.

Lo and behold, in the summer of 2014 the GMAC (the FIFA of the GMAT) decided to change this policy and allow students to see their scores before deciding whether or not to cancel them. This decision was met with jubilation and applause (by me) from most prospective students, as this situation was entirely preferable to the previous circumstances. However, some students still are unclear when they should cancel their scores and when they shouldn’t. As such, I figured this would be a golden opportunity to revisit this topic and discuss cancelling your scores under the new world order.

First, let’s begin with the bad news. If you cancel your score, you are not refunded your 250$ fee for taking the exam. Nor can you retake the exam the next day; the same 31 day waiting period applies. Perhaps most jarringly, your record will still indicate that a score was cancelled, meaning that there will still be some record of the GMAT having been taken, just no accompanying score. Finally, if you do decide to cancel your score, you can subsequently change your mind and ask for the score to be reinstated, although this will incur an additional cost of 100$, and must be done within 60 days of the test date.

Let’s begin with some valid reasons why someone would consider cancelling their scores. Firstly, if you sleep very badly the night before or something goes very wrong in your personal life (worse than Menudo breaking up), you may be incapable of concentrating properly and your score will consequently suffer. In these situations, when you know you can do significantly better, it may be a good idea to cancel your score. Another instance would be if you took the exam and got some score, perhaps a 600, and then retook it and scored 450, a considerably worse result. Since the goal is to try and show improvement from one GMAT to the next, a marked decline could send the wrong message to the schools of your choice. This is another instance where cancelling your score may be a legitimate option.

If we explore some of the situations where it may be less advisable to cancel your score, we can start with a good rule of thumb: If it’s your first GMAT, you should (practically) never cancel your score. Why? Because if you cancel your score, you remove your baseline GMAT score. The best case scenario may be to take the exam once, ace it, and never look back (or possibly go back to teach it years later), but the reality is most people end up taking this exam more than once. The current average number of times someone takes the GMAT is about 2.7, meaning that many people take the exam two or three times before getting the score they want. If you’re aiming for a 650, and only get a 550 on the first try, then subsequent scores will demonstrate perseverance and determination, two skills sought after in business professionals. Cancelling your first score will only raise questions as to how badly it went (210?) and why you elected to remove the only thing on an otherwise blank canvas.

Sometimes, you score a 600 the first time, decide you want a 650, and retake the exam and only get a 610 or 620. This shows some improvement, but many people become depressed that it doesn’t show enough improvement, especially if they studied for several months to achieve this moderate increase. Again, cancelling this updated score will only raise questions as to how badly the test went, and a small improvement is still an improvement. Most GMAT schools take the best GMAT score as their reference, so even a 10 point progress from 600 to 610 could be enough to make a difference in your application. The same principle applies if your score went down slightly, say to 580. While a slight decline isn’t cause for a celebration, it’s a minor hiccup that demonstrates that you can consistently stay within the same range. Also, cancelling a slight drop opens the possibility that you did very badly on this second attempt and opted to cancel the score, artificially exaggerating how poorly the test actually went.

Sometimes, the idea of cancelling your score will come up before you’re even done with the test. Halfway through the verbal section, when you’re wallowing in the fact that you guessed the last three questions, your brain may take solace in the idea of cancelling the exam score. Sometimes you’ll contemplate it during a difficult stretch in the quantitative section (sometimes even on question 1!). The fact that you can now see your score before deciding whether to cancel it is a huge benefit in your choice as it removes the guesswork from the equation. No matter how badly you think you’re doing, at least you can see the score, make a decision, and even potentially reverse that decision within a couple of months.

When it comes to cancelling scores on the GMAT, the rule of thumb is that you shouldn’t cancel your score unless some “force majeure” or act of God came into the equation. The rule change allows us more flexibility in our decision making process, but the same factors must still be considered. If this is the first time you take the exam, your score is higher than any of your previous scores or if you just feel like you’re stinking up the exam (figuratively, not literally), you probably shouldn’t cancel your score. If your score truly is abysmal, then you can take a page from Pacific Rim and say “We are cancelling the apocalypse!” and be confident in your decision. The GMAT is designed to be tricky, but at least all the guesswork about cancelling your score has been removed for 2014 and beyond.

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

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.

How Can I Improve My Focus on the GMAT?

A student recently asked, “How do I learn to focus long enough to make my study sessions worthwhile? While studying for the GMAT I can only study for about an hour at a time.”

My response is, “This is a clearly a problem, not just for study sessions but also for the GMAT itself which requires 4 straight hours of focus.

Luckily, there are simple ways to improve your focus, and these techniques will not only allow you to focus as you study for longer periods of time, but will also have other benefits throughout your life. I have been doing a lot of research into brain science and the GMAT recently, and one thing that comes up in even book or article that I read is meditation/mindfulness. The latest scientific research supports the conclusion that the number one way to increase your ability to focus is to begin a simple meditation and mindfulness practice. 

Meditating is much easier than you think!

When I mention “meditation” people think that I am talking about sitting in an uncomfortable position and meditating for hours at a time. They assume that it has something to do with adopting a particular religion or belief. Nothing could be further from the truth. Meditation and mindfulness basically mean being present wherever you are and not letting your mind wander. In other words, focusing!

In the last several years I have read many books and articles on topics like the ability to focus and how to be more productive and happy – The crazy thing is that every author researching these topics has mentioned meditation and mindfulness. You cannot be focused, you cannot be productive, and it turns out that you cannot even be happy if you do not learn to pay attention to where you are and what you are doing.

How to practice mindfulness? The best-seller author Tich Naht Han talks about brushing your teeth as a chance to focus on the ritual of brushing. Washing the dishes is a chance for you to be present and focus on the dishes – rather than basically ignoring the washing or brushing as your mind races everywhere (this is what we normally do)!

Mindfulness really just means that you are paying attention to where you are and what you are doing (yes, it does sound a little like Yoda from Star Wars). So if you are walking your dog that is what you are focused on, not the things at work you failed to complete today. And if you are at work then give your full attention there and do not worry about the fact that you need to walk the dog later!

“Meditation” simply means that you are taking mindfulness to another level. You are focusing on one thing and noticing when your mind wanders. It is a simple as that. You can meditate on the sunset and really notice the colors as they change. You can meditate on a song and really hear the notes. And as mentioned above you can meditate on your toothbrush or your dish scrubber, too.

One of the most common meditations is to sit quietly in a comfortable chair (or walk slowly if you prefer a walking meditation) and focus on your breathing. Simply say “IN” as you breathe in and “OUT” as you exhale. Do not try to prevent yourself from thinking about other things. Just notice when your mind does wander and bring it back to the breath again. So you are sitting in a chair and softly saying “IN” and “OUT” and suddenly a thought comes into your mind “I should be studying for the GMAT!” Just notice the thought and bring your focus back to the breathing. Then a thought pops up “I am wasting my time sitting here” again just acknowledge it and bring your attention back the breathing. Do this for just 5 minutes and believe it or not you will probably have better focus throughout the rest of the day.

In her ground-breaking work “The Willpower Instinct” Kelly McGonigal, Ph.D. writes of a student who had LOTS of trouble focusing. He was concerned that meditation would be impossible for him – this is because he thought that meditation required an empty mind for long periods of time. His meditation was really bad! He was constantly having thoughts pop up and had to keep bringing himself back to the breathing. He felt like he was “failing” at meditation!

Yet this student found that just 5 minutes of what anyone would consider very bad meditation had great results for him. The rest of the day he was much more focused. You can try five minutes of meditating each day right? Maybe first thing in the morning? 

The scientific research shows the impacts that small amounts of meditation actually have on the brain. From “The Willpower Instinct” (page 25)

  • Just 3 total hours of meditation (so 5 minutes a day for 6 weeks) led to scientifically significant improvements in attention and self-control!
  • Just 8 weeks of daily meditation led to increased self-awareness and increased gray matter in the areas of the brain that control your ability to focus.
  • Just 11 hours total of meditation led to changes in the brain that were visible on brain scans.
  • Meditation actually increases blood-flow to the areas of the brain that help us to focus and to have self-control!

And one more thing – your happiness depends on your ability to focus on what you are doing! A recent study by Harvard psychologists found that a wandering mind was correlated with unhappiness. In fact, the actual activity that a person was doing had less impact on their level of happiness than did their focus (or lack of focus) on the current activity. Lack of focus seems to lead to lack of contentment. (Source Harvard Gazette)

So you can actually be very content studying the GMAT, if you can just cultivate your ability to focus on it!

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

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

Answer the Why in Reading Comprehension GMAT Questions

The most common question type that people tend to waste time on is Reading Comprehension. More than any other question type on the GMAT, students report reading and rereading the same sections of a passage, only to find themselves at the bottom of the page having retained no information. There are many reasons for this, from fatigue to mental inertia to daydreaming about the end of this test. However, it’s fairly common to have not internalized all the information in the passage, and still be able to answer the question asked.

Why would this be? (Rhetorical question) The passage may discuss many different facets, but each question is typically about one specific thing. As such, you don’t need to know everything; you only need to know about the information being asked in the problem. Better than that, the questions on Reading Comprehension passages can be categorized into four broad categories. This means that you can prepare for any question that could be posed, even if you haven’t read a word of the passage yet (like book reports in high school).

Today I’d like to delve deeper into one of the question types: Function questions. Function questions, like an inquisitive toddler, seek only to ask “why”. Why would the author say this? Why would this issue be mentioned? Why would the author use that specific word? The question is more interested in asking you “why” than in asking you “what”. In these instances, we must determine why something was mentioned, be it a word or a sentence, and what function it served in the passage.

The first strategy on these questions is always to read the surrounding sentences. The context often provides the framework for the passage or word in question, and helps explain it in a larger sense. The most important words will be contained in the sentence before or after what you’re being asked to evaluate, but the entire paragraph may be relevant to the issue. We expand our search in concentric circles from the epicenter and evaluate the entire context in order to ensure we capture the essence of what’s being asked.

Let’s look at an example of a function question and how to approach this type of Reading Comprehension question. As on the exam, we will begin with a passage and then the question:

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

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

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

So after a lot of text (340 words), we can finally look at a function question. However, a rudimentary understanding of the passage would be helpful, so let’s can sum up some of the main elements of this text before proceeding. The passage is concerned with worker rights in 1820s at the Lowell Textile Mills, and at one point, these workers went on strike for better conditions. In the end the women who worked there couldn’t do much for themselves but their efforts led to many other workers acquiring better rights, and their legacy is unquestionable (also they may have founded LMFAO). Now that we understand the broad strokes of the passage, let’s look at the question:

The author uses the word “ironically” in the 1st paragraph to indicate that
(A) None of the people who ran the Lowell Mills expected that the workers would organize to express dissatisfaction with working conditions.
(B) The women who worked at the Lowell Mills did not realize how fortunate they were to work at such a place.
(C) It could be considered surprising that an early effort to demand better working conditions began in an environment that was especially designed to promote worker satisfaction.
(D) The people who created the working environment for the women at the Lowell Mills did not really understand what it was they needed.
(E) It was unusual for women workers of the time to organize, regardless of their work environment.

This question is asking about a specific word in the first paragraph, so we can already get a sense that correctly answering this question will hinge entirely on what we retain from the first paragraph. This would be an ideal opportunity to go back and reread the first paragraph (go ahead, I can wait). Apart from discussing how young the women were, the paragraph spends a lot of time going over the conditions of the workers. Specifically, the conditions seemed designed to assuage any fears about the workers’ condition. After several lines about how great the conditions were, and then states that “ironically, it was here that dissatisfaction with the conditions brought about a strike”

There’s a definite disconnect between extolling the features of the slave labor textile mills, and the fact that people actually revolted. The connection is that it’s ironic that a strike would begin here, of all places, as everything was designed to promote worker satisfaction. That’s our prediction, and one of the answer choices should more or less match that prediction. Looking at them one by one we can determine which answer is correct:

(A) None of the people who ran the Lowell Mills expected that the workers would organize to express dissatisfaction with working conditions.

This is close but it’s not about the organizer’s expectations, it’s about the fact that these conditions were likely better than everywhere else. Also the use of the word “none” is strong language and should raise eyebrows. What if one person expected it but nine didn’t? Would it still be valid? It wouldn’t be, which means this choice is incorrect.

(B) The women who worked at the Lowell Mills did not realize how fortunate they were to work at such a place.

How fortunate they were to be working long hours for low wages? Granted other jobs may not have been any better, but the author’s tone here is not this aggressive or patronizing. We cannot defend this choice.

(C) It could be considered surprising that an early effort to demand better working conditions began in an environment that was especially designed to promote worker satisfaction.

Bingo, this perfectly matches our prediction and will be our correct answer. We will evaluate the two others for completeness’ sake, though.

(D) The people who created the working environment for the women at the Lowell Mills did not really understand what it was they needed.

This may or may not be true, but it wouldn’t be ironic. (We could solve this issue with some sensitivity training!) This choice is incorrect.

(E) It was unusual for women workers of the time to organize, regardless of their work environment.

This is true, but again, it is not ironic. The irony is that the conditions were comparatively good, not that it was women organizing together. This choice is incorrect.

It’s important to remember that for many Reading Comprehension questions, having a full 360° understanding of the passage is not required to get the correct response. In this instance, it only took the information contained in the first paragraph to determine that the correct answer was C. Often, simply understanding a single paragraph or sentence can unlock the answer and allow you to move to the next question.

For function questions, the immediate context needs to be evaluated and then the function of the word (or paragraph) becomes apparent. I will delve into the other question types in subsequent blog posts, but for now hopefully you can practice putting the “fun” in function questions.

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

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

4 Things You Control on GMAT Test Day

I recently had the chance to answer a question about overcoming Test Anxiety on the GMAT. The test-taker wanted to know how to avoid being so anxious on test day and how to stop obsessively thinking about the score before and even during the exam itself.

I wrote, “Your job on test day is to focus on the question in front of you. Not to guess at what your score might be or continually estimate how much time you have left per question.

Your anxiety is probably a result of being “at war with the present moment.” In other words, your anxiety is because you want the GMAT to already be over with the result already known. But you know that this cannot happen. You must take the test before you can get the score. This desire to skip over the actual exam and wanting to be done with the exam and know the score, this is the source of the anxiety.

If you had told yourself that you will enjoy the experience then there would be no anxiety. If you have tickets to a movie that you have been waiting to see you do not have anxiety but anticipation. You are not wanting to done with the movie, you are excited for it to begin. However, if you have major surgery scheduled, then you can understandably wish that it was already over and recovery started.

However, the GMAT is not like undergoing surgery. The only pain involved is the pain that we put on ourselves. Nothing bad is going to happen to you in that room. You are not in danger of physical harm or pain. The anxiety is based on the worry that you might not get the score that you want.

But here is the question…does it help to worry about it? 

Did it help you on that last practice test to be worried about your Quant score while still taking the verbal portion? The answer is “no.”

Anxiety ALWAYS comes from being focused on the result rather than the process. This is why the fans of sports teams are so much more anxious than the players! The players are focused on the process, they get to play the game and enjoy the game and influence the outcome. The fans are usually only happy if the team wins and as spectators they cannot even participate, so they are focused on the end result and that creates extreme anxiety.

It is never good in life to be focused more on the result than the process.

Here is what I would hope that you and others can say, “I will do my best on the exam and I will enjoy the challenge. I am looking forward to proving what I can do. I have no control over the result but I have 100% control over my effort, so I will focus on giving my best effort and the score will take care of itself.”

This may sound unrealistic but people do this every day in all areas: artists, athletes, writers, chefs, entrepreneurs, and others. And here is the secret – those who are focused on the process and taking care of the parts they can control are the happiest, least stressed, and yes, most successful.

So on test day YOU take care of

1) Being focused on the question in front of you at that time

2) Not getting distracted by the timer and questions about your score

3) Giving your best effort and really be there in each moment

4) Enjoying yourself!

and the COMPUTER will take care of the score. That part is not up to you.

Can you do that? If so you can have a much more enjoyable experience and the side effect will be a higher score in the end.

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

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

Understanding 1337 GMAT Logic

One of the most difficult tasks on the GMAT is to properly interpret what the question is really asking. The GMAT is loaded with dense terminology, accurate but irrelevant prose and confusing technical jargon (and that’s just the instruction page!) The verbiage is dense on purpose, with the deciphering of the information part of the skills being tested. And since this task only gets more challenging as you get more tired throughout the exam, it’s important to recognize the vocabulary used on the GMAT. To borrow from geek culture, you need to understand the GMAT 1337 speak.

For those unfamiliar with 1337, it is known as “leet” or “leetspeak” wherein English alphabet letters are replaced by the number that resembles them the most. It uses 1 for L, 3 for E and 7 for T, allowing the number 1337 to stand in for leet, cacographic shorthand for “elite”. (Think of it as pig Latin for the 21st Century). In essence, some people have devised a sublanguage of English that is hard to read for the average person, but very easy to understand for anyone versed in the language’s rules. The same logic can be applied on GMAT questions.

Many terms that you’ll encounter on the GMAT are commonplace in math milieus, but most GMAT students don’t spend much time in such environments. Almost all students have also learned many of the terms long ago, like quotient and decimal, but have since forgotten their definitions because they don’t use them in everyday situations. Other concepts, like Data Sufficiency, only really exist on the GMAT and are not used in the same manner in the real world. This melange of issues can sometimes make it feel like the exam is speaking a language you don’t.

The ideal situation would be to avoid encountering any new or exotic word on test day, which hopefully means you’ve seen all of them during your test preparation. Moreover, simply understanding what each individual word means isn’t enough either, the entire meaning of the sentence must be clear in order to get the correct answer. As always, practice makes perfect, so let’s look at a sample GMAT problem and put the pieces together:

If R and S are positive integers, can the fraction R/S be expressed as a decimal with only a finite number of nonzero digits?

(1)    S is a factor of 100

(2)    R is a factor of 100

(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.

For many students, a question worded in this way is dreadful. The question is asking about two positive integers, R and S, and what happens if we divide one by the other. Could the resulting fraction be expressed as a decimal, and if so, would that decimal have a finite number of nonzero digits?

Let’s tackle these issues one at a time. If we divide R by S, could the fraction be written as a decimal? Yes, say the fraction were 2/3, this could be rewritten as 0.666… However this decimal would go on forever with 6’s, as opposed to the fraction 2/4 which would be rewritten as 0.500 and would stop there. The second part of this question is asking us to make this distinction: does the number continue on forever or does it have a finite number of digits after which it is completed. A number like 2/3 continues with an infinite number of 6’s, whereas 2/4 culminates in a finite number of nonzero digits.

Once you understand exactly what the question is asking for, it becomes much simpler to answer it. We can answer “no” if we find a decimal that goes on to infinity (and beyond). We can answer “yes” if the decimal ends at a specific point. We can determine a few simple examples in our heads (1/3, ½, ¾, etc) and then look at statement 1.

Statement 1 tells us that integer S (the denominator) is a factor of 100. A factor means that I can divide 100 by an integer and get another integer, so 1, 2, 4, 5, 10, 20, 25, 50 and 100 are all factors of 100. It wouldn’t take too long to test that every one of these nine numbers, as the denominator, will end in a finite point. Logically, this is because the prime factorization of 100 is 2^2 * 5^2, and therefore all the factors of 100 will be some multiples of 2’s and 5’s, both of which are finite decimals (0.5 and 0.2, respectively). Try as you might, any numerator over 2 will end in x.0 or x.5, and any numerator over 5 will end in x.0, x.2, x.4, x.6 or x.8 (next five series of X-box consoles?). Since it is impossible to get an infinite decimal with these denominators, statement 1 will be sufficient to say the decimal will definitely end.

Statement 2 tells us that integer R (the numerator) is a factor of 100. This means that R can be the same 9 options we had for statement 1 (1, 2, 4, 5, 10, 20, 25, 50 and 100), but it doesn’t provide the same amount of help as defining the denominator does. If the numerator is 1, then the denominator can be 2 (finite) or 3 (not finite) and I’d have completely different answers. For the same reason that the numerator didn’t matter in statement 1, it doesn’t matter in statement 2, either.

If statement 1 gives us a definitive answer and statement 2 can go either way, then the correct answer to this question must be answer choice A. However getting the right answer is dependent on first understanding the question being asked. Just as with any language, maximum exposure will lead to maximum comprehension and retention, even if sometimes the terms seem peculiar. Remember that if you speak the GMAT’s language on test day, you’re more likely to get a 1337 score.

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

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

1 Important Rule for GMAT Sentence Correction

Some sentence structures seemingly stupefy scholarly students. One of the main reasons the GMAT chooses to test logic through sentence correction is that the rules of grammar are much more flexible than most students realize. We (hopefully) remember some of the basic rules of sentences. Sentences should have a subject and a predicate, but you can often shorten sentences in specific contexts. Like this. The rules we’ve learned in high school are relevant, but (to paraphrase Pirates of the Caribbean) they’re more like guidelines.

The one “rule” I’d like to discuss in particular today is the notion that a sentence must always be in the same tense from beginning to end. This parameter is helpful and applicable in most situations, but it is in no way a restriction that can never be circumvented. In the absence of other incentives, it makes sense as a de facto plan, but it doesn’t have to be followed blindly. It’s like taking the subway to work and getting off at the station closest to your work. By default, you should get off at that station, but that doesn’t mean you can’t detour to a different station to pick up your boss’ favorite breakfast once in a while.

In a typical sentence, randomly shifting tenses doesn’t make any sense. Consider a sentence like “Ron watches Frozen on repeat and liked it when Elsa sings” (#Frozen). This sentence doesn’t make sense because it jumps from the present tense of watching the movie to the past tense for liking and then back to the presence for the singing. This sentence would have to be “Ron watches Frozen on repeat and likes it when Elsa sings” or “Ron watched Frozen on repeat and liked it when Elsa sang”. Either alternative provides a cohesive sentence that illustrates Ron’s adulation for animated movies.

However not all sentences are tied to the default structure of always maintaining the same verb tense. The meaning of the sentence will dictate the verb tense, so meaning must always be considered when considering possible answer choices in sentence correction. A sentence could read: “Ron beams with pride when he recalls how Frozen won best animated song at the Oscars”. The sentence discusses Ron’s present pride when thinking back to an event that happened in the past, so the fact that the third verb is in the past makes sense with the meaning of the sentence. The pride actively comes whenever he recalls the one specific moment in the past (performed memorably by Adele Dazeem).

Let’s look at an example of how varying verb tenses shouldn’t slow us down on an actual GMAT problem:

Attempts to standardize healthcare, an important issue to both state and national officials, has not eliminated the difference in the quality of care existing between upper and lower income families.

(A) Has not eliminated the difference in the quality of care existing
(B) Has not been making a difference eliminating the quality of care that exists
(C) Has not made an elimination in the quality of care that exists
(D) Have not eliminated the difference in the quality of care that exists
(E) Have not been making a difference eliminating the quality of care existing

This sentence has more issues than simply verb tense, as we can quickly identify a 3-2 split between has and have in the first word. Simply being able to determine which of these elements is correct will eliminate at least two choices, so it’s the first decision point we should tackle.

The modifier “…an important issue…” can be ignored for the purposes of identifying the subject in this sentence. Thus the sentence essentially reads “Attempts to standardize healthcare has not eliminated…” which highlights the fact that “Attempts” is the subject, and thus the verb should be plural instead of singular. This means that answer choices A, B and C can all be eliminated. The correct answer must be either choice D or choice E.

Looking at answer choice D: “Attempts to standardize healthcare… have not eliminated the difference in the quality of care that exists…”we may notice the verb tense discrepancy I mentioned earlier. The sentence describes issues in the past, but then mentions their ramifications in the present. This is acceptable because the meaning of the sentence is preserved. Attempts to make changes in the past have not yet had the desired effect in the present. Many students eliminate answer choice D because of the verb tense issue, but this is not a valid reason as the sentence structure is logical. Let’s look at answer choice E and see if we can eliminate it and leave D as the last answer standing (coming to NBC this fall).

Answer choice E: “Attempts to standardize healthcare… have not been making a difference eliminating the quality of care existing” is perhaps more tempting because the verb is a participle (existing). However the meaning of this sentence changes from the original meaning, as the attempts now do not make a difference in eliminating the quality of care. This is much worse than the original intent, and can be eliminated because of the meaning alteration alone. Answer choice E is incorrect, and thus the answer must be answer choice D.

When choosing between two (or more) answer choices, it’s important to always consider the meaning of the sentence. If the meaning of the sentence is logical, then the grammar may have been purposely chosen to make you doubt the answer choice. Remember that sentences do not always need to have the same verb tense, and that the logic of the sentence will play a big role in determining whether an answer choice is acceptable. If you keep these elements in mind, you’ll start finding sentence correction much less tense.

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

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

How to Interpret Unfamiliar Symbols on GMAT Quant Questions

Succeeding on the GMAT requires a great many things. Firstly, you must be able to decipher and solve complex logic puzzles in mere minutes. Secondly, you must be able to maintain focus for many consecutive hours. (And thirdly, you must pay to take the exam). The exam can be particularly tricky because the questions asked are rarely straight forward. Indeed, all of these elements are often linked (except potentially the payment) on questions that ask you to decode functions specific to the question at hand.

If you think about mathematics, simple operations like +, -, x and ÷ all have unmistakable meanings because we’ve all been indoctrinated since elementary school to understand what they represent. If you think back to the first time you ever encountered an addition symbol, you were probably a baffled child wondering what this fantastic symbol represented. Now that you’ve undoubtedly done thousands, if not millions of additions in your life, the symbol is mundane. The GMAT gives you that rare opportunity to relive a moment of wonder and discovery by providing you with math questions that pertain to new symbols.

A typical GMAT question will involve some kind of arbitrary symbol and a definition as to what that symbol means for the next 2 minutes or so. Typical symbols used include Greek letters, regular shapes or playing card suits (no word yet on Egyptian hieroglyphics). The symbol is being used as a “house rule”, a definition that is good for the duration of one question. This strategy, however, plays into the GMAT’s overall tactic to discombobulate you and wear you down with tedium. The exam is figuratively asking you to jump through hoops for no other purpose than to jump through said hoops (alleged actual hoop jumping section scheduled for 2015).

Let’s look at a typical symbol question and how we can avoid unnecessarily taxing our brains on these types of questions:

If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 3 € (4 € 5) =

(A) 80
(B) 120
(C) 160
(D) 240
(E) 360

The exam is using the € symbol to stand in for another ad hoc equation, but the fact that your brain has to process this extra information is enough to throw some students out of their comfort zone. Added to this, the question does not ask for a single execution of this operation, but rather the resolution of a nested € equation. These foreign symbols may seem daunting, but remember there’s nothing here that wouldn’t be trivial without the bloated wording.

Let’s break this question down into its component parts. The symbol € is being defined for x and y as 2*x*y, which basically means take the two numbers together and multiply them. Once you’ve finished that, double the result, and you’re done. So if I ask for 5 € 10, I’d take 5*10, which is 50, and then double it. The answer would be 100. It’s relatively simple once you translate the equation into something meaningful, so we’re set up to execute a € equation on any two variables.

Of course the equation doesn’t give us only two variables, it gives us three. It’s logical to assume that the order of operation will matter here (hint: it actually doesn’t in this case), so we should start with the nested arguments before expanding outwardly. Within the bracket is 4 € 5, which would mean we multiply 4 by 5 and then double it, yielding a total of 20 * 2, or 40. The equation now reads 3 € 40, which means we again multiply together and then double, leaving a total of 120 * 2, or 240. Answer choice D is 240, so we have reached the correct answer.

Why did I mention that the order doesn’t matter? Because this specific example uses only multiplication, which is a commutative equation, or in other words: a x b = b x a. This isn’t always the case (think division), so it’s a good habit to always execute operations in the correct order. You may remember the mnemonic PEMDAS, which reminds you that the order of operations is {Parentheses, Exponents, Multiplication, Division, Addition, Subtraction}. In this instance the results would have been the same but that’s one more trap the GMAT test makers have at their disposal.

Another potential solution involves eliminating answer choices that cannot possibly work. If we look at the arguments provided, we have 3, 4 and 5, all of which need to be multiplied together. That product yields 60, which means that the correct answer choice must be a multiple of 60. Answer choices A and C can both be eliminated based on knowing that much. Perhaps from there you can recognize that this number needs to be doubled twice, leading you once again to answer choice D. However, this type of question is not particularly easy to backsolve unless you understand what is going on with the symbols.

In conclusion, people usually fail to correctly answer these questions because they get caught up in the abstract notation. The GMAT is a test about how you think, and the goal of many questions is simply to see if you can successfully navigate unfamiliar terminology. The same question, without the layering mechanism of the € sign would be significantly easier. Similarly, adding in another argument, such as squaring the parentheses, would appear to make this question significantly higher. In both cases, the questions should be solved in the same way, understanding the result of the symbol and methodically applying it to each argument. With some preparation, you can use your ease with these questions as a sign that you’re going to do well on test day.

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

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

Deciding Between the 2 Remaining Answer Choices on the GMAT

There is one feeling that hampers momentum and takes all the wind out of your sails on the GMAT. That feeling is the thrill of quickly eliminating three incorrect answer choices on a question, followed by complete uncertainty between the last two choices. This paralysis is very frustrating, because your progress is halted in dramatic fashion, and you’re left with two options that both seem to make perfect sense as the correct answer.

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.

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

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

How to Correctly Solve Vague GMAT Questions

Questions on the GMAT can be described in many different ways. I’ve heard them described as everything from juvenile to vexing, simple to impossible. One term that appears very infrequently as a characteristic of the questions on the GMAT is the word “clear”.  Indeed, some questions are so convoluted that they appear to be written in Latin (or Aramaic if you happen to already speak Latin). This is not a coincidence or an accident; many GMAT questions are specifically designed to be vague.

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.

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

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

How Well Would Mark Twain Do on the GMAT?

I’ve often contemplated who would excel at the GMAT. After all, the exam is about logic, analytical skills, problem-solving abilities and time management. Surely to shine on the exam a test taker should be smart, methodical, insightful and perceptive (and blindingly handsome). Clearly, some people have done quite well on this exam, but others never got the chance because they never actually took the test. While some have been intimidated by the nature of the test, others simply were born too early to have even heard of this exam.

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 19th 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 19th 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”.

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

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

How to Free Yourself from Calculator Math

There are few things more alluring than shortcuts. Oftentimes we’re aware of how much work, effort or time is required to accomplish a task, but we naturally gravitate towards something that can accomplish that task faster. From buying readymade rice to taking elevators to go up two floors, we’re drawn to things that make our lives even a modicum simpler (including dictionaries). This is why so many people are disappointed when they first learn that the calculator is not allowed on the GMAT.

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:

Marc 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 Marc’s 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.

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

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

Common Errors to Avoid on Sentence Correction GMAT Questions

There are many famous expressions in the English language. Many of them are clever turns of phrase that refer to commonplace ideas and concepts in everyday life. You obviously don’t need to memorize these for the GMAT (A house divided against itself is not an integer), however some expressions can be easily applied to various GMAT problems. One common expression is that you’re comparing apples and oranges. This expression typically means that you are attempting to compare two elements that are not analogous and therefore incomparable. This idiom can be particularly apt in sentence correction problems.

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 22nd (and 24th) 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 24th (and 22nd) 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.

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

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

Laughter is the Best Medicine When You’re Agonizing Over the GMAT

Steven Wright is a comedian known for his deadpan delivery, and, it turns out, has a lot to say – in his dry, paraprosdokian way – about the logic of the GMAT.  Never ones to let insight go to waste, we can (somewhat, perhaps) better understand the GMAT with his Wit and Wisdom:

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 to Understand Your GMAT Practice Test Results and Score Higher Next Time

GMAT Practice TestsPanic starts to creep in.

“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!

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

By Bill Robinson

Should You Double Check Your Answer Choices on the GMAT?

A common mantra heard when studying for the GMAT is that you have to be fast when answering questions. This is absolutely true, as the exam is testing not only your reasoning skills but also your time management skills. This does not, however, necessarily mean that you must solve every question quickly. Indeed, there may be times where you feel fairly confident in the answer choice you’ve selected, but you don’t feel 100% certain (maybe a strong 60%). In these situations, it’s perfectly acceptable to double check your answer manually.

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.

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

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

How to Approach Mimic the Reasoning GMAT Questions

The GMAT is known to be a demanding exam. Most students recognize that a lot of preparation is required in order to get the best score possible. Most students undertaking the GMAT are also used to studying for tests and have worked out their own strategies and their own methods of preparation. Indeed, people overwhelmingly study the GMAT in an orderly and structured way. This is a positive thing, but it can have its drawbacks.

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.

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

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

How to Do Math on the GMAT Without Actually Doing Math

On the GMAT quantitative section, the exam is testing your logic and analytical skills using mathematics as a medium. The topics used include geometry, algebra and arithmetic, all concepts that have been covered in high school curriculums around the world. However, the emphasis is really on the logic more than the math. In short, the question is simply asking you to solve a given problem by any means at your disposal. As such, many questions can be solved without doing any math whatsoever.

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.

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

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

How to Successfully Complete Your Thoughts on Critical Reasoning GMAT Questions

In today’s world of instant gratification and ubiquitous mobile phone usage, we are becoming used to things going fast. Multitasking has become the new norm, and it seems like no one takes the time to finish anything before jumping off to the next task. While this hectic pace may allow more tasks to be accomplished (although not necessarily well), it also makes it harder for any one task to be attentively completed. In short, it’s becoming harder to finish any one thought.

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.

B) The availability of fossil fuels does mean an increased use of the same.

C) The amount of confirmed deposits of fossil fuels is sufficient to serve the world energy needs at least over the next two centuries.

D) There is an increasing sense of acceptance across the world on the harmful effects of the use of fossil fuels on the environment.

E) Non-polluting sources of energy are less cost-effective than fossil fuels.

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…

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

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

Find Out How Algebra Could Be Your Key to Success on the GMAT Quant Section

If you want to bring your “A Game” on the Quant section you need to be very comfortable with Algebra.

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!

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

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

Distract Yourself During Your GMAT Studies with This Question

In life, it’s important to have a hobby or pastime that you find interesting. Sometimes, when the daily grind of work, school, family, social responsibilities, (updating Facebook) and preparing for the GMAT just seems like too much to handle, it’s good to take a step back. Diving into a hobby helps take your mind off things by pausing everything else and concentrating on something personal and somewhat intimate to you. One of my favorite diversions is watching movies and immersing myself in the fictional world created on screen. Surprisingly, this same distraction can be applicable to GMAT studying as well.

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?”

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

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

5 Errors to Look For in Sentence Correction Questions on the GMAT

I recently received the following question from a student. “I often get into trouble with ambiguous pronouns. If it is not clear what “they” or “it” refers to I eliminate the answer choice. I like to do this because it seems easy, but I keep getting burned using this technique. So my question is, if it is not clear what a pronoun refers to is that answer choice wrong?”

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, 13th 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 13th  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.

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

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