How to Evaluate the Entire Sentence on Sentence Correction GMAT Questions

Ron Point_GMAT TipsAs the Donald Trump sideshow continues to dominate American news, politics is again being pushed to the forefront as the country gears up for an election in 15 months. The nominees are not yet confirmed, but many candidates are jockeying for position, trying to get their names to resonate with the American population. This election will necessarily have a new candidate for both parties, as Barack Obama will have completed the maximum of two elected terms allowed by the Constitution (via the 22nd amendment).

This means that we can soon begin to discuss Barack Obama’s legacy. As with any legacy, it’s important to look at the terms globally, and not necessarily get bogged down by one or two memorable moments. A legacy is a summary of the major points and the minor points of one’s tenure. As such, it’s difficult to sum up a presidency that spanned nearly a decade and filter it down to simply “Obamacare” or “Killing Bin Laden” or “Relations with Cuba”. Not everyone will agree on what the exact highlights were, but we must be able to consider all the elements holistically.

On the GMAT, Sentence Correction is often the exact same way. If only a few words are highlighted, then your task is to make sure those few words make sense and flow properly with the non-underlined portion. If, however, the entire sentence is underlined, you have “carte blanche” (or Cate Blanchett) to make changes to any part of the sentence. The overarching theme is that the whole sentence has to make sense. This means that you can’t get bogged down in one portion of the text, you have to evaluate the entire thing. If some portion of the phrasing is good but another contains an error, then you must eliminate that choice and find and answer that works from start to finish.

Let’s look at a topical Sentence Correction problem and look for how to approach entire sentences:

Selling two hundred thousand copies in its first month, the publication of The Audacity of Hope in 2006 was an instant hit, helping to establish Barack Obama as a viable candidate for president.

A) Selling two hundred thousand copies in its first month, the publication of The Audacity of Hope in 2006 was an instant hit, helping to establish Barack Obama as a viable candidate for president.
B) The publication in 2006 of the Audacity of Hope was an instant hit: in two months it sold two hundred thousand copies and helped establish Barack Obama as a viable candidate for president.
C) Helping to establish Barack Obama as a viable candidate for president was the publication of The Audacity of Hope in 2006, which was an instant hit: it sold two hundred thousand copies in its first month.
D) The Audacity of Hope was an instant hit: it helped establish Barack Obama as a viable candidate for president, selling two hundred thousand copies in its first month and published in 2006.
E) The Audacity of Hope, published in 2006, was an instant hit: in two months, it sold two hundred thousand copies and helped establish its author, Barack Obama, as a viable candidate for president.

An excellent strategy in Sentence Correction is to look for decision points, significant differences between one answer choice and another, and then make decisions based on which statements contain concrete errors. However, when the whole sentence is underlined, this becomes much harder to do because there might be five decision points between statements, and each one is phrased a little differently. You can still use decision points, but it might be simpler to look through the choices for obvious errors and then see if the next answer choice repeats that same gaffe (not a giraffe).

Looking at the original sentence (answer choice A), we see a clear modifier error at the beginning. Once the sentence begins with “Selling two hundred thousand copies in its first month,…” the very next word after the comma must be the noun that has sold 200,000 copies. Anything else is a modifier error, whether it be “Barack Obama wrote a book that sold” or “the publication of the book” or any other variation thereof. We don’t even need to read any further to know that it can’t be answer choice A. We’ll also pay special attention to modifier errors because if it happened once it can easily happen again in this sentence.

Answer choice B, unsurprisingly, contains a very similar modifier error. The sentence begins with: “The publication in 2006 of the Audacity of Hope was an instant hit:…”. This means that the publication was a hit, whereas logically the book was the hit. This is an incorrect answer choice again, and so far we haven’t even had to venture beyond the first sentence, so don’t let the length of the answer choices daunt you.

Answer choice C, “helping to establish Barack Obama as a viable candidate for president was the publication of The Audacity of Hope in 2006, which was an instant hit: it sold two hundred thousand copies in its first month” contains another fairly glaring error. On the GMAT, the relative pronoun “which” must refer to the word right before the comma. In this case, that would be the year 2006, instead of the actual book. Similarly to the first two choices, this answer also contains a pronoun error because the “it” after the colon would logically refer back to the publication instead of the book as well. One error is enough, and we’ve already got two, so answer choice C is definitely not the correct selection.

Answer choice D, “The Audacity of Hope was an instant hit: it helped establish Barack Obama as a viable candidate for president, selling two hundred thousand copies in its first month and published in 2006” sounds pretty good until you get to the very end. The “published in 2006” is a textbook dangling modifier, and would have been fine had it been placed at the beginning of the sentence. Unfortunately, as it is written, this is not a viable answer choice (you are the weakest link).

By process of elimination, it must be answer choice E. Nonetheless, if we read through it, we’ll find that it doesn’t contain any glaring errors: “The Audacity of Hope, published in 2006, was an instant hit: in two months, it sold two hundred thousand copies and helped establish its author, Barack Obama, as a viable candidate for president.” The title of the book is mentioned initially, a modifier is correctly placed and everything after the colon describes why it was regarded as a hit. Holistically, there’s nothing wrong with this answer choice, and that’s why E must be the correct answer.

Overall, it’s easy to get caught up in one moment or another, but it’s important to look at things globally. A 30-word passage entirely underlined can cause anxiety in many students because there are suddenly many things to consider at the same time. There’s no reason to panic. Just review each statement holistically, looking for any error that doesn’t make sense. If everything looks good, even if it wasn’t always ideal, then the answer choice is fine. It’s important to think of your legacy, and on the GMAT, that means getting a score that lets you achieve your goals.

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 Strategy That Will Lead You to Better Pacing on the GMAT

Keep the PaceLet’s look at a vastly important testing issue that is largely misunderstood and its seriousness under-appreciated.  Throughout multiple years of tutoring, this has been one of the most common and detrimental problems that I have had to work to correct in my students.  It pertains to the entire GMAT exam, but is typically more relevant to the quant section as students often struggle more with pacing during quant.

No single question matters unless you let it.

Reflect on that for a second, because it’s super important, weird, true, and again…important.  The GMAT exam is not testing your ability to get as many questions right as you can.  You can get the exact same percentage of questions right on two different exams and end up getting very different scores as a result of the complicated scoring algorithm.  Mistakes that will crush your score are a large string of consecutive incorrect answers, unanswered questions remaining at the end of the section (these hurt your score even more than answering them incorrectly would), and a very low hit rate for the last 5 or 10 questions.  These are all problems that are likely to arise if you spend way too much time on one/several questions.

Each individual question is actually pretty insignificant.  The GMAT has 37 quantitative questions to gauge your ability level (currently ignoring the issue of experimental questions), so whether you get a certain question right or wrong doesn’t matter much.  Let’s look at a hypothetical example and pick on question #17 for a second (just because it looked at me wrong!).  If you start question 17, realize that it is not going your way, and ultimately make an educated guess after about 2 minutes and get it wrong…that doesn’t hurt you a lot.  You missed the question, but you didn’t let it burn a bunch of your time and you live to fight another day (or in this case question).

Now let’s look at question 17 again, but from the perspective of being stubborn.  If you start the question and are struggling with it but refuse to quit, thinking something like “this is geometry, I am so good at geometry, I have to get this right!”, then it will become very significant.  In a bad way.  In this example you spend 6 minutes on the question and you get it right.  Congratulations!  Except…you are now statistically not even going to get to attempt to answer two other questions because of the time that you just committed to it (with an average of 2 minutes per question on the quant section, you just allocated 3 questions’ worth of time to one question).

So your victory over infamous question 17 just got you 2 questions wrong!  That’s a net negative.  Loop in the concept of experimental questions, the fact that approximately one-fourth of quant questions don’t count, and therefore it is entirely possible that #17 isn’t even a real question, and the situation is pretty depressing.

Pacing is critical, and your pacing on quant questions should very rarely ever go above 3 minutes.  Spending an excess amount of time on a question but getting it right is not a success; it is a bad strategic move.  I challenge you to look at any practice tests that you have taken and decide whether you let this happen.  Were there a few questions that you spent way over 2 minutes on and got right, but then later in the test a bunch of questions that you had to rush on and ended up missing, even though they may not have been that difficult?  If that’s the case, then your timing is doing some serious damage.  Work to correct this fatal error ASAP!

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!

Brandon Pierpont is a GMAT instructor for Veritas Prep. He studied finance at Notre Dame and went on to work in private equity and investment banking. When he’s not teaching the GMAT, he enjoys long-distance running, wakeboarding, and attending comedy shows.

Find Time-Saving Strategies for GMAT Test Day

Ron Point_GMAT TipsI’ve often heard from people studying for the GMAT that they would score much higher on the test if there were no time limit to each section. The material covered on the exam is not inherently complicated, but the combination of subtle wordplay and constant stress about time management creates an environment where test takers often rush through prompts and misinterpret questions. Unfortunately, time management and stress management are two of the major skills being tested on the GMAT, so the time limit isn’t going away any time soon (despite my frequent letters to the GMAC). Instead, it’s worth mastering simple techniques to save time and extrapolate patterns based on smaller samples.

As an example, consider a simple question that asks you how many even numbers there are between 1 and 100. Of course, you could write out all 100 terms and identify which ones are even, say by circling them, and then sum up all the circled terms. This strategy would work, but it is completely inefficient and anyone who’s successfully passed the fourth grade would be able to see that you can get the answer faster than this. If every second number is even, then you just have to take the number of terms and divide by 2. The only difficulty you could face would be the endpoints (say 0 to 100 instead), but you can adjust for these easily. The next question might be count from 1 to 1,000, and you definitely don’t want to be doing that manually.

Other questions might not be as straight forward, but can be solved using similar mathematical properties. It’s important to note that you don’t have a calculator on the GMAT, but you will have one handy for the rest of your life (even in a no-WiFi zone!). This means that the goal of the test is not to waste your time executing calculations you would execute on your calculator in real life, but rather to evaluate how you think and whether you can find a logical shortcut that will yield the correct answer quickly.

Let’s look at an example that can waste a lot of time if you’re not careful:

Brian plays a game in which he rolls two die. For each die, an even number means he wins that amount of money and an odd number means he loses that amount of money. What is the probability that he loses money if he plays the game once?

A) 11/12
B) 7/12
C) 1/2
D) 5/12
E) 1/3

First, it’s important to interpret the question properly. Brian will roll two die, independently of one another. For each even number rolled, he will win that amount of money, so any given die is 50/50. If both end up even, he’s definitely winning some money, but if one ends up even and the other odd, he may win or lose money depending on the values. The probability should thus be close to being 50/50, but a 5 with a 4 will result in a net loss of 1$, whereas a 5 with a 6 will result in a net gain of 1$. Clearly, we need to consider the actual values of each die in some of our calculations.

Let’s start with the brute force approach (similar to writing out 1-100 above). There are 6 sides to a die, and we’re rolling 2 dice, so there are 6^2 or 36 possibilities. We could write them all out, sum up the dollar amounts won or lost, and circle each one that loses money. However, it is essentially impossible to do this in less than 2 minutes (or even 3-4 minutes), so we shouldn’t use this as our base approach. We may have to write out a few possibilities, but ideally not all 36.

If both numbers are even, say 2 and 2, then Brian will definitely win some money. The only variable is how much money, but that is irrelevant in this problem. Similarly, if he rolls two odd numbers, say 3 and 3, then he’s definitely losing money. We don’t need to calculate each value; we simply need to know they will result in net gains or net losses. For two even numbers, in which we definitely win money, this will happen if the first die is a 2, a 4 or a 6, and the second die is a 2, a 4 or a 6. That would leave us with 9 possibilities out of the 36 total outcomes. You can also calculate this by doing the probability of even and even, which is 3/6 * 3/6 or 9/36. Similarly, odd and odd will also yield 9/36 as the possibilities are 1, 3, and 5 with 1, 3, and 5. Beyond this, we don’t need to consider even/even or odd/odd outcomes at all.

The interesting part is when we come to odds and evens together. One die will make Brian win money and the other will make him lose money. The issue is in the amplitude. Since we’ve eliminated 18 possibilities that are all entirely odd or even, we only need to consider the 18 remaining mixed possibilities. There is a logical way to solve this issue, but let’s cover the brute force approach since it’s reasonable at this point. The 18 possibilities are:

Odd then even:                                                                                                                Even then odd:

1, 2                         3, 2                         5, 2                                                         2, 1                         4, 1                         6, 1

1, 4                         3, 4                         5, 4                                                         2, 3                         4, 3                         6, 3

1, 6                         3, 6                         5,6                                                          2, 5                         4, 5                         6, 5

Looking at these numbers, it becomes apparent that each combination is there twice ((2,1) or (1,2)). The order may matter when considering 36 possibilities, but it doesn’t matter when considering the sums of the die rolls. (2,1) and (1,2) both yield the same result (net gain of 1), so the order doesn’t change anything to the result. We can simplify our 18 cases into 9 outcomes and recall that each one weighs 1/18 of the total:

(1,2) or (2,1): Net gain of 1$

(1,4) or (4,1): Net gain of 3$

(1,6) or (6,1): Net gain of 5$

Indeed, no matter what even number we roll with a 1, we definitely make money. This is because 1 is the smallest possible number. Next up:

(3,2) or (2,3): Net loss of 1$

(3,4) or (4,3): Net gain of 1$

(3,6) or (6,3): Net gain of 3$

For 3, one of the outcomes is a loss whereas the other two are gains. Since 3 is bigger than 2, it will lead to a loss.  Finally:

(5,2) or (2,5): Net loss of 3$

(5,4) or (4,5): Net loss of 1$

(5,6) or (6,5): Net gain of 1$

For 5, we tend to lose money, because 2/3 of the possibilities are smaller than 5. Only a 6 paired with the 5 would result in a net gain. Indeed, all numbers paired with 6 will result in a net gain, which is the same principle as always losing with a 1.

Summing up our 9 possibilities, 3 led to losses while 6 led to gains. The probability is thus not evenly distributed as we might have guessed up front. Indeed, the fact that any 6 rolled with an odd number always leads to a gain whereas any 1 rolled with an even number always leads to a loss helps explain this discrepancy.

To find the total probability of losing money, we need to find the probability of reaching one of these three odd-even outcomes. The chance of the dice being odd and even (in any order) is ½, and within that the chances of losing money are 3/9: (3, 2), (5, 2), and (5, 4). Thus we have 3/9 * ½ = 3/18 or 1/6 chance of losing money if it’s odd/even. Similarly, if it ends up odd/odd, then we always lose money, and that’s 3/9 * 3/9 = 9/36 or ¼. We have to add the two possibilities since any of them is possible, and we get ¼ + 1/6, if we put them on 12 we get 3/12 + 2/12 which equals 5/12. This is answer choice D.

It’s convenient to shortcut this problem somewhat by identifying that it cannot end up at 50/50 (answer choice C) because of the added weight of even numbers. Since 6 will win over anything, you start getting the feeling that your probability of losing will be lower than ½. From there, your choices are D or E, 15/36 or 12/36. Short of taking a guess, you could start writing out a few possibilities without having to consider all 36 outcomes, and determine that all odd/odd combinations will work. After that, you look at the few possibilities that could work ((5,4), (4,5), etc) and determine that there are more than 12 total possibilities, locking you in to answer choice D.

Many students struggle with problems such as these because they appear to be simple if you just write out all the possibilities. Especially when your brain is already feeling fatigued, you may be tempted to try and save mental energy by using brute force to solve problems. Beware, the exam wants you to do this (It’s a trap!) and waste precious time. If you need to write out some possibilities, that’s perfectly fine, but try and avoid writing them all out by using logic and deduction. On test day, if you use logic to save time on possible outcomes, you won’t lose.

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.

When You’ll Need to Bring Outside Knowledge to the GMAT

Ron Point_GMAT TipsIt is often said that outside knowledge is not required on the GMAT. The idea is that everyone should be on relatively equal footing when starting to prepare for this exam, minimizing the advantage that someone with a B.Comm might have over someone with an engineering or philosophy degree. Of course, it’s difficult to determine at what point does outside knowledge begin and end. Knowing that there are 26 letters in the (English) alphabet or that blue and red are different colors is never explicitly mentioned in the GMAT preparation, but the concepts certainly can come up in GMAT questions.

This statement “No outside knowledge is required on the GMAT” is true in spirit, but a fundamental understanding of certain basic concepts is sometimes required. The exam won’t expect you to know the distance between New York and Los Angeles (19,600 furlongs or so), but you should know that both cities exist. The exam will always give you conversions when it comes to distances (miles to feet, for example), temperatures (Fahrenheit to Celsius) or anything else that can be measured in different systems, but the basic concepts that any human should know are fair game on the exam.

If you think about the underlying logic, it makes sense that a business person needs to be able to reason things out, but the reasoning must also be based on tenets that people can agree on. You won’t need to know something like all the variables involved in a carbon tax or on the electoral process of Angola, but you should know that Saturday comes after Friday (and Sunday comes afterwards).

Let’s look at a relatively simple question that highlights the need to think critically about outside knowledge that may be important:

Tom was born on October 28th. On what day of the week was he born?

1) In the year of Tom’s birth, January 20th was a Sunday.
2) In the year of Tom’s birth, July 17th was a Wednesday.

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.

Since this is a data sufficiency question, it’s important to note that we must only determine whether or not the information is sufficient, we do not actually need to figure out which day of the week it is. Once we know that the information is knowable, we don’t need to proceed any further.

In this case, we are trying to determine Tom’s birthday with 100% certainty. There are only 7 days in a week, but we need a reference point somewhere to determine which year it is or what day of the year another day of that same year falls (ideally October 27th!).

Statement 1 gives us a date for that same year. This should be enough to solve the problem, except for one small detail: the day given is in January. Since the Earth’s revolution around the sun is not an exact multiple of its rotation around itself, some years contain one extra day on February 29th, and are identified as leap years. The day of January 20th gives us a fixed point in that year, but since it is before February 28th, we don’t know if March 1st will be 40 days or 41 days away from January 20th.   Since this is the case, October 28th could be one of two different days of the week, depending on whether we are in a leap year, and so this statement is insufficient.

Statement 2, on the other hand, gives us a date in July. Since July is after the possible leap day, this means that the statement must be sufficient. Specifically, if July 17th was a Wednesday, then October 28th would have to be a Monday. You could do the calculations if you wanted to: there are 14 more days in July, 31 in August, 30 in September and 28 in October, for a total of 103 days, or 14 weeks and 5 days. The 14 weeks don’t change anything to the day of the week, so we must advance 5 days from Wednesday, taking us to the following Monday. Statement 2 must be sufficient, even if we don’t need to execute the calculations to be sure.

Interestingly, if you consider January 20th to be a Sunday, then you could get a year like 2013 in which the 28th of October is a Monday. 2013 is not a leap year, so July 17th is also a Wednesday and either statement would lead to the same answer. However, if you consider January 20th to be a Sunday, you could also get a year like 2008, which was a leap year, and then October 28th was a Tuesday. July 17th would no longer be a Wednesday, which is why the second statement is consistently correct whereas the first statement could lead to one of two possibilities. Some students erroneously select answer choice D, that both statements together solve this issue. While the combination of statements does guarantee one specific answer, you’re overpaying for information because statement 2 does it alone. The answer you should pick is B.

On the GMAT, it’s important that outside knowledge not be tested explicitly because it’s a test of how you think, not of what you know. However, some basic concepts may come up that require you to use logic based on things you know to be true.  You will never be undone on a GMAT question because “I didn’t know that,” but rather because “Oh, I forgot to take that into account.” The GMAT is primarily a test of thinking, and it’s important to keep in mind little pieces of knowledge that could have big implications on a question. As they say, knowing is half the battle (G.I. Joe!).

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.

Interpreting the Language of the GMAT

Ron Point_GMAT TipsEveryone who writes the GMAT must speak English to some degree. Since English is the default language of business, the GMAT is administered exclusively in that language. Some people feel that this is unfair. If you take an exam in your mother tongue, you tend to do better than if you took the exam in your second, third or even fourth language (I consider Klingon as my fourth language). However, even if you’re a native English speaker, the GMAT offers many linguistic challenges that make many people feel that they don’t actually speak the language. (¿Habla GMAT?)

There are different ways of asking the same thing on the GMAT. Sometimes, the question is simply: Find the value of x. Other times, you get a convoluted story that summarizes to: Find the value of x. While these two questions are essentially the same, and both have the same answer, the first scenario is easier for most students to understand than the second scenario. This is because the second question is exactly the first question but with an extra step at the beginning (watch your step!), and if you don’t solve the first step, you never even get to the crux of the question.

Consider the following two problems. The first one simply asks you to divide 96 by 6. Even without a calculator, this question should take no more than 30 seconds to solve. Now consider a similar prompt: “Sally goes to the store to buy 7 dozen eggs. When she leaves the store, she accidentally drops one carton containing 12 eggs. Unable to salvage any, she goes back into the store and buys two more cartons of 12 eggs each. Once home, she separates the eggs into bags of 6, in order to save space in the fridge. How many bags of eggs does Sally make?”

The second prompt is exactly the same as the first question, but takes much longer to read through, execute rudimentary math of (7 x 12 – 12 + 24) / 6, and yield a final answer of 16. Anyone who can solve the first question should be able to solve the second question, but fewer students answer the second question correctly. Between the two is the fine art of translating GMATese (patent pending) to a simple mathematical formula. Even for native English speakers, this can be difficult, and is often the difference between getting the correct answer and getting the right answer to a different question.

Let’s look at such a question that looks like it needs to be deciphered by a team of translators:

“X and Y are both integers. If X / Y = 59.32, then what is the sum of all the possible two digit remainders of X / Y?”

A) 560
B) 616
C) 672
D) 900
E) 1024

While this question may appear to be giving you a simple formula, it’s not that easy to interpret what is being asked. One integer is being divided by another, and the result is a quotient and a remainder. The remainder is then only one of multiple possible remainders, and all these possible remainders must be summed up to give a single value. The GMAT isn’t giving us a story on this question, but there’s a lot to chew on.

First off, the quotient doesn’t actually matter in this equation. X / Y = 59.32, but it could have been 29.32 or 7.32 or any other integer quotient, the only thing we care about is the remainder. This means that essentially X/Y is 0.32, and we must find possible values for that. Clearly, X could be 32 and Y could be 100, thus leaving a remainder of 32 and the equivalent of the fractional component of 0.32 in the quotient. This could work, and is two digits, which means that it’s one possible remainder on the list that we must sum up.

What could we do next? Well if 32/100 works, then all other fractional values that can be simplified from that proportion should work as well. This means that 16/50, which is half of the original fraction, should work as well. If we divide by 2 again, we get 8/25. This value satisfies the fraction of the quotient, but not the requirement that it must be two digits. We cannot count 8 as a possible remainder, but this does help open up the pattern of the remainders.

The fraction 8/25 is the key to solving all the other fractions, because it cannot be reduced any further. From 8/25, every time we increase the numerator by 8, we can increase the denominator by 25, and we will maintain the same fractional value. As such, we can have 16/50, 24/75, 32/100, 40/125, etc, without changing the value of the fraction. How far do we need to go? Well the question is asking for 2-digit remainders, so we only need to increase the numerator by 8 until it is no longer 2-digits. The denominator can be truncated, because when it comes to 40/125, all the question wants is 40.

Once we understand what this question is really asking for, it just wants the sum of all the 2-digit multiples of 8. There aren’t that many, so you can write them all down if you want to: 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 and 96. Outside this range, the numbers are no longer 2-digits. This whole question could have been rewritten as: “Sum up the 2-digit multiples of 8” and we would have saved a lot of time (more than last month’s leap second brouhaha).

Solving for our summation is simple when we have a calculator, but there is a handy shortcut for these kinds of calculations. Since the numbers are consecutive multiples of 8, all we need to do is find the average and multiply by the number of terms. The average is the (biggest + smallest) / 2, which becomes (96 + 16) / 2 = 56. From there, we wrote out 11 terms, so it’s just 56 x 11 = 616, answer choice B.

It’s worth mentioning that there’s a formula for the number of terms as well: Take the biggest number, subtract the smallest number, divide by the frequency, and then add back 1 to account for the endpoints. This becomes ((96 – 16) /8) + 1, or (80 / 8) + 1 or 10 + 1, which is just 11.  If you only have about a dozen terms to sum up, it’s not hard to consider writing each one down, but if you had to sum up the 3-digit multiples of 8, you wouldn’t spend hours writing out all the different values (hint: there are 112). It’s always better to know the formula, just in case.

On the GMAT, you’re often faced with questions that end up throwing curveballs at you. Interpreting what the question is looking for is half the difficulty, and solving the equations in a relatively short amount of time is the other half. If all the questions were written in straight forward mathematical terms, the exam would be significantly easier. As it is, you want to make sure that you don’t give away easy points on questions that you know how to solve. On test day, the exam will ask you: “¿Habla GMAT?” and your answer should be a resounding “¡si!”

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.

Attack Data Sufficiency GMAT Questions from the Weakest Point

Study for the GMATIt is a common axiom that the best strategy in any competition is to attack your opponent at his weakest point. If you’ve been studying for the GMAT for any length of time, you’ve probably noticed that not all Data Sufficiency statements are created equal. At times the statements are mind-bendingly complex. Other times we can evaluate a statement almost instantaneously, without needing to simplify or calculate.

Anytime you’re confronted with a question that offers one complex statement and one simple statement, you’ll want to attack the question at its weakest point and start with the simpler of the two. Evaluating the easier statement will not only allow you to eliminate some wrong answer choices, but will offer insights into what might be happening in the more complex statement. (And generally speaking, whenever you’re confronted with this dynamic, it is more often than not the case that the complex statement is sufficient on its own.)

Let’s apply this strategic thinking to a complex-looking official problem*:

Data Sufficiency 1

You can see immediately that the first statement is a tough one. So let’s start with statement 2. In natural language, it’s telling us that ‘x’ is less than 5 units away from 0 on the number line. So x could be 4, in which case, the answer to the question “Is x >1?” would be YES. But x could also be 0, in which case the answer to the question would be NO, x is not greater than 1. So statement 2 is not sufficient, and we barely had to think. Now we can know that the answer cannot be that 2 Alone is sufficient and it cannot be Either Alone is sufficient.

Now take a moment and think about this from the perspective of the question writer. It’s obvious that statement 2 is not sufficient. Why bother going to the trouble of producing such a complex statement 1 if this too is not sufficient? This isn’t to say that we know for a fact that statement 1 will be sufficient alone, but I’m certainly suspicious that this will be the case.

When evaluating statement 1, we’ll use some easy numbers. Say x = 100. That will clearly satisfy the statement as (100+1)(|100| – 1) is greater than 0. Because 100 is greater than 1, we have a YES to the question, “Is x >1?” Now the question is: is it possible to pick a number that isn’t greater than one, but that will satisfy our statement?  What if x = 1? Plugging into the statement, we’ll get (1+1)(|1| – 1) or (2)*(0), which is 0. Well, that doesn’t satisfy the statement, so we cannot use x = 1. (Note that we must satisfy the statement before we test the original question!) What if x = -1? Now we’ll have: (-1+1)(|-1| – 1) = 0. Again, we haven’t satisfied the statement. Maybe you’d test ½. Maybe you’d test -3. But you’ll find that no number that is not greater than 1 will satisfy the statement. Therefore x has to be greater than 1, and statement 1 alone is sufficient. The answer is A.

Alternatively, we can think of statement 1 like this: anytime we multiply two expressions together to get a positive number, it must be the case that both expressions are positive or both expressions are negative. In this statement, it’s easy to make (x+1) and (|x| – 1) both positive. Just pick any number greater than 1. However, as mentioned in the previous paragraph, we can immediately see that x=1 will make the second term 0, and x = -1 will make the first term 0. Multiplying 0 by anything will give us 0, so we can rule those options out. Moreover, we can quickly see that any number between -1 and 1 (not inclusive) will make (|x| – 1) negative and make (x+1) positive, so that range won’t work. And any term less than -1 will made (x+1) negative and (|x| – 1) positive, so that range won’t work either. The only values for x that will satisfy the condition must be greater than 1. Therefore the answer to the question is always YES, and statement 1 alone is sufficient to answer the question.

The takeaway: this question became a lot easier once we tested statement 2, saw that it obviously would not work on its own, and became suspicious that the complex-looking statement 1 would be sufficient alone. Once we’ve established this mindset, we can rely on our conventional strategies of picking numbers or using number properties to prove our intuition. Anytime the GMAT does you the favor of giving you a simple-looking statement, take advantage of that favor and adjust your strategic thinking accordingly.

*GMAT Prep question courtesy of the Graduate Management Admissions Council.

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

How to Interpret GMAT Critical Reasoning Questions

Ron Point_GMAT TipsInterpreting what is being asked on a question is arguably the most important skill required in order to perform well on the GMAT. After all, since the topics are taken from high school level material, and the test is designed to be difficult for college graduates, the difficulty must often come from more than just the material. In fact, it is very common on the GMAT to find that you got “the right answer to the wrong question.” This phrase is so well-known that it merits quotation marks (and eventually perhaps its own reality show).

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

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

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

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

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

A) When planning a trip, some people first decide where they want to go and then plan accordingly, but, for most of us, much financial planning must be done before we can choose where we are going.
B) In planting a vegetable garden, you should prepare the soil first, and then decide what kind of vegetables to plant.
C) Good architects do not extemporaneously construct their plans in the course of an afternoon; an architectural design cannot be divorced from the method of constructing the building.
D) In solving mathematical problems, the best method is to try out as many strategies as possible in the time allotted. This is particularly effective if the number of possible strategies is fairly small.
E) To make a great tennis shot, you should visualize where you want the shot to go. Then you can determine the position you need to be in to execute the shot properly.

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

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

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

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

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

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

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

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

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

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

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

99th Percentile GMAT Score or Bust! Lesson 5: Procrastinate to Calculate

raviVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

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

Lesson Five:

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

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

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

By Brian Galvin

The Importance of Recognizing Patterns on the GMAT

Ron Point_GMAT TipsIn life, we often see certain patterns repeat over and over again. After all, if everything in life were unpredictable, we’d have a hard time forecasting tomorrow’s weather or how long it will take to go to work next week. Luckily, many patterns repeat in recurring, predictable patterns. A simple example is a calendar. If tomorrow is Friday, then the following day will be Saturday, and Sunday comes afterwards (credit: Rebecca Black). Moreover, if today is Friday, then 7 days from now will also be Friday, and 70 days from now will also be Friday, and onwards ad infinitum (even with leap years). These patterns are what allow us to predict things with 100% certainty.

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

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

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

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

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

(A) 9
(B) 7
(C) 4
(D) 3
(E) 1

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

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

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

Dissecting these terms one by one, we get:

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

7^2, which is just 49.

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

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

81 * 49 * 729 as

1 * 9 * 9.

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

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

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

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

The GMAT Shortcut That Can Help You Solve a Variety of Quantitative Questions

GMAT StudyingOne thing I’m constantly encouraging my students to do is to seek horizontal connections between seemingly disparate problems. Often times, two quantitative questions that would seem to fall into separate categories can be solved using the same approach. When we have to sift through dozens of techniques and strategies under pressure, we’re likely to become paralyzed by indecision. If, however, we have a small number of go-to approaches, we can quickly consider all available options and arrive at one that will work in any given context.

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

Average Number of Terms Sum
Country A 92 a 92a
Country B 86 b 86b
Total 90 a + b 90a + 90b

 

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

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

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

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

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

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

b              Tot       a

86——–90—-92

Gap:  4           2

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

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

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

A. 10%
B. 33 1/3%
C. 40%
D. 50%
E. 66 2/3%

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

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

Y          Tot             X

25—–30———40

Gap: 5             10

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

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

Let’s try another one*:

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

a) 180
b) 170
c) 156
d) 150
e) 105

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

Remaining             Total           First 100

50—————70———-80

Gap           20                     10

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

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

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

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

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

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

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

The Easiest Type of Reading Comprehension Question on the GMAT

Ron Point_GMAT TipsReading comprehension questions on the GMAT are primarily an exercise in time management. If you gave yourself 30 minutes to complete a single Reading Comprehension passage along with four questions, you would find the endeavour very easy. Most questions on the GMAT feature some kind of trap, trick or wording nuance that could easily lead you astray and select the wrong answer. Reading Comprehension questions, while occasionally tricky, are typically the most straightforward questions on the entire exam.

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

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

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

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

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

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

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

(A) Describe the labor reforms that can be attributed to the workers at the Lowell mills
(B) Criticize the proprietors of the Lowell mills for their labor practices
(C) Suggest that the Lowell mills played a large role in the labor reform movement
(D) Describe the conditions under which the Lowell mills employees worked
(E) Analyze the business practices of early American factories

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

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

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

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

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

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

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

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

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.

The Importance of Sorting Answer Choices on the GMAT

Ron Point_GMAT TipsOn the GMAT, as in life, you have multiple choices you can make at every juncture you face. On the standardized test, your choices are limited to only five, which is more manageable than the plethora of choices you encounter every day. However, even five answer choices can cause a lot of frustration for people who have difficulty differentiating among them.

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

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

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

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

A) -3

B) -2

C) -2/3

D) 2/3

E) 3

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

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

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

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

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

___________________________________________________________________

0     1/32           1/16                      1/8                                                                                                             1

x^5            x^4                      x^3

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

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

x^2 = 4/9

x^3 = -8/27

x^4 = 16/81

x^5 = -32/243

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

________________________________________________________________________

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

x^3                       x^5                                      x^4

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

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

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.

99th Percentile GMAT Score or Bust! Lesson 4: Think Like a Lawyer on Critical Reasoning

raviVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

 

Lesson Four:

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

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

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

By Brian Galvin

Avoid the Tempting Trap Answer on GMAT Questions

Ron Point_GMAT Tips

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

2 Ways to Improve Your Pattern Recognition on GMAT Questions

patternIn 1946, a fascinating study about chess masters revealed that, for the most part, they had unexceptional working memories. This finding flew in the face of conventional wisdom, which held that chess masters must have had photographic memories to absorb thousands and thousands of scenarios they’d encountered throughout their years of training. Instead of relying on superior recall, it turns out that they were simply better than most at recognizing patterns.

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

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

Take this Official Guide* problem, for example:

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

A) Empire, fashioned either from the spotted sandstone of Mathura or
B) Empire, fashioned from either the spotted sandstone of Mathura or from
C) Empire, either fashioned from the spotted sandstone of Mathura or
D) Empire and either fashioned from the spotted sandstone of Mathura or from
E) Empire and were fashioned either from the spotted sandstone of Mathura or from

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

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

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

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

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

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

Let’s try another example*:

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

A) Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted
B) Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both
C) Jazz pianist and composer Thelonious Monk, who produced a body of work rooted
D) Jazz pianist and composer Thelonious Monk produced a body of work that was rooted
E) Jazz pianist and composer Thelonious Monk produced a body of work rooted both

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

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

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

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

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

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

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

Don’t Let Your Prior Knowledge Get in the Way on GMAT Questions

Ron Point_GMAT TipsAs a true Canadian, I’m always on the lookout for questions that are specifically about Canada. Sometimes a question is about trains travelling from Toronto to Montreal, and other times a Reading Comprehension passage deals with a certain Canadian prime minister. Sometimes, the question is just very polite!

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

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

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

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

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

A) 120
B) 169
C) 196
D) 230
E) 256

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

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

We seem to have something of a pattern here, but let’s do a third team just to compare our hypothesis (H0: It will be 13 matches. HA: We’ll have to find another way). Team 3 has already faced teams 1 and 2, meaning that their schedule begins at team 4, and then goes on to team 5, etc up until team 16. This does indeed add up to 13 more games being played. The pattern seems to hold up logically, every team plays one fewer game than the last because they’ve already faced any opponent with a team number lower than theirs.

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

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

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

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

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

Solving for the subtraction gives us:

16! / (2! * 14!)

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

16 * 15 / 2.

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

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

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.

Fishing for the Right Answer to Critical Reasoning GMAT Questions

Ron Point_GMAT TipsWhile preparing for the GMAT, there will be certain question types that will appear over and over again. If you’re studying math, you know that you’ll see at least a couple of exponent problems that you’ll need to solve through algebra. If you’re studying sentence correction, you know that you’ll see at least a couple of misplaced modifiers that need to be modified in the correct answer choice. Some question types are so obvious that you know you have to prepare for them, even if you somehow manage to not see a single one on test day (kind of like fishing).

However, there are other question types that you rarely see on the GMAT. Questions about the volume of spheres (or the winds of winter), or conjugating verbs in the subjunctive mood just don’t come up that often on the GMAT. This means that some people feel like they can skip these lessons and concentrate on the “big fish”, as it were (more fishing analogies).

The problem is that, when you inevitably stumble upon a question you haven’t bothered to prepare for, you start panicking. Sometimes, the panic is not noticeable, but subconsciously you begin to lose confidence and wonder how you’re going to answer this question. The sad truth is that there’s a good chance you’ll have to take an educated guess and move on. This isn’t so bad, as long as the negative effects are limited only to the question being asked. Unfortunately, these qualms tend to linger with most test takers for at least a few questions afterwards.

The best strategy for someone who wants to do really well on the GMAT is to know every type of question that can be asked of you. Understandably, you should spend more time on the broad topics that are sure to be covered more frequently, but there should not be any “oh gosh” moments on the GMAT (unless you took the exam in the ‘50s) to zap your confidence.

Let’s look at an example and what to do if we’re really not sure what to do on a question.

Economic analysts predict that by 2030 populations of urban areas will have increased by 60%. This will have tremendous impact on the demand for water in these areas. The increased demand will exhaust the local supplies of water and potable water sources will be drawn to urban areas from longer distances, resulting in a dramatic rise in the price of water.

Which of the following roles do the two boldfaced portions play?

A) The first is the conclusion of the argument; the second is a prediction that serves as the basis for the argument.

B) The first is a prediction that serves as the basis for the argument; the second is the conclusion of the argument.

C) The first is a conclusion that serves as the basis of the argument; the second is a prediction that follows from the conclusion and is used to support the argument.

D) The first is a prediction that serves as the basis for the argument; the second is a prediction that follows from the conclusion.

E) The first is a prediction that serves as the basis for the argument; the second is a consequence that follows from the prediction and is used to support the argument.

Questions that ask about the roles of boldface sections fall under the Method of Reasoning subsection of Critical Reasoning.  These questions are somewhat rare on the GMAT, and as a result students don’t tend to have much experience with them. Trying to decipher them without much experience is eminently doable, but a little practice ahead of time will help ensure that your grade doesn’t sink on test day (I’ve definitely jumped the shark with these water metaphors).

The beauty of roles of boldface questions is that they’re asking you to evaluate two phrases, and the answer choices contain two elements. This means that you can look at them one at a time, independently of the other half of the answer choice, and eliminate the choices that don’t match up to your expectations.

Let’s look at the first section “Economic analysts predict that by 2030 populations of urban areas will have increased by 60%.The five answer choices all have a selection that ends with a semi-colon to describe this phrase. Looking at the choices above, A and C state “the first is a conclusion of the argument”, while B, D and E state “the first is a prediction that serves as the basis for the argument”. This section certainly seems like a prediction (the third word is even “predict”), but let’s dive into the passage more to identify the conclusion. This should be easy; as you’re tasked with finding the conclusion for any strengthen or weaken Critical Reasoning questions.

Using the “why?” test, it becomes apparent that the conclusion is the last line: “resulting in a dramatic rise in the price of water.” Why? Because of the increase in demand. Why? Because the increased demand will mean water will come from further away. Why? Because people are moving more and more to urban areas. Why? (I feel like Steve Austin here) We don’t know that, it’s just stated as a premise. Now that we’ve identified what the conclusion of this passage is, we can more convincingly knock off incorrect answer choices.

The first section is clearly a prediction, and the conclusion of the passage is the following sentence, so we can eliminate answer choices A and C because they do not correctly identify the role of this phrase. We then move on to the second bolded section of the passage: potable water sources will be drawn to urban areas from longer distances. Looking at the second half of the three remaining choices, we have:

B) “The second is the conclusion of the argument”

D) “The second is a prediction that follows from the conclusion”

E) “The second is a consequence that follows from the prediction and is used to support the argument”

Since we’ve already identified the conclusion of the passage, we can quickly eliminate answer choice B. The conclusion is that the price of water will increase given the increased demand, so answer choice D inverses the relationship between the bolded section and the conclusion. Logically, the fact that water will need to be drawn from further away will contribute to the increase in the price of water, not the other way around. Since this is used to support the argument, answer choice E will be the correct choice.

Logically, you should spend most of your time on question types you know are going to show up on the exam. That means that there may be some instances of seeing question types for the first time on test day. If that happens, remember that the GMAT is primarily a test of how you think, so use the same logical tenets you would use on any other question. Here, we identified the conclusion of a passage, eliminated answer choices inconsistent with our analysis, and ultimately found the only correct answer choice. If you do the same on test day, you’ll end up with a whale of a 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.

Expecting the Unexpected on GMAT Quant Questions

Ron Point_GMAT TipsAfter studying for the GMAT for a few months (or years, in my case), you start to form expectations of exam questions. If you’re doing sentence correction, and you see a pronoun, there’s a good chance that the various answer choices will have different pronouns to ensure that you pick the correct one. If you’re doing math with three or four digit numbers, there’s a good chance that you have to deal with unit digits in order to shortcut the calculations. And if you’re doing geometry, there’s a good chance that the Pythagorean Theorem will show up, directly or indirectly. (My money is on directly.)

However, it does sometimes happen that a question shatters your expectations. You see the question, you peruse the answer choices, and you immediately look for the properties that you expect to show up. Then, after reading the question, you still don’t have what you expect, and you’re a little lost as to how you should proceed. After all, if you’ve seen the same type of question ten times in a row, a deviation on the 11th time can be somewhat discombobulating.

And yet, this is a strategy that the GMAT frequently employs. At the mid level questions (think 25th-75th percentile), the exam tests the same concepts repeatedly, driving home some crucial ideas through repetition. At the higher level questions (above 75th percentile), the questions tend to get trickier by using your own crutches against you. This throws you out of your comfort zone, and forces you to have to look at a problem through a different vantage point.

Let’s look at such a problem:

In right triangle ABC, BC is the hypotenuse. If BC = 13 and AB + AC = 15, what is the area of the triangle?

A) 2 √7
B) 2 √14
C) 14
D) 28
E) 56

Reading through this problem, we note that it’s a right angle triangle with a hypotenuse of 13. Immediately, my brain jumps to the fairly common 5-12-13 triangle that the GMAT likes to use. Apart from the ubiquitous 3-4-5 right angle triangle, the 5-12-13 triangle is the next smallest right triangle with all integer sides. Perusing the rest of the question, I fully expect AB + AC to be 5 + 12 or 17. However, the question states that AB + AC is not equal to 17, which takes me completely by surprise (and almost makes me question my very existence).

Now, knowing that this isn’t a 5-12-13 triangle isn’t that big of a deal, but it does shatter my expectations of this problem. Clearly, there’s still a solution because the question is being asked, but it deviates from what I thought I had to do. It’s like going to work and your usual route is blocked off. You won’t head back home and sulk, you just have to find an alternate route. Similarly, I now have to take a different approach to solve this geometry question.

Let’s review what we know: it’s a right angle triangle, which means it’s almost guaranteed that we’ll need to use the Pythagorean Theorem. The area is being asked, which is ½ Base * Height, as long as Base and Height are orthogonal to one another. The fact that it’s a right angle triangle and BC is the hypotenuse assures us that AB and AC will be the 90 degree angle we need. All we need to do is multiply AB by AC and divide the product by 2 to get our area.

The problem is that we only have one equation given: AB + AC = 15. To solve for two unknowns, we need two (independent) equations. The second equation will have to come from Pythagoras (possibly by text message). We know that the square of the two right angle sides will equal the square of the hypotenuse, meaning here we know AB^2 + AC^2 = BC^2. Since we know BC is 13, we really have

AB^2 + AC ^2 = 13^2 or

AB^2 + AC ^2 = 169

Combine this with our earlier equation of

AB + AC = 15

And we have two equations and two unknowns. This should be solvable, but the fact that one equation is linear and the other is quadratic can be somewhat disconcerting. We can square the second equation and use the elimination method to isolate variables and get to the right answer.

AB + AC = 15. We now want to square both sides.

(AB + AC)^2 = (15)^2. Remember to square each side, not the individual elements.

AB^2 + 2 AB*AC + AC^2 = 225. This is a perfect square on the left hand side.

Bringing back in the Pythagorean equation:

AB^2 + AC^2 = 169. Using the elimination method to subtract one statement from the other, we can eliminate two variables in one fell swoop, leaving us with:

AB^2 + 2 AB*AC + AC^2 = 225

AB^2 + AC^2 = 169

 

AB^2 + 2 AB*AC + AC^2 = 225

AB^2 + AC^2 = 169

 

2 AB*AC = 56.

Meaning that AB*AC = 28.

Finally, AB * AC is really just the Base * the Height. Since that is what we’re looking for, we don’t need to manipulate the algebra any further. However, there is one final step. The equation we’re looking for is ½ Base * Height, so we need to divide the result by 2 again, yielding just 14. Answer choice C is thus correct.

There are several clues that this solution is on the right track. Firstly, the answer we found is among the answer choices. Moreover, two other answer choices are steps we had to pass through in order to find the final answer, making for perfect trap answer choices for overzealous students. Finally, the area of the triangle is very small, which makes sense because the hypotenuse is 13 and the sum of the other two sides is 15. Even the 5-12-13 triangle, which is a relatively thin triangle with an area of 30 (Pythagoras FTW) is twice as big as this thin triangle. The sides of this triangle won’t be integers, but given their relative sizes, it’s something like 2.5-12.5-13, which is quite thin.

If you know the Pythagorean Theorem and can apply the elimination method to two equations, this problem isn’t that difficult once you start solving for variables. The difficulty lies primarily in getting started and not getting caught in trying to backsolve or pick numbers for this problem. When going through it, your mind might automatically think of 5-12-13, or whatever typical information is provided for similar questions. Sometimes you have to think of the problem from a different vantage point in order to solve it. Indeed, on the GMAT, you should expect the unexpected.

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.

GMAT Tip of the Week: Serenity and Sentence Correction

GMAT Tip of the WeekIf you’re reading this, you’re probably hoping for a 700+ score on the GMAT.  You’re probably wishing for a 700+ score on the GMAT.  And you may well be praying for a 700+ score on the GMAT.

And if you’re praying, one prayer in particular is your best hope to maximize your GMAT Verbal performance, regardless of whether you can benefit from divine intervention.  No matter your faith or belief system, the Serenity Prayer is critical to your Sentence Correction success:

 

God, grant me the serenity to accept the things I cannot change,
The courage to change the things I can,
And the wisdom to know the difference.​

You can view this as a prayer or simply a personal mantra.  But you’d better keep it close to heart.  On GMAT Sentence Correction problems you MUST maintain the serenity to accept that there will be sentence structures and word choices that you cannot change, and you MUST instead focus on changing those things that you can. Now let’s supply the wisdom to know the difference.

YOU CANNOT CHANGE:

The non-underlined portion.  Particularly when studying, many GMAT students love to protest problems on the basis that the non-underlined portion “doesn’t sound right” or “is awkward and clumsy” or “I think it has an error…this question is flawed!”.  In truth, the GMAT (and reputable creators of replica study problems) intentionally uses strange structures in large part to test your ability to maintain that serenity.  You can only change what they give you the option to change, and those who can’t handle the stress of having limited control are at a distinct disadvantage.

The five answer choices.  For many GMAT problems we all would prefer to just rewrite our own sentence.  How many times have you started to write a sentence in an email or essay then realized “I’m not sure if this is grammatically correct” and then deleted and written a brand-new sentence to avoid that uncertainty?  We all do that, regularly, and so on the GMAT you have that primal desire to want to write your own sentence. But you don’t have that option.  You have to accept that you can’t write your own answer choice and that “the game” is largely about your ability to play it by the test’s rules.

The author’s intent.  GMAT students love to ask “what if?” on Sentence Correction problems, motivated in part by fear “but what if they had two right answers?” and in part by protest “I don’t like the right answer so let me suggest this other right answer (like the point above) – okay hotshot teacher what would you do now?”.  This is virtually never a productive discussion, so accept the serenity that it’s a waste of your time.  There will always be exactly one correct answer and exactly four incorrect answers.  And whether that correct answer feels wrong or strange to you, it’s correct. And whether you think you could change that wrong answer you picked through a word change here or there, that’s not what the question was about.  The GMAT spends roughly $5,000 per question in research, development, and administration costs; these problems are “scientifically” chosen to look exactly the way they look. You can’t change the problem; your job is to learn from it.

YOU CAN CHANGE:

The underlined portion of the sentence.  They give you five ways to phrase that section and the only real choice you have in the matter is which of those five provides a logical meaning and is free from error.  That’s your job, so harness your “courage to change the things you can” toward making that choice effectively.

The way that you approach SC problems.  Most of us read from left to right and from top to bottom, but on Sentence Correction problems you can and should change that approach to suit your strengths. Attack major grammatical errors first, emphasizing those that you know you’re best at (for most of us those include subject-verb agreement, pronoun agreement, and verb tenses).  Defer choices that you’re not 100% certain on while you search for better ones; no one said you have to make a decision on A first, then B, then C…  You can hunt for the errors you feel most comfortable spotting, then work your way toward major differences between the remaining answer choices.

Your study mindset.  Much more on the verbal section than on the quant, students have a tendency to fight for their answer choice.  “But wait…”  “But what if…”  “But I thought…”  Which in and of itself isn’t a terrible thing; the fact that you’re heavily invested in the problem is a great sign.  But (there’s that word again) what’s most important isn’t being right in practice, it’s being right on test day.  Learning how the GMAT uses strange structures to throw you off is helpful; when you don’t like a correct answer, think about that structure or phrasing and pay attention to it when you see it in writing elsewhere.  When you fall victim to a trap, think about what tempted you with the wrong answer and how the testmaker threw you off the scent of the correct answer.  GMAT Sentence Correction rewards serenity, courage, and knowledge.  You have to have the serenity to accept that you can’t change most of what you’re reading and that you will undoubtedly find correct answers that aren’t written the way you’d write them.  You have to have the courage to deflect decisions you know you’re not good at and the patience to scan until you find decisions that you know you can make.  And you have to have the knowledge that it’s all part of the game and that those who succeed on these questions are the ones who recognize and embrace that.  You may not be able to pray your way to 700+, but the Serenity Prayer is a great start in that direction.

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

Watch Movies with a Critical Eye as You Study for the GMAT This Summer

Ron Point_GMAT TipsWith the summer blockbuster season around the corner, it’s easy for your studying motivation to wane. After all, the GMAT doesn’t have the same allure as the big budget Hollywood movies people line up to see every summer. However, while seeing a movie can be a welcome distraction, there is a lot we can learn from movies when studying for the GMAT.

As an example, when Tony Stark verbally jousts with Ultron in the latest Avengers movie, he is demonstrating critical reasoning and trying very hard to weaken his opponents’ argument. In Jurassic World, a hybrid dinosaur is created using data from various sources, as a conclusion would be created from various sources on a Reading Comprehension question. And in Terminator Genisys, a fractured timeline is created that resembles many tense errors in Sentence Correction (to say nothing of misspelling the title).

Arguably, every movie you see this summer will incorporate some elements of what’s covered on the GMAT (I’m still working on Magic Mike XXL).  The exam is designed to test your knowledge of logic using elements you have already covered previously in an academic environment. Moreover, the topics on the GMAT often arouse your own interests and pertain to things you care about. Indeed, sometimes the questions asked will even make you think of the movie you saw the week before to take your mind off the GMAT!

Let’s look at such an example, combining movies and GMAT in one sleek Sentence Correction question:

At major Hollywood studios, a much greater proportion of the population is employed than is employed by independent movie production companies.

A) At major Hollywood studios, a much greater proportion of the population is employed than is employed by independent movie production companies.

B) At major Hollywood studios they employ a much greater proportion of the population than independent movie production companies do.

C) A much greater proportion of the major Hollywood studios’ population is employed than independent movie production companies employ.

D) Major Hollywood studios employ a much greater proportion of the population than the employment of independent movie production companies.

E) Major Hollywood studios employ a much greater proportion of the population than independent movie production companies do.

This question begins with an absolute phrase “At major Hollywood studios…” that modifies the rest of the sentence. The second half of the sentence is a comparison between big budget studios and independent companies, highlighted by the trigger word “than”. With comparisons, we must always ensure that we are comparing similar elements and that these elements are in a parallel form.

Looking specifically at answer choice A, the absolute phrase “At major Hollywood studios” would need to apply to the rest of the sentence. (This is similar to the classic trailer opening “In a world…”). This structure would only be correct if the rest of the sentence were limited in scope to the major Hollywood studios. Anything outside of this scope would create an illogical discord between the modifying phrase and the rest of the sentence. Since the sentence deals with the entire population, it does not make sense to limit it only to the Hollywood studios, and this answer choice can be eliminated for this error in logical meaning.

Answer choice B, “At major Hollywood studios they employ a much greater proportion of the population than independent movie production companies do”, there is a pronoun error in the first five words. The antecedent for “they” is nebulous, because it conceivably refers to the studios, or the executives at the studios, or perhaps the HR department at the studios, or something else. The rest of the sentence isn’t great either, but one glaring pronoun error is enough to definitively eliminate this choice from contention.

Answer choice C, “A much greater proportion of the major Hollywood studios’ population is employed than independent movie production companies employ” changes the meaning into something that is not exactly English. The population has now been restricted to only the Hollywood studios’ population, and the comparison being made is illogical as well, as it is now comparing a population proportion to a movie production. Answer choice C is perhaps the worst phrase of the bunch and hopefully can be eliminated rather quickly.

Answer choice D, “Major Hollywood studios employ a much greater proportion of the population than the employment of independent movie production companies” starts off well, but makes the same comparison error that we saw in answer C. If the sentence begins by comparing major studios to something else, then that something else has to be a studio (or something analogous, my cousin’s garage for example). By comparing studios to employment, the answer choice makes an illogical apples-to-oranges comparison that precludes it from consideration.

Answer choice E, “Major Hollywood studios employ a much greater proportion of the population than independent movie production companies do” correctly compares studios to production companies, and makes no other type of error along the way. By process of elimination, this had to be the correct choice, but it’s always nice when the last remaining choice doesn’t contain any obvious errors or omissions. This answer choice is correct, and we can confidently select E as our answer before moving on to the sequel (or next question, as the case may be.)

When it comes to summer blockbusters, there’s always something to learn. Sometimes we learn something helpful in grammar, and sometimes we learn that physics don’t always apply (thank you Furious 7!). This summer, if you’re studying for the GMAT, don’t forget to take the occasional break to go and enjoy a good movie to give your mind a break from the rigors of Sentence Correction problems. Just don’t get butter on your GMAT books.

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.

99th Percentile GMAT Score or Bust! Lesson 3: The Long Way is the Wrong Way

GMAT Instructor - Ravi SreeramaVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

 

Lesson Three:

The Long Way is the Wrong Way.  For much of your math education you’ve been urged to go step-by-step and show all your work.  On a timed test like the GMAT, however, you don’t have that luxury of taking your time.  As Ravi demonstrates in this video, however, “the long way is the wrong way” on many GMAT problems, which instead are designed to reward you for making quality estimates, using answer choices as clues, and employing other shortcuts to definitively answer correctly without doing all the work.

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

We also 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

The Concept of Abstraction on the GMAT

Ron Point_GMAT TipsThe concept of abstraction involves taking things from specific values to general ideas. On the GMAT, abstraction is one of the simplest ways to turn an easy problem into a difficult one. A simple example would be to ask someone what “5 times 6” would be, and then to expand that to “x times y” or “odd number times even number.” Abstraction helps by giving broad strokes to concepts, but it also requires a deeper understanding of the underlying principles. (This is the same principle as abstract art… apparently).

The GMAT is known for employing abstraction to make simple questions harder to grasp. Sometimes, a concrete problem using specific numbers can be very difficult, but the difficulty lies in the execution of the solution. An abstract problem, however, introduces an entirely different level of complexion, where even understanding the question at hand isn’t obvious (think of a Georgia O’Keefe painting). Once you’ve figured out what the problem is asking, then you can go about solving it. But until then you’re scratching your head wondering what the next step could be.

There is a lot of value in understanding the abstract, overarching theme of a question. After all, instead of saying that 2 + 2 gives you an even number, and 2 + 4 gives you an even number, and 2 + 6 gives you an even number, you can summarize that the sum of any two even numbers will be even. Once you understand this principle, it makes all future questions on this topic easier to solve. However, if you happen to see something on test day that you’re unfamiliar with, you might be better off concentrating on the question at hand than the unbreakable rule that guarantees the consistency of the answer.

As such, digging into why problems work is important during the time you prepare for the GMAT, so that problems seem easier on test day. Let’s explore one such relatively simple problem, made difficult by the abstract phrasing of the question:

If the operation ∆ is one of the four arithmetic operations addition, subtraction, multiplication, and division, is (6 ∆ 2) ∆ 4 = 6 ∆ (2 ∆ 4)?

  1. 3 ∆ 2 > 3
  2. 3 ∆ 1 = 3

 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.

Data sufficiency questions tend to be somewhat abstract on their own because they are asking whether something is sufficient or not. There aren’t specific values you are being asked to evaluate, but rather the entire spectrum of possibilities. To make things even more abstract, the question is asking about some equation (which looks isosceles to me), which could represent any of the four basic operations. This question is very abstract, and contains a pitfall or two if you’re not careful.

Before even looking at the statements, let’s revisit the equation in the question:

(6 ∆ 2) ∆ 4 = 6 ∆ (2 ∆ 4)

This equation is actually asking about the commutative property of operations, because the numbers are all the same, but the order of operations is different. Replace all the operations by +, and we quickly see that the answer is 12 on both sides. You may already know that addition and multiplication are commutative, whereas subtraction and division are not (and this holds for all problems, so it’s a great shortcut). However, we may as well demonstrate it to ourselves here:

(6 + 2) + 4 = 6 + (2 + 4) –> 8 + 4 = 6 + 6 –>  12 = 12. This holds, meaning the operation is commutative.

(6 x 2) x 4 = 6 x (2 x 4) –> 12 x 4 = 6 x 8 –> 48 = 48. This holds, meaning the operation is commutative.

(6 – 2) – 4 = 6 – (2 – 4) –> 4 – 4 = 6 – (-2) –> 0 = 8. This doesn’t hold, meaning the operation is not commutative.

(6 ÷ 2) ÷ 4 = 6 ÷ (2 ÷ 4) –> 3 ÷ 4 = 6 ÷ ½ –> ¾ = 12. This doesn’t hold, meaning the operation is not commutative.

This means that we will have sufficient data if a statement can narrow down the choices to any one operation or to either multiplication & addition or division & subtraction. The data will be insufficient if we cannot narrow down the operations or have at least one commutative operation (x or +) and a non-commutative operation (- or ÷) as possibilities.

Next, we must look through the statements and see what information we can glean. For simplicity’s sake, I’m going to begin by evaluating statement 2. This is because the equation will yield less abstraction than the inequality of statement 1. If the equation can satisfy this equation, it’s a possible answer. If it cannot, we can remove it from the list of potential equations.

Statement 2 says that 3 1 = 3. We can replace this by the four basic equations and see which ones hold:

3 + 1 = 3 –> This should give 4. Doesn’t hold. Eliminate addition.

3 – 1 = 3 –> This should give 2. Doesn’t hold. Eliminate subtraction.

3 x 1 = 3 –> This should give 3. Holds. Keep multiplication.

3 ÷ 1 = 3 –> This should give 3. Holds. Keep division.

You may be able to quickly ascertain that addition and subtraction do not hold for this equation, so only multiplication and division could work. Since we have two operations that could work, one of which is commutative and one of which is not, we can definitely say that this statement is insufficient.

Moving on to statement 1, we approach it in the same way and see if the operations can hold (i.e. the answer is greater than 3):

3 + 2 > 3  –> This gives 5. Holds. Keep addition.

3 – 2 > 3 –> This gives 1. Doesn’t hold. Eliminate subtraction.

3 x 2 > 3 –> This gives 6. Holds. Keep multiplication.

3 ÷ 2 > 3 –> This gives 1.5. Doesn’t hold. Eliminate division.

For this statement alone, we see that addition and multiplication both work, but the other two equations don’t. This means that we don’t know exactly which operation this represents, but either way it will give the same answer to the question given. The two operations left standing (last operation standing?) both yield the same answer to the statement, which means we don’t need to narrow down the choices or put the statements together. A common pitfall on this question is to put the statements together, because then only multiplication can work for both statements. However, that’s a trap, as you don’t need statement 2 at all. The correct answer is A, because statement 1 is sufficient on its own to answer the question posed.

For abstract problems, it’s easy to get lost in the generalization of the problem. What happens whenever I add two even numbers together? The magnitude of the scope is almost overwhelming, and as such the best strategy is to turn it concrete using simple examples. If no numbers are provided, try picking small, useful numbers like 2, 3 and 10. If the numbers are given but other variables, such as the operations, are left blank, then just go through all the possibilities until the rule becomes clear. The best way to overcome abstraction is to make it concrete.

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.

99th Percentile GMAT Score or Bust! Lesson 2: If the Answers Smell the Same, They Stink

raviVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

 

Lesson Two:

If Answers Smell the Same, They Stink.  GMAT verbal problems all carry the same basic instruction: select the best answer from this list of five; while that may sound straightforward enough, it actually lends itself to a powerful strategy.  Since there cannot be two correct answers, if two answer choices are too similar, you can infer that neither is correct.  In this video, Ravi explains how to leverage that strategy to save yourself from trap answers and ensure that your decision process takes place on the proper grounds.

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

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

By Brian Galvin

Planning for Retirement (& the GMAT)

Ron Point_GMAT TipsWhen preparing for the GMAT, most prospective students start thinking about the schools they want to attend, the jobs they want to land and the opportunities they want to seize. After all, embarking on a new degree is an adventure that must be carefully prepared and thought out. Some students with long term thinking even begin thinking about something that most people dream of regularly: retirement.

Now, if you’re studying for an advanced degree, perhaps retirement is still many decades (or centuries) off. However, the day will likely come when you at least want to consider retirement, even if you don’t opt to do it for various reasons. Sometimes your economic reality keeps you gainfully employed, but often it becomes an issue of boredom, trepidation and even fear. Why would anyone fear retirement? Isn’t it supposed to be the culmination of your hard work so that you can enjoy your golden years without worrying about work and money? It is, at least in theory. However, in practice, it is a project that should be prepared for just like any other major life change.

In North America, many people retire and move to a sunny, warm climate such as Arizona or Florida. The temperate weather allows many people to enjoy outdoor activities regularly, sometimes in stark contrast to the cooler northern climates. (Winter is coming.) Many people are even opting to retire in other countries to take advantage of the increased buying power of their home currency. No matter whether you plan on retiring tomorrow or in 50 years, it is something you must consider at one point or another in your life.

The GMAT often features questions that discuss relevant topics and that arouse your own interests in order to make the questions more relatable. This is also a double-edged sword because the question must be solvable with only the information contained within the stimulus. Any outside information can’t help you, but the topic may still concern something you’ve contemplated in the past. Let’s look at an example that plays into the retirement theme:

In the United States, of the people who moved from one state to another when they retired, the percentage who retired to Florida has decreased by three percentage points over the past ten years. Since many local businesses in Florida cater to retirees, these declines are likely to have a noticeably negative economic effect on these businesses and therefore on the economy of Florida.

Which of the following, if true, most seriously weakens the argument given?

A) People who moved from one state to another when they retired moved a greater distance, on average, last year than such people did ten years ago.

B) People were more likely to retire to North Carolina from another state last year than people were ten years ago.

C) The number of people who moved from one state to another when they retired has increased significantly over the past ten years.

D) The number of people who left Florida when they retired to live in another state was greater last year than it was ten years ago.

E) Florida attracts more people who move from one state to another when they retire than does any other state.

This problem is a Critical Reasoning Weaken problem, which means that we should be able to identify the conclusion, examine the supporting evidence and find the gap between the two. The conclusion is that the economy of Florida will suffer based on shifting demographics. The evidence is that a smaller percentage of people are retiring to Florida than 10 years ago, coupled with the fact that Florida’s economy is dependent on these retirees. (Nothing about hurricanes or floods, though.)

If we had to predict an answer to this question, it would likely hinge on the fact that the evidence is a 3% decrease of all retirees who choose to move to Florida. Whenever you see a percentage as evidence, it should make you think that you may need to consider the absolute value as well (the reverse is also often true). Just because the percentage went down by 3%, that doesn’t mean that fewer people are actually going. You might still be growing, just growing slower than you were 10 years ago. Let’s look at the answer choices and see if any of them match our expectations.

Answer choice A, people who moved from one state to another when they retired moved a greater distance, on average, last year than such people did ten years ago, discusses the distance of these moves. This is clearly out of scope, as the question is only interested with the destination state, not in the original state. One mile (maybe you’re right on the border?) or one thousand miles are identical in this regard, so the distance travelled won’t matter. We can eliminate A.

Answer choice B,  people were more likely to retire to North Carolina from another state last year than people were ten years ago, is only concerned with North Carolina. There are clearly many other states that people can move to, but none of them are pertinent to the question about Florida. This answer choice is thus incorrect as well (and paid for by the North Carolina tourism board).

Answer choice C, the number of people who moved from one state to another when they retired has increased significantly over the past ten years, plays right into our prediction. Just because a smaller proportion than before is moving to Florida does not mean that there is economic collapse on the horizon. If 20% of one million people moved to Florida ten years ago, we could have more immigration by reducing the percentage to 17% but increasing the number of people to two million. As such, answer choice C weakens the argument significantly, as it could justify a sizable increase in relocations to the sunshine state. Let’s look at the other choices to confirm.

Answer choice D, the number of people who left Florida when they retired to live in another state was greater last year than it was ten years ago, turns the argument on its ear by discussing the number of people leaving Florida. While there is some merit in arguing that people are leaving the state in bigger numbers, it would actually support the argument that local businesses are in trouble. This answer choice is a 180° because it strengthens the argument instead of undermining it.

Finally, answer choice E, Florida attracts more people who move from one state to another when they retire than does any other state, is most likely true in the real world, but doesn’t help us in this question. If I have the most water in a drought, I may still not have much water at all. This answer choice doesn’t weaken the argument because it’s still entirely possible that the economy of Florida will suffer. Answer choice E can be eliminated. We now can confirm that it must be answer choice C.

For strengthen and weaken questions, it’s often best to attempt a logical guess at the answer choice based on the disconnect between the conclusion and the supporting evidence. Some statistical errors appear frequently on the GMAT, such as percentage and absolute number data that can be interpreted differently depending on the context. Like anything else in life, preparation is the key to success. Once you’ve mastered the finer elements of the GMAT, you can even start preparing your own retirement plan.

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.

Simplifying Algebraic Equations on Data Sufficiency GMAT Questions

GMAT QuantIn the past few weeks, I’ve written a couple of posts extolling the virtues of using strategies in lieu of doing difficult algebra. But over the course of the quant section, there’s no getting around it: at times, algebra will be an effective tool that you’ll want to deploy. The key is for us to use this tool judiciously.

Because the GMAT is largely a test of pattern recognition, it’s worthwhile to first discuss the structural clues that we’ll want to be on the lookout for when determining whether algebra will be the most effective approach. My older posts discussed two scenarios when algebra would be problematic: the first was problem-solving questions involving difficult quadratic simplification, and the second was problem-solving percent questions that involved variables. In both cases, we’re better off either picking numbers or back-solving. Alternatively, when we see Data Sufficiency word problems, algebra serves a much more useful function, allowing us to distill complex information in simpler, more concrete form.

Once we recognize that we’ll be attacking a question algebraically, the next step is to consider how we can make our equations and expressions as simple as possible. Say, for example, that we’re told that the ratio of men to women to children in a park is 6 to 5 to 4. One way to depict this information is to write M:W:C = 6:5:4. The problem with this approach is that it leaves us with three variables. Hardly the simplicity and elegance that we’re looking for if we’re dealing with a time constraint. The alternative is to use only one variable and depict the information in terms of x:

Men:  6x

Women: 5x

Children: 4x

Now when we receive additional information about how these values are related, the equations we can assemble will be far more straightforward. Let’s try a GMATPrep* question to see this in action.

A certain company divides its total advertising budget into television, radio, newspaper, and magazine budgets in the ratio of 8:7:3:2 respectively. How many dollars are in the radio budget?

(1) The television budget is $18,750 more than the newspaper budget

(2) The magazine budget is $7,500.

We’ve got a Data Sufficiency word problem, so let’s start by putting all of the relevant information into algebraic form. Rather than using four different variables, we’ll organize our information like so:

Television: 8x

Radio: 7x

Newspaper: 3x

Magazine: 2x

Our ultimate goal is find the radio budget, which is 7x. Clearly, if we have the value of x, we can find 7x, so we can rephrase the question as: ‘What is the value of x?’

Statement 1 tells us that the television budget, 8x, is 18,750 more than the newspaper budget, 3x. In algebraic form, that will be: 8x = 18750 + 3x. Obviously, we can solve for x here, so SUFFICIENT.

Statement 2 tells us that the magazine budget, or 2x, is 7500. So 2x = 7500. Again, we can clearly solve for x, so SUFFICIENT.

And the answer is D; either statement alone is sufficient to answer the question.

Let’s try another.

Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and 1/7 of the remaining shares are shares of Company Y stock. How many shares of Company X stock does the investor own?

(1) The investor owns 100 shares of Company Y stock.
(2) The investor owns 200 more shares of Company X stock than of Company Y stock.

Same drill: we recognize that we’re dealing with a Data Sufficiency word problem, so let’s convert the initial into algebraic form.

If we designate our total shares of stock ‘T,’ and we know that 30% of those are Company X, we’ll have .3T shares of company X. We’re told that 1/7 of the remaining shares are Company Y. If .3T shares are company X, we’ll have .7T shares left over. If 1/7 of those .7T shares belong to Company Y, we can designate Company Y’s shares as (1/7) * .7T =   .1T.

Summarized, we have the following information:

Company X: .3T

Company Y: .1T

We’re asked about Company X, so we want .3T. Clearly, if we have T, we can solve for .3T, so our rephrased question is just: “What is the value of T?”

Statement 1 tells us there are 100 share of Y, so .1T = 100. We can solve for T, so SUFFICIENT.

Statement 2 tells us that the investor has 200 more shares of X than Y. Algebraically: .3T = 200 + .1T. Again, we can solve for T, but no need to actually do the math. SUFFICIENT.

The answer is D; either alone is sufficient to answer the question.

Takeaway: preparation for the GMAT is not about learning which strategies are ‘best.’ Different strategies will work well in different scenarios, and for some test-takers, it will be a matter of taste to determine which they prefer. If you do decide to approach a question algebraically – and again, in Data Sufficiency word problems, this will often work nicely – try to diminish the complexity of the problem by minimizing the number of variables you use to depict the relevant information.

*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. You can find more articles by him here

99th Percentile GMAT Score or Bust! Lesson 1: Drywall vs. Door

raviVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99th” video series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

 

Lesson One:

Drywall vs. Door.  Many GMAT quantitative problems resemble an everyday situation you see frequently: you need to get out of this room, so are you going to break through the drywall you might be facing, or will you look for a door for easy exit? As Ravi demonstrates in this video, too often students are inclined to break through the proverbial drywall on quant problems, when looking at them from a slightly different angle would show them an open door and a cleaner exit.

 

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

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

By Brian Galvin

Start from the Beginning of GMAT Questions to Understand the Pattern

Ron Point_GMAT TipsIf you’ve ever walked into a conversation that was in progress, you know how hard it can be to figure out what’s going on without starting at the beginning. People often timidly ask “What are we talking about?” or “Could you please start over?” in such situations. This is because being parachuted into an ongoing conversation can be quite disorienting.

Most of the time, you can eventually figure out what’s happening, but sometimes you missed an important point near the beginning and just can’t understand the situation. As frustrating as this situation may seem, imagine if, at the end of the conversation, everyone turned to you and asked you to give your detailed opinion on the debate!

On the GMAT, you will frequently be parachuted into a situation that is already in progress. This type of scenario discombobulates most people, because we’re used to a gradual progression starting from the beginning. Since you won’t be at the beginning, you will need to figure out the beginning and the end given what you know from your position in the middle. (In essence, you’re Malcolm). You may not immediately know how to solve the issue, but you can deduce the beginning by seeing where you are in the middle and attempting to reverse engineer the process.

In many ways, this is similar to the dichotomy between multiplication and division. They are, in effect, the exact same operation (multiplying by 2 is dividing by ½ and vice versa). However, people tend to find multiplication easier because you’re going forward. Going backwards is typically harder, in no small part because your brain is not used to going in that (one) direction. When you do something a hundred times a day, it becomes second nature. If you start something for the first time on the GMAT, it may seem almost impossible to solve.

Let’s look at an example of a problem that starts you off in the middle of the action:

A term an is called a cusp of a sequence if an is an integer but an+1 is not an integer. If a5 is a cusp of the sequence a1, a2,…,an,… in which a1 = k and an = -2(an-1 / 3) for all n >1, then k could be equal to:

  • 3
  • 16
  • 108
  • 162
  • 243

Sequences are excellent examples of this parachuting phenomenon because you typically need to have the previous entry in order to find the next element (like a scavenger hunt!). If you find a3, you should be able to find a4. But if you have a4, it’s a lot harder to identify a3. Since you tend to have the pattern, you have to start at the beginning to uncover the progression.

This particular sequence is made easier if you manipulate the algebra a little to get a more manageable form. Instead of the way the sequence is defined, change the pattern to an = -2/3 an-1. This small change highlights the fact that the new element is just the old element multiplied by -2/3. And since the question hinges on when the sequence changes from integers to non-integers, it’s really the denominator that will be of interest to us.

Since this is fairly abstract, let’s go through plugging in answer choice A to see what happens to the series. If k = 3, then the second element of the series would be -2/3 (3). This gives us just -2, and is still an integer. However, the next iteration, a3, would call for -2/3 (-2), which is 4/3, and not an integer. Indeed, this sequence is just calling for us to continually divide by 3, and then determine when the result will no longer be an integer. Clearly, answer choice A won’t be the right choice, as we just found that a3 was not an integer, and thus a2 would be the “cusp” as defined in the question.

Now, using the brute force approach of plugging in each answer choice will eventually yield the correct answer, but it can be tedious and time-consuming. A more logical approach would involve determining that we need a number that has many 3’s in its prime factors. Every time we divide by 3, we will get another integer, provided that we still have 3’s in the numerator. Once we’re left with a number that is not a multiple of 3, the sequence will spit out a non-integer, and the previous number will be the cusp.  Using the prime factorization of the four remaining answer choices, we get:

16 = 2^4

108 = 2 * 54 –) 2 * 2 * 27 –) 2^2 * 3^3

162 = 2 * 81 –) 2 * 3 * 27 –) 2 * 3^4

243 = 3 * 81 –) 3^5

So as we can see, one answer choice has three 3’s, the other has four and the final one has five (the seventh would be Furious). How many 3s do we actually need? Well if the fifth one must be the cusp, then we need to divide by 3 four separate times to get rid of all the 3s. After that, the fifth element will be an integer (also, an action movie), and the sixth element will be a non-integer. Since answer choice D is our educated guess, let’s double check our answer by executing the sequence on 162.

A1 = 162

A2 = -2/3 (162) = -108

A3 = -2/3 (-108) = 72

A4 = -2/3 (72) = -48

A5 = -2/3 (-48) = 32

A6 = -2/3 (32) = -64/3.

This is exactly what we wanted. We can see that each time we are multiplying the previous item by 2/3 and changing the sign. Once we get to 32, that is just 2^5 and dividing it by 3 will no longer yield an integer.

If you’d gone through the complete trial and error process, you’d quickly see that answer choices A and B are incorrect. Answer choice C, 108, comes pretty close, but cusps at A4, not A5. If you then pick answer choice D, 162, you find that you get to 108 on the second iteration, and you can skip the next four steps because you just did them. Finally, answer choice E is a tempting number to start testing with, because it is a perfect exponential of 3. However, you will get to an integer at A6, and thus you need a number with fewer 3s in the numerator.

On test day, you might be able to recognize patterns or you might have to bite the bullet and try each answer choice one by one. However, if you recognize that you need to determine what happens at the beginning before moving on to the middle and the end, you’ll have more success. You always need to understand the pattern, and that starts at the beginning. If you keep this strategy in mind, you won’t find yourself stuck in the middle (with you).

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.

Simplify Your Calculations on Data Sufficiency GMAT Questions

Student StudyingIn a previous post, I emphasized the importance of minimizing the number of variables we assign when tackling word problems in Data Sufficiency. This philosophy also works quite well when dealing with complicated geometry questions. Let’s say, for example, that you had an isosceles triangle. We know that in isosceles triangles, two sides will be equal and the angles opposite those sides will be equal to each other. Rather than call the angles ‘x,’ ‘y,’ and ‘z,’ we can designate the two equal angles as ‘x.’ Because these two angles sum to 2x, the remaining angle must be 180-2x, as the interior angles of a triangle always sum to 180.  Now we have one variable to deal with, rather than three, and this greatly simplifies any future calculations we’ll have to make.

Let’s apply this logic to an extremely challenging 700+ level Data Sufficiency question*:

We’re given the following:

GMAT1

In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

  • The degree measure of angle COD is 60
  • The degree measure of angle BCO is 40

That is a complicated-looking figure. Your instinct might be that you don’t have time to draw it, but these kinds of questions will be designed specifically to thwart our intuition if we attempt to do too much work in our heads. So the first thing to do is draw the figure on our scratch pad, and mark the relationships we’re given. We’re told that segment CO is equal to AB, so we’ll designate that relationship. We’ll also call angle BAO, which we’re asked about, ‘x.’ Now we have the following:

GMAT2

Fight the impulse to jump to the statements now. In a harder question like this, we’ll benefit from taking more time to derive additional relationships from the question stem. Psychologically, this is often a struggle for test-takers. You’re conscious of your time constraint. You want to work quickly. The trick is to trust that this pre-statement investment of time will allow you to evaluate the information provided in the statements more efficiently, ultimately saving time.

Now the name of the game is to try to label as much of this figure as we can without introducing a new variable. Notice that segments CO and BO are both radii of the circle, so we know those are equal. Our diagram now looks like this:

GMAT3

Next, look at triangle ABO. Notice that segments AB and BO are equal. If angles opposite equal angles are equal to each other, we can then designate angle AOB as ‘x’ because it must be equal to angle BAO, as those two angles are opposite sides that are of equal length. Moreover, if the three interior angles of a triangle will sum to 180, the remaining angle, ABO, can be designated 180-2x. This gives us the following.

GMAT4

No reason to stop here. Notice that angles ABO and CBO lie on a line. Angles that lie on a line must sum to 180. If angle ABO is 180-2x, then angle CBO must be 2x. Now we have this:

GMAT5

Analyzing triangle CBO, we see that sides BO and CO are equal, meaning that the angles opposite those sides must be equal. So now we can label angle BCO as ‘2x.’ If angles CBO and BOC sum to 4x, the remaining angle, BOC, must then be 180-4x, so that the interior angles of the triangle will sum to 180.

GMAT6

We’ve got enough at this point that we can very quickly evaluate our statements, However, there is one last interesting relationship. Notice that angle COD is an exterior angle of triangle CAO. An exterior angle, by definition, must be equal to the sum of the two remote interior angles. So, in this case, Angle COD is equal to the sum of angles BCO and BAO. Therefore COD = 2x + x = 3x, which I’ve circled in the figure. (Triangle CAO is outlined in blue in the figure below to more clearly demarcate the exterior angle.)

GMAT7

That’s a lot of work. Determining all of these relationships will likely take close to two minutes. But watch how quickly we can evaluate our statements if we’ve done all of this preemptive groundwork:

Statement 1: Angle COD = 60. We’ve designated angle COD as 3x, so 3x = 60. Clearly we can solve for x. Sufficient. Eliminate BCE.

Statement 2: Angle BCO  = 40. We’ve designated angle BCO as 2x, so 2x = 40. Clearly we can solve for x. Sufficient. Answer is D.

Notice, all of the heavy lifting for this question came before we even so much as glanced at our statements.

Takeaway: For a challenging Data Sufficiency question in which you’re given a lot of information in the question stem, the best approach is to spend some time taming the complexity of the problem before examining the statements. When you work out these relationships, try to minimize the number of variables you use when doing so, as this will simplify your calculations once you’re ready to go to the statements. Most importantly, don’t do too much work in your head. There’s no need to rely on the limited bandwidth of your working memory if you have the option of putting everything into a concrete form on your scratch pad.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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

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

GMAT Tip of the Week: Writing the AWA Without Engaging Your Brain

GMAT Tip of the WeekWriting a Friday GMAT Tip of the Week post on a tight deadline is a lot like writing the AWA essay in 30 minutes.

30 minutes is not a lot of time, many say, and because an effective essay needs to be well-organized and well-written it is therefore impossible to write a 30-minute essay.

Let’s discuss the extent to which we disagree with that conclusion, in classic AWA style.

In the first line of a recent blog post, the author claimed that writing an effective AWA essay in 30 minutes was impossible. That argument certainly has at least some merit; after all, an effective essay needs to show the reader that it’s well-written and well-organized. But this argument is fundamentally flawed, most notably because the essay doesn’t need to “be” well-written as much as it needs to “appear” well-written. In the paragraphs that follow, I will demonstrate that the conclusion is flawed, and that it’s perfectly possible to write an effective AWA essay in 30 minutes or less.

Most conspicuously, the author leans on the 30-minute limit for writing the AWA essay, when in fact the 30 minutes only applies to the amount of time that the examinee spends actually typing at the test center. In fact, much of the writing can be accomplished well beforehand if the examinee chooses paragraph and sentence structures ahead of time. For this paragraph, as an example, the transition “most conspicuously” and the decision to refute that claim with “in fact” were made long before I ever stopped to type. So while the argument has merit that you only have 30 minutes to TYPE the essay, you actually have weeks and months to have the general outline written in your mind so that you don’t have to write it all from scratch.

Furthermore, the author claims that the essay has to be well-written. While that’s an ideal, it’s not a necessity; if you’ve followed this post thus far you’ve undoubtedly seen a number of organizational cues beginning and then transitioning within each paragraph. However, once a paragraph’s point has been established the reader is likely to follow the point even if it’s a hair out of scope. Does this sentence add value? Maybe not, but since the essay is so well-organized the reader will give you the benefit of the doubt.

Moreover, while the author is correct that 30 minutes isn’t a lot of time, he assumes that it’s not sufficient time to write something actually well-written. Since the AWA is a formulaic essay – like this one, you’ll be criticizing an argument that simply isn’t sound – you can be well-prepared for the format even if you don’t see the prompt ahead of time. Knowing that you’ll spend 2-3 minutes finding three flaws in the argument, then plug those flaws into a template like this, you have the blueprint already in place for how to spend that time effectively. Therefore, it really is possible to write a well-written AWA in under 30 minutes.

As discussed above, the author’s insistence that 30 minutes is not enough time to write an effective AWA essay lacks the proper logical structure to be true. The AWA isn’t limited to 30 minutes overall, and if you’ve prepared ahead of time the 30 minutes you do have can go to very, very good use. How do I know? This blog post here took just under 17 minutes…

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

Exploit the Gap in Logic on Critical Reasoning GMAT Questions

Ron Point_GMAT TipsWhen dealing with strengthen or weaken Critical Reasoning questions, it’s important to have a rough idea of what the correct answer should look like. This process is often called “predicting” the correct answer, and it helps tremendously to avoid tempting but incorrect answer choices. It’s important to note that you won’t always be able to guess the exact answer choice provided, but you can get within the ballpark. After all, the correct answer is something that will hinge on the inevitable disconnect between the conclusion stated and the evidence provided in the passage.

Let’s focus on this disconnect first. If the GMAT provided you airtight arguments that were absolutely perfect, there would be no simple way to strengthen or weaken them. As such, the arguments provided inevitably have some kind of gap in logic contained between the conclusion and the evidence that theoretically supports that conclusion. Your goal is to identify that gap and either attempt to seal it up (strengthen) or rip it apart (weaken).

Of course, a dozen different answers could all weaken the same conclusion, so it’s not always possible to predict the exact answer ahead of time. However, all the answers that weaken the conclusion stem from the same gap (not banana republic) in logic, whereby the evidence provided does not quite support the conclusion stated. If you can identify the conclusion and the gap in logic, you tend to do quite well on these types of questions.

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

Researchers have recently discovered that approximately 70% of restaurant lemon wedges they studied were contaminated with harmful microorganisms such as bacteria and fungal pathogens. The researchers looked at numerous different restaurants in different regions of the country. Most of the organisms had the potential to cause infectious disease. For that reason, people should not order lemon wedges with their drinks.

Which of the following, if true, would most weaken the conclusion above?

A. The researchers could not determine why or how the microbial contamination occurred on the lemon wedges.

B. The researchers failed to investigate contamination of restaurant lime wedges by harmful microorganisms.

C. The researchers found that people who ordered the lemon wedges at restaurants were equally likely to contact the diseases caused by the discovered bacteria as were people who did not order lemon wedges.

D. Health laws require lemons to be handled with gloves or tongs, but the common practice for waiters and waitresses is to handle them with their bare hands.

E. Many factors affect the chance of an individual contracting a disease by coming into contact with bacteria that have nothing to do with lemons. These factors include things such as health and age of the individual, as well as the status of their immune system.

There is a lot of text to review for this question, so let’s begin by identifying the conclusion. (Pauses an appropriate amount of time for review). The final sentence “For that reason, people should not order lemon wedges with their drinks” is the conclusion. In fact, the first three words can be removed, as they simply point to the fact that everything previous to that sentence is evidence to back up the ultimate conclusion. The passage concludes that we should not order lemon wedges (Antilles).

Let’s examine the evidence provided to back this up: 70% of the wedges observed are contaminated, and this contamination can lead to infectious diseases. Furthermore, the study was conducted in various locations across the country. This means we can’t weaken the conclusion by simply going two towns over. Apart from that, the sky’s the limit.

At first blush, this passage seems like a classic causation/correlation problem. The majority of lemon wedges are contaminated, so we shouldn’t order the lemon wedges in order to avoid falling ill. Well what if something else (say the water) was contaminated, leading to tainted lemon wedges. Then we’d avoid the wedges without avoiding the underlying cause of the diseases. In the general sense, avoiding the lemon wedges may not have the desired effect because there is nothing guaranteeing that it is solely the wedges that cause infectious diseases.

Now let’s look at the answer choices, keeping in mind that the correct answer choice should weaken the conclusion that the wedges are somehow responsible for any potential illness.

Answer choice A, “the researchers could not determine why or how the microbial contamination occurred on the lemon wedges”, doesn’t help in any real way. Just because you don’t understand how a virus works doesn’t make it any less dangerous to you (e.g. the Walking Dead). The problem is still the lemon wedges, even if no one is sure why. This answer choice can be eliminated.

Answer choice B, “the researchers failed to investigate contamination of restaurant lime wedges by harmful microorganisms” is quite obviously out of scope. Lime wedges have very little to do with lemon wedges (despite what Sprite says), so the cleanliness of the lime wedges is irrelevant to avoiding the lemon wedges. It is possible to be tempted by this answer choice if you conflate lemon with lime, especially if you’re tired, but a thorough analysis convincingly knocks this choice out.

Answer choice C, “the researchers found that people who ordered the lemon wedges at restaurants were equally likely to contact the diseases caused by the discovered bacteria as were people who did not order lemon wedges” is spot on. We had predicted that the problem was about lemon wedges being correlated to infectious disease without necessarily causing them. This answer choice tells us that people who didn’t order the lemon wedges were exactly as likely to fall sick as those who did. Therefore, avoiding the lemon wedges (the conclusion) will have no effect on your likelihood of feeling sick. This will be the correct answer, but we should look through the remaining two choices nonetheless.

Answer choice D, “health laws require lemons to be handled with gloves or tongs, but the common practice for waiters and waitresses is to handle them with their bare hands.” is almost certainly true, but does not weaken the conclusion. Newsflash: Not everyone follows health code guidelines. (I’ve seen Ratatouille). If anything, knowing such an uncouth practice is commonplace would strengthen the idea of not ordering lemon wedges. Answer choice D is incorrect, as our goal is to weaken the conclusion.

Finally, answer choice E, “Many factors affect the chance of an individual contracting a disease by coming into contact with bacteria that have nothing to do with lemons. These factors include things such as health and age of the individual, as well as the status of their immune system” is also true, but orthogonal to the issue of lemon wedges. Perhaps you could claim that healthy people have fewer risks in ordering lemon wedges, but still it would be a health risk. This answer does not weaken the conclusion in any way, and must therefore be discarded as well.

As indicated before, your prediction might not match exactly the correct answer choice, but it will exploit the gap in logic between the conclusion and the evidence. There will inevitably be (at least) one disconnect between the conclusion and the supporting evidence presented, your goal is to identify and elaborate upon that gap. If you successfully do that on test day, you can go toast your score with a celebratory drink, lemon wedges and all.

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 Simple Shortcut to Help You on the Quantitative Section of the GMAT

A New IdeaThere are certain strategies that we all know, and yet, for whatever reason, sometimes hesitate to use during the exam. Some students are unusually skilled in algebra, for example, and so when we discuss the option of picking numbers, they dutifully nod and decide that this approach isn’t for them, that picking numbers is an unsatisfying shortcut that robs them of the opportunity to display their algebraic virtuosity.

The problem with this line of thinking is that our goal on the test isn’t simply to answer the questions correctly, but to do them within the confines of a challenging time constraint. So while it might feel more satisfying for the quantitatively-inclined to solve a complicated system of equations than it would feel to use a strategy, a strictly algebraic approach can be counterproductive, even if done correctly.

Take this Official Guide* question, for example:

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine’s average speed for the entire trip? 

A. (1800 – x) /2
B. (x + 60) /2
C. (300 – x ) / 5
D. 600 / (115 – x )
E. 12,000 / ( x + 200)

Here’s what happens if we do this algebraically: let’s say that the total distance traveled is ‘D.’ If x% of the trip is spent traveling 40mph, then this distance can be represented as (x/100)*D. This means that the remaining distance, during which Francine will be traveling at 60mph, will be [1 – (x/100)]*D.

Here’s what this will look like in a standard rate table:

R T D
Part 1 40 [(x/100) * D]/40 (x/100) * D
Part 2 60 [[1 – (x/100)]*D]/60 [1 – (x/100)]*D
Total Ugh D

 

Well, good luck. Incidentally, this is how the Official Guide solves this question in their explanations. This approach will get you to the answer. But it will likely be difficult and time-consuming.

So rather than suffer through the brutal algebra required above, we can pick numbers. I always appreciate symmetry in my math problems, so let’s say that Francine went the same distance at 40mph as she did at 60mph. If this is the case, then she went 50% of the distance at 40mph, and x = 50.

Next, we can pick any distance we like for both parts of the trip. To make the arithmetic as simple as possible, let’s pick a number that’s a multiple of both 40 and 60. 120 will work nicely. Now our table will look like this:

R T D
Part 1 40 120
Part 2 60 120
Total

 

Life is much improved. We can see that Francine spent 3 hours going 40mph and 2 hours going 60mph, so now we can fill in the rest of the table:

R T D
Part 1 40 2 120
Part 2 60 3 120
Total R 5 240

 

Solving for R, we get R*5 = 240. R = 48.

Not so bad. So we know that if x = 50, the average rate should be 48. Now all we have to do is plug 50 in place of ‘x’ in all the answer choices, and once we get to 48, we’ll have our answer.

Before we proceed, let’s think about this from the perspective of the question-writer for a moment. If we were trying to make this question more challenging, where would we put the correct answer? Considering that the average test-taker will start with A and work her way down, it makes sense to put the correct answer towards the bottom of our options, as this will require more work for the test-taker. Let’s get around this by starting with E and working our way up.

E. 12,000 / (x + 200)

Substituting 50 in place of ‘x’ we get:

12,000 / 250

Rather than doing long division, I’ll rewrite 12,000 as 12*1000 to get

12*1000/250

That becomes 12 * 4 = 48. That’s what we want. We’re done. The answer is E.

Takeaway: There are no style points on the GMAT. We don’t want the approach that would most impress our fellow test-takers, we want the approach that gets us the right answer in the shortest amount of time. Percent questions that involve variables are excellent opportunities for simplifying matters by picking numbers.

Moreover, when we find ourselves in a situation that requires testing the answer choices, we want to remember that the problem will be more challenging if the correct answer is D or E, so while this won’t always be true, it is the case often enough that it’s beneficial to start by testing E and systematically working our way up. As soon as we have our answer, we’re finished. We can save the impressive mathematical flourishes for our finance classes.

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

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

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

When Do You Have Enough Information on Data Sufficiency GMAT Questions?

Ron Point_GMAT TipsHabitually, data sufficiency questions give students cause for concern on the GMAT quantitative section. This is primarily due to the fact that data sufficiency questions are rarely seen in high school and college, and are therefore relatively unknown to most prospective test takers.  If you remember the first data sufficiency question you encountered while studying for the GMAT, it may have looked like it was written in another language.

In many ways, data sufficiency questions are like being in a foreign land. Even if you understand the rules, you’re often not as comfortable as in your native environment that you’ve acclimated to over many years (e.g.  an Englishman in New York). It is normal to feel a little discombobulated, especially at first. However, once you’ve done a few (hundred) data sufficiency questions, you tend to get a feel for the question type. One issue still eludes a lot of test takers: When is it enough?

Data sufficiency is asking about (drum roll, please) when the data is sufficient. It’s pretty easy to disprove something if you can find a counter-example right away, but if you struggle with finding definitive proof, how long should you try to work at it.

Suppose a question asks whether X^2 = Y^3, that is asking whether any perfect square is also a perfect cube, you could spend a lot of time meandering towards a solution. What if we try 2^3, which gives 8? Well 8 isn’t a perfect square of any number, so we keep going. 3^3 is 27, which isn’t a perfect square of any number either. How far should we go? The next number, 4^3, gives 64, which is a perfect square, so we found an example relatively quickly, but we could conceivably spend several minutes calculating various permutations. Imagine a question asking if X^2 = Z^5 and see how long it would take to find an example.

The good news is that the question is almost always solvable using logic, algebra and mathematical properties. The bad news is it’s not always obvious how to proceed with these definitive approaches, and the brute force strategy is often employed. We can try various options and see if any of them work, while at the same time looking for patterns that tend to repeat or signal the underlying logic of the situation. While this strategy certainly has its place, it can sometimes be very wearisome.

Let’s look at a data sufficiency question that highlights this issue:

W, X, Y and Z represent distinct integers such that WX * YZ = 1,995. What is the value of W?

   WX

* YZ

_____

1,995

  • X is a prime number
  • Z is not a prime number
  • Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
  • Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
  • Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
  • Each statement alone is sufficient to answer the question.
  • Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

This question can be very tempting to start off with brute force. We can limit our choices by looking at the unit digits. If the unit digit of the product is 5, then there are only a few digits that are possible for X and Z. They all have to be odd, and, more than that, one of them must be exactly 5, as no other digits combine to give a 5. If one of them is 5, the other one is some odd number, 1, 3, 5, 7 or 9. Unfortunately, multiple options exist at both prime (3, 5 and 7) and non-prime (1, 9) for these digits, so it will be hard to narrow down the choices (where’s a dart board when you need one?)

Let’s look at this problem another way, which is: these two numbers must multiply to 1,995. We know one number ends with a 5, so we arbitrarily set it to be 25 and see what that gives if we set the other number to be 91. That comes to 2,275, which is way above what we need. How about 25 * 81, that yields 2,025. That’s too big, but just barely. How about 25 * 79? That will give us 1,975, which is slightly too small. We can’t get 1,995 with 25, but that’s all we’ve demonstrated so far. We can eliminate some choices as number like 15 can never be multiplied by a 2-digit number and yield 1,995, but there are still numerous choices to test.

It’s pretty easy to see how the brute force approach when you have dozens of possibilities will be very tedious. There’s another element that’s even worse, which is let’s say you manage to find a combination that works (such as 21 * 95), how can you be sure that this is the only way to get this product? Short of trying every single possibility (or calling the Psychic Friends hotline), you can’t be sure of your answer.

This problem thus requires a more structured approach, based on mathematical properties and not dumb luck. If two numbers multiply to a specific product, then we can limit the possibilities by using factors. We thus need to factor out 1,995 and we’ll have a much better idea of the limitations of the problem.

1,995 is clearly divisible by 5, but the other number might be hard to produce. The easiest trick here is to think of it as 2,000, and then drop one multiple of 5. Since 2,000 is 5 x 400, this is 5 x 399. Now, 399 is a lot easier than it looks, because it’s clearly divisible by 3 (since the digits add up to 21, which is a multiple of 3). Afterwards, we have 133, which is another tough one, but you might be able to see that it’s divisible by 7, and actually comes to 7 x 19. Finally, since 19 is prime, we have the prime factors of 1,995: 3 x 5 x 7 x 19.

How does this help? Well there may be 16 factors of 1,995, but the limitations of the problem tell us that we only have two two-digit numbers. Thus something like 15 * 133 breaks the rules of the problem. Our only options to avoid 3-digits are 19*3 and 5*7 or 19*5 and 3*7. This gives us either 57 * 35 or 95 * 21. At least at this point we’re 100% sure that these are the only two-digit permutations that combine to give 1,995.

Let’s get back to the problem. Statement 1 tells us that X (the unit digit of the first number) is prime, which knocks out 21 from the running. However the three other options all end with a prime unit digit, meaning that any of them are still possible. At this point it’s very important to note that the problem specified that W, X, Y and Z were all distinct integers. Since they must all be different, the option of 57 * 35 is not valid because the 5 is duplicated. As such, the only option is 95*21, and the prime number restriction confirms that it’s really 95 * 21 (and not 21 * 95). Variable W must be 9, and thus this statement ends up being sufficient.

Statement 2 essentially provides the same information, as Z is not a prime number and thus necessarily 1 given our choices. This confirms that the multiplication is 95 * 21 and W is still 9. Either statement alone is sufficient, so answer choice D is the correct option here. It’s important to note how close this question was to being answer choice B, as the non-prime limitation ensured we knew where the 1 was. But the fact that these digits had to be distinct changed the answer from B to D, reinforcing the adage that you should read the questions carefully.

This question can be solved without factors, but it is very hard to confidently answer it using only a brute-force approach. Solving through mathematics and number properties is not always the easiest route to success on data sufficiency. Sometimes you can write down a few options and see exactly how the problem will unfold, but if you use concrete concepts, you’ll know when it’s been enough.

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.

Take Notes on Critical Reasoning Questions to Increase Your GMAT Score

writing essayImagine that you were tasked with writing questions for the GMAT. You have to produce questions that have a clear answer but will trip up a certain percentage of test-takers. How do you do that reliably? The most straightforward way I can think of is to simply inundate the test-taker with information. What elicits the loudest groans during Reading Comprehension? Long, technical passages. What is the most unpleasant thing to see in a Data Sufficiency question? Lots of complex information in the question stem.

It’s not that these questions are asking you to do hard things, but the information overload makes it hard to determine what it is that you have to do. In fact, there is a vast body of literature demonstrating that the human brain has fairly circumscribed limits when it comes to working memory. Certain questions are designed to exploit this hard-wired deficit.

So how do we combat the brain’s working memory limitations? As we learn more and more about how working memory functions, researchers have discovered effective techniques for improving it. One technique, which I mentioned in a previous post, is mindfulness meditation. Another proposed technique is the judicious use of certain kinds of brain-training games. (Note that the research on the efficacy of brain training is decidedly mixed. Some studies show a robust improvement in general fluid intelligence. Other studies conclude that the improvements participants make in the game are not transferrable to other realms. I’ll explore this in more detail in a future post.)

Though I am a proponent of practicing mindfulness – both for improving standardized test scores and for boosting our mental and physical health – and I certainly have nothing against brain-training, the best way to combat the strain that the GMAT puts on our working memory is simply to write things down. There’s no need to juggle all the dizzying elements in a complex question in your head. Break hard questions into smaller, more manageable bites.

Consider the following GMATPrep* Critical Reasoning argument.

Kernland imposes a high tariff on the export of unprocessed cashew nuts in order to ensure that the nuts are sold to domestic processing plants. If the tariff were lifted and unprocessed cashews were sold at world market prices, more farmers could profit by growing cashews. However, since all the processing plants are in urban areas, removing the tariff would seriously hamper the government’s effort to reduce urban unemployment over the next five years.

Which of the following, if true, most seriously weakens the argument?

  1. Some of the by-products of processing cashews are used for manufacturing paints and plastics
  2. Other countries in which cashews are processed subsidize their processing plants
  3. More people in Kernland are engaged in farming cashews than in processing them
  4. Buying unprocessed cashews at lower than world market prices enables cashew processors in Kernland to sell processed nuts at competitive prices
  5. A lack of profitable crops is driving an increasing number of small farmers in Kernland off their land and into the cities

When I read this and try to internalize all the information, I can actually feel the strain. It’s unpleasant. So let’s boil this way down. When there is a tariff, domestic farmers are forced to sell to domestic producers. This is bad for farmers because they don’t have access to all relevant markets, and it’s good for domestic producers, because they’re competing against fewer potential buyers. As an arrow diagram, it might look like this:

Tariff –> hurt farmers –> helps domestic producers

The argument is about removing the tariff, which would, presumably, produce the opposite result. Now the farmers benefit because they have an additional market to sell to, and the domestic producers are harmed because they have to compete with foreign producers to buy the raw cashews. Our new arrow diagram would look like this:

No Tariff –> helps farmers –> hurt domestic producers.

The argument’s conclusion is that because removing the tariff will harm the domestic producers, the end result will be rising unemployment in cities. So we can tack that on to the arrow diagram:

No Tariff –> helps farmers –> hurt domestic producers –> rising unemployment in cities

If we want to weaken this argument, we want an answer choice that shows that removing the tariff will not cause unemployment to rise in cities, but rather, that not having a tariff might be good for the urban employment rate. (And note the scope here: we’re talking about urban unemployment. Attention to language detail is always crucial in CR questions).

To the answers:

  1. Hard to see how the use of the by-products will shed much light on urban unemployment. Out of Scope.
  2. Other countries? We’re talking about urban unemployment in Kernland. Out of scope.
  3. This one is interesting. We know that removing the tariff benefits farmers. If more people are farming than processing, it stands to reason that more people benefit from the tariff’s removal. But does this tell us anything about urban unemployment? The farmers don’t live in the city. The producers do. So if those producers are hurt, urban unemployment can still go up, even if they’re outnumbered by farmers. No good.
  4. We’re told specifically that if the tariff were lifted, cashews would sell “at world market prices.” Any benefit from selling at below market prices could only be realized if there were a tariff. But we’re trying to show that removing the tariff is a good thing! This answer choice does the exact opposite.
  5. This is correct, but requires a little unpacking. Remember that the tariff hurt the farmers. So back in the tariff days, the farmers were struggling, and, according to this answer choice, were forced to flee to the cities. There’s no reason to believe that these farmers had jobs waiting for them, so this chain of events would raise urban unemployment. But, if we remove the tariff, the farmers benefit, and if farmers are doing well, they won’t have to flee to the city, which would actually reduce Exactly what we want. (Note also that we’re talking about urban employment. This is the only answer choice that even mentions cities.)

This was a tough one. The point here is that the best way to grapple with complexity is to distill information into digestible bits. Write down what you want in a single phrase or two. A full paragraph laden with terminology can be hard to work with. A simple arrow diagram, like “No tariff –> lower urban unemployment” is far more manageable. You have a scratch pad for a reason – to give your working memory a break.

* 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. You can find more articles by him here.

Find Logical Meaning in Sentence Correction Questions on the GMAT

Ron Point_GMAT TipsOne of the hardest things about Sentence Correction is that it tests so much more than just grammar. Many students erroneously conflate Sentence Correction problems with high school grammar problems, and this can lead to avoidable mistakes on test day. Indeed, the rules you learned in high school still apply, but you must be able to recognize them among various other potential problems.  It’s fairly simple to spot an agreement error on a verb (there are one problem) or a misplaced comma (good, job bro), but sometimes you have to eliminate an answer choice because the sentence just doesn’t make sense.

Think about a sentence like “This table has four arms.” Grammatically, the sentence is flawless (although I use the term loosely). However, from a logical point of view, it doesn’t make any sense at all. Tables are colloquially said to have “legs,” even if these don’t exactly fit the Darwinian definition of the term, but they are not typically said to have “arms”. On the GMAT, this sentence is as incorrect as “This table have four arms,” but it’s much harder to see for most people. The error lies not in the grammar, but in the meaning.

In fact, there are two broad categories of illogical meanings on the GMAT. The first is the type described above: A sentence that just doesn’t make sense. The second type can be more subtle, as it constitutes the array of answer choices that change the meaning of the sentence. This error often occurs when the structure of the sentence is changed and no longer meshes with the rest of the sentence. A typical example would be changing from “Human beings have skulls…” to “The skulls of human beings”… Within the underlined portion, everything can seem fine. But if the rest of the sentence is discussing how human beings are remarkable adaptable creatures, this simple switch can have serious ramifications as it changes the meaning dramatically. Originally, human beings were remarkable creatures. Now only their skulls are remarkable creatures, which is completely nonsensical and thus not a valid sentence on the GMAT.

Let’s look at an example and see if we can keep the meaning of this sentence.

The Buffalo Club has approved tenets mandating that members should volunteer time to aid the community.

A) that members should volunteer time

B) that time be volunteered by members

C) the volunteering of time by members

D) members’ volunteering of time

E) that members volunteer time

This sentence is not particularly long, and the underlined portion is only five words, so each word should be weighed carefully. Most of the words are not underlined, so the sentence tells us that the Buffalo Club is mandating something specific, and the goal of this endeavor is to aid the community. The only options we have are the few words (Malcolm) in the middle of the sentence.

Using the original sentence (answer choice A) as a benchmark, we see that the club is mandating that members should volunteer their time. This sentence doesn’t have a glaring grammatical error, but the logical error here is quite noticeable. Mandating something means that it is required, so the verb “should” is illogical within the sentence. It’s like telling someone that they’ve arrived late to work for the past two weeks, and that they’re definitely fired. Maybe. Answer choice A is illogical because the word “should” contradicts the logic of the sentence and undermines the entire message.

Answer choice A is the only one to use the word “should”, so we cannot use that decision point to knock out any other choices. However, A does correctly begin with the word “that”, which is a correct idiom to be used with mandated. When something is mandated, it must either be “The club mandated that Ron win” or “the club mandated the victory be awarded to Ron”. Either way, the directive must be clear, and Ron must be declared the victor (now that’s what I call a win-win situation). Answer choices C and D can be eliminated because they do not follow either idiom of the verb, and the meaning of the sentence is distorted.

This only leaves answer choices B and E. Let’s evaluate answer choice B first, and we quickly notice that the sentence is more verbose than it needs to be. Furthermore, the sentence is switched to the passive voice because “time” is now the subject of the sentence, not “members”. Since the members are being mandated to do something, they must be the subject of the sentence, not the time they are volunteering. Answer choice B can be eliminated.

This leaves only answer choice E, and it is indeed the correct answer. Comparing it with answer choice A, it is exactly the same, except that it removes the superfluous “should”. In reality, the members are being mandated to help out the community, and this is non-negotiable (House of Cards’ Victor Petrov style) so there is no room for ambiguity by adding in a rider.

On the GMAT, the difference between a correct answer and an incorrect answer often comes down to which selection actually makes sense. Nowhere is this more common than on sentence correction problems, where the inclusion or exclusion of one word can dramatically alter the meaning of a phrase. Indeed, if you master the strategies of logical meaning on the GMAT, you will (not should) do well on the exam.

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.

Succeed on Critical Reasoning GMAT Questions with This Causation Tip

causation goslingOh, causation on the GMAT.  Why do you cause so much stress in people’s lives?

Success on many Critical Reasoning questions really comes down to understanding whether one thing (“X”) causes another thing (“Y”) or not. For example, I moved to New York in 2007. Shortly thereafter, there was a huge drop in the New York stock market. Did I cause the crash (Y) simply by moving to New York (X)?

Of course I did! But that’s beside the point.

Take a look at the following question from an MBA.com practice CAT:

The growing popularity of computer-based activities was widely predicted to result in a corresponding decline in television viewing. Recent studies have found that, in the United States, people who own computers watch, on average, significantly less television than people who do not own computers. In itself, however, this finding does very little to show that computer use tends to reduce television viewing time, since_______.

Which of the following most logically completes the argument?

Let’s not even look at the answer choices yet. We can do quite a bit of “pre-work” on a question like this before the answer choices begin to sway us in various directions.

In the simplest terms, the argument states that some believe:

An Increase in Computer Usage (ICU) causes a Decrease in Television Watching (DTW).

And this makes some logical sense, right? We only have a certain number hours per day, and if we spend some time on our laptops, we might not have as much time to catch up on Girls and Shark Tank.

The argument then goes on to state a bit of evidence that seems to support the initial prediction:

Computer Owning (not quite the same as ICU, but in the same ballpark) actually correlates with Watching Less Television (DTW).

However, the argument then, a bit paradoxically, states that even though “Computer Owning and DTW” seem to happen at the same time, it is not the case that “ICU causes DTW.” Interesting.

Well, whenever you see a case like this on the GMAT, you’re better off coming up with a possible answer or two before checking out the answer choices. When the GMAT says that “X and Y happen together, but X did not cause Y,” a very strong possibility is that “Z” actually caused Y. What is Z? Z is anything else that might have caused Y.

Here are some possible answer choices that would work:

  • People can generally only afford either one computer or one television (implying that ICU doesn’t cause the DTW, but the price of a computer might).
  • Computer owners tend to be overworked professionals who have very little leisure time (implying that ICU doesn’t cause DTW, but a pre-existing condition of computer owners is strongly correlated with DTW before the computer usage is even mentioned).
  • Computers create an electromagnetic field that disables televisions from turning on (implying that ICU doesn’t cause DTW, but the physical properties of owning a computer might).
  • Computer owners, at the point of purchase, were forced by the Illuminati to sign a document swearing never to watch television under the penalty of jail time (implying that ICU doesn’t cause DTW, but intense pressure from an underground fraternity might).

At this point, you might be saying, “Whoa, those answers were totally out of left-field.” Indeed, you’re right. When the argument concerns X’s and Y’s, and we’re looking for a Z (something else that might have caused Y), then the correct answer might very well be out of left-field. Do not eliminate an answer simply because it seems random or unexpected. Instead, simply focus on the chain of logic. If your out-of-left-field Z supersedes X as the primary cause of Y, you’ve done a great job of weakening the causal link between X and Y.

Now let’s look at the real answer choices:

(A) many people who watch little or no television do not own a computer.

(B) even though most computer owners in the United States watch significantly less television than the national average, some computer owners watch far more television than the national average.

(C) computer owners in the United States predominately belong to a demographic group that have long been known to spend less time watching television than the population as a whole does.

(D) many computer owners in the United States have enough leisure time that spending significant amounts of time on the computer still leaves ample time for watching television.

(E) many people use their computers primarily for tasks such as correspondence that can be done more rapidly on the computer, and doing so leaves more leisure time for watching television.

Boom. Answer choice C basically says that ICU doesn’t necessarily cause DTW, because the demographics of computer users correlate strongly with DTW independently of actually using the computer. While this answer choice does not exactly provide a direct cause of DTW, it does strongly weaken the causal link between ICU and DTW, and that should be your main goal.

Does a “Z” always represent the answer on GMAT causation weakeners? Not always, but it occurs frequently enough that it’s worth spending 5-10 seconds coming up with one or two Z’s on a question like this. If nothing else, doing so can help solidify a more complete understanding of the argument.

Hopefully this Blog Post (BP) will cause you to Do Well on Your GMAT (DWYG). When was the last time BP caused something good to happen?

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 David Ingber

How a 99th Percentile GMAT Instructor Approaches Sentence Correction Questions

99The other night, in class, I had a student come up to me and ask how I really approached Sentence Correction. We’d done our Sentence Correction lesson a few weeks before, so the implication was that there was a little more to it than the framework we’d covered. The mundane truth is that there isn’t. Not really.

When I’m evaluating an SC problem, and nothing jumps out at me immediately, I really do run through the mental checklist we discuss in the lesson: is the meaning logical? Are the modifiers placed appropriately? Is there an issue with parallel construction? Etc. But I saw what this student was saying. In class, we move systematically from one kind of error to another, so they’re much easier to classify than when you’re taking a test and the sentence’s errors either aren’t terribly conspicuous or encompass multiple categories.

As much as I like to preach that it’s best to attack these questions systematically, no test-taker is an algorithm, so I thought it would be worthwhile to go through a few official examples and discuss how my approach, while always rooted in the framework I teach in class, leaves some room for instinctive adjustments. Put another way, the GMAT is a test of pattern recognition. If the pattern is immediately apparent, I think about a question one way, and if it isn’t obvious, my strategy shifts accordingly.

Here’s one example from the Official Guide where the pattern is pretty conspicuous.

Published in Harlem, the owner and editor of The Messenger were two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader.

(A) Published in Harlem, the owner and editor of The Messenger were two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader.

(B) Published in Harlem, two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader, were the owner and editor of The Messenger.

(C) Published in Harlem, The Messenger was owned and edited by two young journalists, A. Philip Randolph, who would later make his reputation as a labor leader, and Chandler Owen.

(D) The Messenger was owned and edited by two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader, and published in Harlem.

(E) The owner and editor being two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader, The Messenger was published in Harlem.

In this case, the ol’ lizard brain jumps immediately into action. Anytime a sentence begins with an –ing or –ed verb, I’m immediately thinking about participial modifiers. This sentence begins with a the participal “published” so I know right away that I want who or what is published to immediately follow the phrase.  Well, it makes most sense to say that The Messenger was published, so I want The Messenger to come right after that initial participial phrase. The answer is C. In this case, after you’ve done dozens and dozens of examples that involve misplaced participles, the issue is glaring. For many test-takers, there’s no need to systematically go through that internal checklist. You’ll still want to read your answer choice with the original sentence and make sure the meaning is logical, etc. but you don’t have to process this problem with the kind of comprehensive rigor you’ll need for more challenging problems.

Now consider this Official Guide problem, which, to me, isn’t categorized nearly as easily as the previous example:

Over 75 percent of the energy produced in France derives from nuclear power, while in Germany it is just over 33 percent.

(A) while in Germany it is just over 33 percent

(B) compared to Germany, which uses just over 33 percent

(C) whereas nuclear power accounts for just over 33 percent of the energy produced

in Germany

(D)whereas just over 33 percent of the energy comes from nuclear power in Germany

(E) compared with the energy from nuclear power in Germany, where it is just over 33 percent

The original sentence doesn’t feel right to me, but it’s not as immediately evident what the problem is. So now I have to be a bit more systematic. Okay, maybe the answer choices will offer some clues. Still not obvious, but I do notice that B and E have the word “compared,” which means one potential issue is an inappropriate comparison. I also notice that the word “it” appears in A and E, so maybe there’s a pronoun issue. With these notions in mind, I’ll start going through my mental checklist. First, is the meaning logical, and if not, is a faulty comparison or inappropriate pronoun to blame?

The first thing I ask myself is “what does the “it” refer to?” Is the original sentence really saying, “Over 75 percent of the energy produced in France derives from nuclear power, while in Germany the energy produced in France is just over 33 percent?” That doesn’t make sense. So A is out because of illogical meaning/inappropriate pronoun.

Now in B, we see “compared.” Read literally, the sentence seems to be comparing the percent of energy produced in France to Germany, the country. That’s no good. We’d like to compare energy to energy and country to country. B is out.

C jumps out at me because we’ve eliminated both “compared” and “it.” “Whereas” signals a new clause entirely. So I have the first clause: Over 75 percent of the energy produced in France derives from nuclear power. And then I get a second clause: nuclear power accounts for just over 33 percent of the energy produced in Germany. The meaning is clear. Additionally, there seems to be a nice parallel construction, both clauses containing a variation of: X% of energy produced in Y. Not something I noticed initially, but a promising development. Hold onto C.

D also eliminates “compared” and “it,” so I need to focus on meaning here. If I read this literally, it seems to say 33% of the energy in France comes from nuclear power in Germany. Well, that would be an awfully generous gesture by Germany, but I can’t imagine this is the intended meaning of the sentence. D is out.

E We see “compared” again. Here, we seem to be comparing the percent of energy produced in France to the energy in Germany. So that’s not really logical. We’d want to compare the percent of energy produced in France to the percent of energy produced in Germany. And then that last phrase, ”where it is just over 33 percent” is a bit mystifying. 33% of what? Is “it” referring to Germany or to energy? E is out.

And we’re left with C.

Notice that on a superficial level, I’m using the same general principles for both of these questions, but my thought process looks a lot different when the problem is obvious than when the underlying issue is a bit more obscure. So our goal as test-takers is first, to do enough practice problems that we become adept at recognizing conspicuous patterns like the one we saw in the first example. And second, we want to have a systematic approach to address more complicated questions when they arise. A single approach or mindset just won’t work for every single question – the GMAT isn’t that kind of test.

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

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

How to Avoid Tedious Calculations on the Quantitative Section of the GMAT

Ron Point_GMAT TipsOne of the hardest things for people to get used to on the GMAT is that there is no calculator for the quantitative section. The reasoning behind this is simple: human beings will not be faster than machines at pure calculations. Human beings, however, will be better at logic, reasoning and deduction than a machine (at least until Skynet is developed).

The GMAT wants to determine how good the test taker is at solving problems through logic and analytical reasoning, not brute strength. Despite this stated goal, the GMAT frequently features questions that can turn students into mindless calculators. The goal is to avoid falling for this sinister trap and solving the problem with sound strategy and logical applications of mathematical theory.

The quintessential large calculation will be something like “Multiply all the integers from 1 to 10” (or more succinctly, find 10!).  Now, such a calculation is possible within the 2 minutes we typically have to solve a question, but even when you get the result, there is often another portion to the question that must be solved. Even if the end goal is just to find one number, the brute force approach is time-consuming and error-prone (and frequently cramps up my hand). You are much better off approaching the problem using either order of magnitude or unit digit properties.

Generally speaking, asking someone to compute 10! can be tedious. However, the GMAT is in fact asking you which of the five choices provided is 10! The answer choices provided are typically fairly far apart, so an approach that cares only about the order of magnitude of the answer will help narrow down the possibilities tremendously. Sometimes there may still be two contending answer choices, and additional calculations may be required to confirm which one is correct.

For 10!, we can calculate the small numbers easily and approximate the rest. You can get much more detailed than this, but 5! = 120, and then multiplying by 6 and then 7 is like multiplying by 5 and then 5 again, so 120 x 25 = approximately 3,000. Multiplying by 8, 9, and then 10 is like multiplying by 10 thrice, so the answer will be somewhere around 3,000,000. I approximated a couple of numbers up and a couple of them down to somewhat balance out. You can approximate more closely to reality but you should still get an answer in the same ballpark (actual retail price: 3,628,800).

Another potential shortcut is to consider only the unit digit. The answer choices will tend to be far apart and have different unit digits, so if you can calculate which number should be the unit digit, you can eliminate several answers quickly. In our case, we know we’re multiplying by 10, so the unit digit will be zero. Furthermore, we are multiplying by 5 as well, and there are many 2’s (including 2 itself), so there will be a second zero as a tens digit. In this case knowing factors simplified the process, but even trying to figure out the unit digit of 2^88 is simply an exercise in pattern recognition.

The above example may have been somewhat abstract as there were no answer choices to compare, so let’s look at an actual GMAT question and apply these same strategies:

A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has a depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled? (Note: 1 foot = 12 inches)

  • 246 cubic inches
  • 300 cubic inches
  • 11,964 cubic inches
  • 13,824 cubic inches
  • 16,348 cubic inches

This question is considered geometry because it’s dealing with a 3-dimensional shape, but the question is primarily concerned with converting cubic feet to cubic inches. As such, the question is really asking for a laborious calculation. Therefore, we need to find a shortcut to avoid spending the rest of the hour calculating cubic inches in our aquarium. (Hey, fishy fishy fishy!)

A cubical aquarium with three sides of 1 foot is 1 cubic foot (or foot^3), but that doesn’t help much in terms of cubic inches. The easiest thing is to convert to inches from the get go, which leaves us with a cube that has height, width and depth of 12 inches. Since the formula for the volume of a cube is side^3, we know that the volume of the aquarium is 12^3 cubic inches. 12^2 is easy, so now we must multiply 144 by 12. It might take a few seconds, but we can break it down to 144 x 10 + 144 x 2, which yields a total of 1,728 cubic inches.

At this point, a lot of people would think about removing the volume that is being filled by the big fish. While this is technically correct, if we’re considering this problem from an order of magnitude point of view, it will be a drop in the bucket (or aquarium), taking the total volume from 1,728 down to 1,684 if you subtract 44 cubic inches. Both of these numbers are essentially 1,700, so there’s not much value in taking the time to remove the fish. I’m more concerned with shortcutting the calculation for the big aquarium.

The big aquarium has sides of 2 feet, or 24 inches. This means that it will be twice as wide, twice as tall and twice as deep as the small aquarium, leading to an overall eight-fold increase from the original aquarium. This means that I can take the 1,728 I calculated earlier and multiply it by 8 to get the total volume (sans fish) of the big aquarium. However, the problem eventually asks for the difference in water between the two aquariums (or aquaria), which means I’ll have to take the 8Y volume and subtract the original Y volume. This means we’re better off shortcutting the calculation and just multiplying the original volume by 7. It’s tantamount to saying I’ll lend you 100$ then you lend me 20$. I think we can just make one transaction for 80$ and call it a day.

Multiplying 1,728 by 7 isn’t necessarily trivial, but remember that we’re mostly interested in the order of magnitude of the answer. This means we can ignore some digits and think of it as approximately 1,700 x 7, which is (1,000 x 7 =) 7,000 + (700 x 7=) 4,900, yielding a total of about 11,900. It should be a little higher than this because we rounded 1,728 downward. This is almost exactly answer choice C, with answer choice D looking about 1,700 bigger and thus likely the volume of the bigger aquarium only. The other three answer choices are way off.

At this point we’re essentially done, but you can confirm the number, particularly with the consideration of the fish (plural but hard to tell). The volume of the small aquarium is 1,728, and of the big aquarium is indeed 13,824 cubic inches. If we subtract the 44 cubic inch fish from the small aquarium, we get 1,684. If we subtract the 176 cubic inches (88×2) of the big aquarium fish, we get 13,648. Finding the difference of these two numbers yields exactly 11,964 cubic inches. Answer choice C is correct, but you don’t have to meticulously calculate every element in order to know it given the five choices provided.

It’s worth noting that unit digits don’t help much on this problem. The smaller aquarium has a volume of 12^3, and the 2^3 unit digit will yield an 8. Subtracting the 44 cubic inches for the fish (which we must do if we’re being precise), the water in the small aquarium should end with a 4. The big aquarium has a total volume of 24^3, which will give a unit digit of 4. Subtracting the 176 cubic inches for the fish leaves us with a unit digit of 8. Finally, subtracting the 4 of the little aquarium from the 8 of the big aquarium means the answer choice must end with a 4. Despite all that abstract and confusing math, we still can’t choose between answer choices C and D, and must therefore perform additional calculations.

Sometimes the GMAT likes to ask questions that would take 15 seconds if you had a calculator, but 5 minutes if you stubbornly decided to use an inflexible brute force approach. Sometimes unit digits will be faster, and sometimes order of magnitude will be faster, but both have their place in your tool belt. Each question on the GMAT is like a door, and you may be able to knock down the door with brute strength, but you’ll go faster with a deft touch (also: fewer shoulder surgeries).

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.

The Pitfalls of Confusing Correlation and Causation on GMAT Critical Reasoning Questions

causation goslingIn Stephen Pinker’s book, The Blank Slate, there’s an entertaining discussion illustrating the pitfalls of confusing correlation and causation. Pinker cites an old Russian folktale in which a Tsar discovers that, of his many provinces, the one that has the highest disease rate also has the most doctors. So he orders all the doctors killed. I’ll often make reference to this passage when I’m teaching Critical Reasoning because the absurdity of the argument is immediately apparent. Just because two variables are correlated, it doesn’t mean that one is necessarily causing the other.

Causality arguments show up frequently on the GMAT and they can be quickly encapsulated with a simple arrow diagram. So the above discussion involving the Tsar could be depicted on scratch paper like so:

Doctors –> Disease

x –> y

Typically, if we need to weaken one of these arguments, we’ll do so in one of two ways. First, it’s possible that cause and effect are reversed. Here it would mean that the disease was causing the doctors to come to the province. In arrow diagram form, it would look like this:

Disease –> Doctors

y –> x

Secondly, there may be a different underlying cause. In the case of our folktale, maybe it’s the case that poor sanitation is causing the disease.

Poor sanitation –> Disease

z –> y

To summarize: whenever we see a causality argument that needs to be weakened, we can distill it into an arrow diagram and then search for one of the two above scenarios.

Here’s an example from the Official Guide:

In the last decade there has been a significant decrease in coffee consumption.  During this same time, there has been increasing publicity about the adverse long-term effects on health from the caffeine in coffee.  Therefore, the decrease in coffee consumption must have been caused by consumers’ awareness of the harmful effects of caffeine.

Which of the following, if true, most seriously calls into question the explanation above?

A. On average, people consume 30% less coffee than they did 10 years ago.
B. Heavy coffee drinkers may have mild withdrawal symptoms, such as headaches, for a day or so after, significantly decreasing their coffee consumption.
C. Sales of specialty types of coffee have held steady, as sales of regular brands have declined.
D. The consumption of fruit juices and caffeine-free herbal teas has increased over the past decade.
E. Coffee prices increased steadily in the past decade because of unusually severe frosts in coffee-growing nations.

This one is straightforward enough to diagnose – we actually get the phrase “caused by” in the argument! As an arrow diagram, it looks like this:

Awareness of harmful effects of caffeine –> decrease in coffee consumption

According to our earlier analysis, this can be weakened in one of two ways. If cause and effect were reversed, the diagram be:

Decrease in coffee consumption –> Awareness of harmful effects of caffeine

Well, that doesn’t make sense. How could a decrease in coffee consumption cause a heightened awareness of the ill effects of caffeine? So we must be looking for an alternative cause:

Something else –> decrease in coffee consumption.

So that’s what we’re after: that alternative underlying cause.

A. On average, people consume 30% less coffee than they did 10 years ago.

There’s no different underlying cause here. In fact, this is reiterating the notion that coffee consumption has decreased. We already knew this. Eliminate A.

B. Heavy coffee drinkers may have mild withdrawal symptoms, such as headaches, for a day or so after, significantly decreasing their coffee consumption.

This isn’t an alternative reason for why people are drinking less coffee. In fact, the unpleasant withdrawal symptoms would be a pretty compelling reason to continue drinking plenty of coffee! Eliminate B.

C. Sales of specialty types of coffee have held steady as sales of regular brands have declined.

Again, no real alternative cause presented here. And, logically, this doesn’t weaken the argument at all. It’s certainly possible that while many coffee drinkers have cut back on their coffee consumption, the kind of aficionados who drink specialty coffee will continue to drink their double latte espressos without reservation. Eliminate C.

D. The consumption of fruit juices and caffeine-free herbal teas has increased over the past decade.

This one is often tempting. Students sometimes argue that it’s the appeal of fruit juices that is the alternative underlying cause we’re looking for. The problem is that we’re trying to weaken the argument, and this answer choice really isn’t incompatible with the conclusion. To see why, imagine that the argument is true: people find out that caffeine is bad for them, and so drink less coffee. It would be perfectly reasonable for them to then replace that morning coffee with alternatives like fruit juice and herbal tea. In other words, the increase in the consumption of other beverages wouldn’t be a cause of the decrease in coffee, but rather, a consequence of that decrease. D is out.

E. Coffee prices increased steadily in the past decade because of unusually severe frosts in coffee-growing nations.

Now we have our alternative cause. Perhaps it’s not the awareness of the ill effects of caffeine that’s caused this drop in coffee consumption, it’s an increase in price. The new arrow diagram looks like this:

Increase in price –> Decrease in consumption

And this makes perfect sense. E is our answer.

The takeaway: A simple arrow diagram can powerfully simplify the logic of any causality argument.

* Official Guide® question courtesy of the Graduate Management Admissions Council.

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

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

What Figure Skating Can Teach You about GMAT Sentence Correction Questions

Figure SkatingLike many Americans, I get caught up in figure skating for exactly two weeks every four years. It’s a fascinating sport, but because I don’t follow it consistently, as I do with the NBA and NFL, I really have no idea how the figure skaters are being judged.

I see what appears to a be hiccup in the routine; the announcer says that it was a flawless set-up for an impressive jump. I see what appears to be a perfect routine; the scores come back and the skater is firmly in 13th.

When you see a GMAT question, you need to know exactly what criteria to use to “judge” a question, even if your first instinct is not correct. Check out the following question from a GMAC practice pack:

GMAT Question

At first, I thought “We do need the structure to be parallel!” Why did I think this? Because I saw the word whereas. When I see a comparison word like that, the first thing I look for is consistency between the two things we’re comparing. “Language areas” comes after the comma and is not underlined; like it or not, that phrase is not going anywhere.

Wanting to retro-fit my comparison to match my non-underlined portion, I hope and pray that I see something like, “Whereas language areas in adult brains are X, language areas in a child’s brain are Y.” Clearly, we can compare language areas to other language areas, so my next thought is that I’ll eliminate any answers that don’t satisfy this rule.

However, a quick scan of the underlined terms of comparison in each answer choice reveals that we don’t have such an opportunity.

  1. A) each language
  2. B) (ignorable prepositional phrase) each language
  3. C) each language
  4. D) each language
  5. E) each language

Whoa. I guess we’re going to have to go with “each language.”

What’s really going on here? “Whereas in some situations X happensthere are other situations in which Y occurs.” We aren’t comparing a thing to a thing; we’re comparing a situation to an analogous situation.

So, what do I focus on next? Simply making a complete sentence that comes right after a semicolon, and eliminating any answer choice that fails to make a sentence. If the answer doesn’t make a grammatical sentence anyway, then why should we care what it’s comparing?

Answer choice B just blows through the existence of a two-part comparison: “Whereas Situation X is a thing and Situation Y is a thing.” That’s not a sentence! We need it to say “Whereas Situation X is a thing <COMMA> Situation Y is also a thing.”

Answer choice C misuses a pronoun by having the plural word “they” refer to the singular noun “language.”

Answer choice D wrongly employs the past tense “occupied,” as the language ceased to exist before the study ended. (Or the adults all tragically died during the study.)

Answer choice E wrongly tries to pass off “Incomplete sentence + comma + AND + Complete sentence” as a grammatical structure to put after a semicolon. Nope.

So let’s recap. In a question that seems to be about comparisons, we just eliminated four answer choices on the basis of No Verb, Bad Pronoun, Bad Verb Tense, and Bad Sentence Structure. None of the wrong answers had anything to do with comparisons!

Meanwhile, I haven’t yet said a word about the correct answer A, and that’s because truthfully, I didn’t love A when I read it for the first time. When you don’t love A, but you can’t identify a tangible error, you just let it hang around. If you can drop four answer choices like the bad habits they are (as we did in B through E), then Mr. Lingering Around Answer A becomes your default champion.

Congrats, Answer Choice A. You’re the “Only Figure Skater Who Didn’t Fall on His Butt So He Wins By Default” of answer choices.

I don’t know much about figure skating, but I know that falling on your butt is not ideal.

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 David Ingber

Solving Inference Questions in Reading Comprehension on the GMAT

Ron Point_GMAT TipsOne of the most common things you’re going to do on the GMAT is to infer things. Inferring things is something we inherently do on a daily basis as human beings. If your friend tells you they’re preparing for a big presentation, you generally automatically infer they’re presenting to an audience and are nervous about public speaking. However, on the GMAT, inferring carries a little more baggage than in your everyday life. What if your friend is in charge of logistics for the presentation, or running the slideshow behind the presenter? Perhaps they are being presented in the debutante ball definition of the term? (niche, I know). On the GMAT, inferences have a high threshold they must always attain: the inferences must be true.

After preparing countless Critical Reasoning inference questions, this “must be true” mantra should already be indoctrinated into most GMAT test takers. However, this type of question also shows up in Reading Comprehension, offering a rare opportunity to excel at two different question types using the same concept. By the same token, it’s a concept that’s sure to show up on your test, and you shouldn’t lose easy points because you assumed something that wasn’t explicitly stated.

The approach I always use with students is to ask them: “Is this always true?” If it’s Thursday or a solar eclipse or you pass on the 1 yard line or Venus is in Scorpio… is this still true? Imagine every obscure, unlikely scenario, and make sure the answer choice still holds in that situation. (Seriously, who passes on the 1 yard line?) If this is the case for any scenario you can dream up, your inference holds. If you can imagine even one nice corner case (e.g. a prime number being even) where this doesn’t hold, then it cannot be the correct answer.

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

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

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

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

The author of the passage implies that the efforts of the women workers at the Lowell Mills ________________?

(A) Were of less direct benefit to them than to other workers.

(B) Led to the creation of child labor laws that benefited the youngest workers at the Lowell mills.

(C) Forced the New England Labor Reform League to include three women on its board.

(D) Were addressed in the poetry included in the Offering.

(E) Were initially organized by Sarah Bagley.

The question is phrased in such a way that you must complete the sentence. Looking over the sentence, the active verb is “implies”, which means that we’re dealing with an inference question. This means that the correct conclusion to this sentence must be unimpeachable with regards to the passage. We must go through all the answer choices because inference questions inherently have multiple answers that could be correct. Our advantage is that four of the answer choices will be flawed and only one unassailable choice shall remain.

Let’s begin with option A. It essentially reads: “…the efforts of the women workers at the Lowell Mills were of less direct benefit to them than to other workers”. This seems about right because the passage states that the Lowell Mills workers couldn’t go on strike for long (paragraph 2). Conversely, it is also mentioned that “other mill workers took note of the Lowell strikes, and were successful in getting better pay, shorter hours and safer working conditions”. This makes it pretty hard to argue with answer choice A, but let’s continue and see if any other answer choices seem like contenders.

Answer choice B reads “…the efforts of the women workers at the Lowell Mills led to the creation of child labor laws that benefited the youngest workers at the Lowell Mills.” This seems like it could be correct, because the passage ends with a sentence about how some child labor laws can be traced back to the efforts of these women. However, there is no indication that these laws benefitted anyone at the Lowell Mills, and in fact were likely only instituted many years later. This answer choice affords a positive outcome to the situation, but is unfortunately unsupported by the passage.

Answer choice C reads “…the efforts of the women workers at the Lowell Mills forced the New England Labor Reform League to include three women on its board.” This might be the easiest answer choice to eliminate. Three members of the Reform League were women, but it is not guaranteed that this is due entirely to the worker strife. It is likely correlated, but it is impossible to defend that it is caused by the conflict. If we’re looking for bulletproof arguments, this one is full of holes.

Answer choice D reads “…the efforts of the women workers at the Lowell Mills were addressed in the poetry included in the Offering”. This is another strong candidate. The Lowell Offering was established as a journal written by the workers that contained at least some poetry in the first paragraph. Would it then be logical that the Offering would address worker malcontent during a strike? Likely, yes, but not guaranteed. Furthermore, would worker dissatisfaction necessarily show up as poetry versus an opinionated peace or an invitation to protest? It is likely that this happened, but there is no guarantee, and therefore this type of answer is incorrect for a GMAT inference question.

Answer choice E reads “…the efforts of the women workers at the Lowell Mills were initially organized by Sarah Bagley”. This answer choice is similar to answer choice D. It is quite possibly true, as Sarah Bagley seemingly had a powerful voice at the Lowell Mills, but there is no indication that she spearheaded the movement in any way. Had this been mentioned somewhere, it would have been unsurprising given the situation. However, on its own, it’s plausible at best, speculation at worst.

Since we’ve systematically eliminated answer choices B through E, the correct answer must be answer choice A. This makes sense because answer choice A seemed completely supported by the passage. Inference questions are typically exercises in process of elimination. If four answer choices can be purged (:anarchy), the remaining answer choice must be correct. If you can accomplish this task on the GMAT, you can infer with absolute certainty that you’ll select the correct answer.

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