GMAT Tip of the Week: Jim Harbaugh Says Milk Does A GMAT Score Good

GMAT Tip of the WeekSomeday when he’s not coaching football, playing with the Oakland Athletics, visiting with the Supreme Court, or Tweeting back and forth with Lil Wayne and Nicki Minaj, Jim Harbaugh should sit down and take the GMAT.

Because if his interaction with a young, milk-drinking fan is any indication, Harbaugh understands one of the key secrets to success on the GMAT Quant section:

 

Harbaugh, who told HBO Real Sports this summer about his childhood plan to grow to over 6 feet tall – great height for a quarterback – by drinking as much milk as humanly possible – is a fan of all kinds of milk: chocolate, 2%… But as he tells the young man, the ideal situation for growing into a Michigan quarterback is drinking whole milk, just as the ideal way to attend the Ross School of Business a few blocks from Harbaugh’s State Street office is to use whole numbers on the GMAT.

The main reason? You can’t use a calculator on the GMAT, so while your Excel-and-calculator-trained mind wants to say calculate “75% of 64” as 0.75 * 64, the key is to think in terms of whole numbers whenever possible. In this case, that means calling “75%” 3/4, because that allows you to do all of your calculations with the whole numbers 3 and 4, and not have to set up decimal math with 0.75. Since 64/4 is cleanly 16 – a whole number – you can calculate 75% by dividing by 4 first, then multiplying by 3: 64/4 is 16, then 16 * 3 = 48, and you have your answer without ever having to deal with messier decimal calculations.

This concept manifests itself in all kinds of problems for which your mind would typically want to think in terms of decimal math. For example:

With percentages, 25% and 75% can be seen as 1/4 and 3/4, respectively. Want to take 20%? Just divide by 5, because 0.2 = 1/5.

If you’re told that the result of a division operation is X.4, keep in mind that the decimal .4 can be expressed as 2/5, meaning that the divisor has to be a multiple of 5 and the remainder has to be even.

If at some point in a calculation it looks like you need to divide, say, 10 by 4 or 15 by 8 or any other type of operation that would result in a decimal, wait! Leaving division problems as improper fractions just means that you’re keeping two whole numbers handy, and knowing the GMAT at some point you’ll end up having to multiply or divide by a number that lets you avoid the decimal math altogether.

So learn from Jim Harbaugh and his obsession with whole milk. Whole milk may be the reasons that his football dreams came true; whole numbers could be a major reason that your business school dreams come true, too.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure tofind us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

A Secret Shortcut to Increase Your GMAT Score

Ron Point_GMAT TipsThe GMAT is an exam that aims to test how you think about things. Many people have heard this mantra when studying for the GMAT, but it’s not always clear what it means. While there are many formulae and concepts to know ahead of taking the exam, you will be constantly thinking throughout the exam about how to solve the question in front of you. The GMAT specializes in asking questions that require you to think about the solution, not just to plug in numbers mindlessly and return whatever your calculator tells you (including typos and misplaced decimals).

There are many ways the GMAT test makers ensure that you’re thinking logically about the solution of the question. One common example is that the question will give you a story that you have to translate into an equation. Anyone with a calculator can do 15 * 6 * 2 but it’s another skill entirely to translate that a car dealership that’s open every day but Sunday sells 3 SUVs, 5 trucks and 7 sedans per day for a sale that lasts a fortnight (sadly, the word fortnight is somewhat rare on the GMAT). Which skill is more important in business, crunching arbitrary numbers or deciphering which numbers to crunch? (Trick question: they’re both important!) The difference is a computer will calculate numbers much faster than a human ever will, but being able to determine what equation to set up is the more important skill.

This distinction is rather ironic, because the GMAT often provides questions that are simply equations to be solved. If the thought process is so important, why provide questions that are so straight forward? Precisely because you don’t have a calculator to solve them and you still need to use reasoning to get to the correct answer. An arbitrarily difficult question like 987 x 123 is trivial with a calculator and provides no educational benefit, simply an opportunity to exercise your fingers (and they want to look good for summer!) But without a calculator, you can start looking at interesting concepts like unit digits and order of magnitude in order to determine the correct answer. For business students, this is worth much more than a rote calculation or a mindless computation.

Let’s look at an example that’s just an equation but requires some analysis to solve quickly:

(36^3 + 36) / 36 =

A) 216
B) 1216
C) 1297
D) 1333
E) 1512

This question has no hidden meaning and no interpretation issues. It is as straight forward as 2+2, but much harder because the numbers given are unwieldy. This is, of course, not an accident. A significant number of people will not answer this question correctly, and even more will get it but only after a lengthy process. Let’s see how we can strategically approach a question like this on test day.

Firstly, there’s nothing more to be done here than multiplying a couple of 2-digit numbers, then performing an addition, then performing a division. In theory, each of these operations is completely feasible, so some people will start by trying to solve 36^3 and go from there. However, this is a lengthy process, and at the end, you get an unwieldy number (46,656 to be precise). From there, you need to add 36, and then divide by 36. This will be a very difficult calculation, but if you think of the process we’re doing, you might notice that you just multiplied by 36, and now you’ll have to divide by 36. You can’t exactly shortcut this problem because of the stingy addition, but perhaps we can account for it in some manner.

Multiplying 36 by itself twice will be tedious, but since you’re dividing by 36 afterwards, perhaps you can omit the final multiplication as it will essentially cancel out with the division. The only caveat is that we have to add 36 in between multiplying and dividing, but logically we’re adding 36 and then dividing the sum by 36, which means that this is tantamount to just adding 1. As such, this problem kind of breaks down to just 36 * 36, and then you add 1. If you were willing to multiply 36^3, then 36^2 becomes a much simpler calculation. This operation will yield the correct answer (we’ll see shortly that we don’t even need to execute it), and you can get there entirely by reasoning and logic.

Moreover, you can solve this question using (our friendly neighbour) algebra.  When you’re facing a problem with addition of exponents, you always want to turn that problem into multiplication if at all possible. This is because there are no good rules for addition and subtraction with exponents, but the rules for multiplication and division are clear and precise. Taking just the numerator, if you have 36^3 + 36, you can factor out the 36 from both terms. This will leave you with 36 *(36^2 + 1). Considering the denominator again, we end up with (36 *(36^2 + 1)) / 36. This means we can eliminate both the 36 in the numerator and the 36 in the denominator and end up with just (36^2 + 1), which is the same thing we found above.

Now, 36*36 is certainly solvable given a piece of paper and a minute or so, but you can tell a lot from the answer by the answer choices that are given to you. If you square a number with a units digit of 6, the result will always end with 6 as well (this rule applies to all numbers ending in 0, 1, 5 and 6). The result will therefore be some number that ends in 6, to which you must add 1. The final result must thus end with a 7. Perusing the answer choices, only answer choice C satisfies that criterion. The answer must necessarily be C, 1297, even if we don’t spend time confirming that 36^2 is indeed 1,296.

In the quantitative section of the GMAT, you have an average of 2 minutes per question to get the answer. However, this is simply an average over the entire section; you don’t have to spend 2 minutes if you can shortcut the answer in 30 seconds. Similarly, some questions might take you 3 minutes to solve, and as long as you’re making up time on other questions, there’s no problem taking a little longer. However, if you can solve a question in 30 seconds that your peers spend 2 or 3 minutes solving, you just used the secret shortcut that the exam hopes you will use.

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.

Dr. Larry Rudner Endorses Veritas Prep’s GMAT Practice Tests

GMACThree years ago this month, the team here at Veritas Prep launched a new project to completely reinvent how we build and administer GMAT practice tests for our students. A home-built system that started with the GMAT Question Bank (launched in October, 2012) soon grew into a whole computer-adaptive testing system containing thousands of questions and employing Item Response Theory to produce some of the most authentic practice tests in the industry. We launched our new practice test in May, 2013, and five months later we made five tests available to everyone. We later added two more tests, bringing the total number to seven that anyone could get. (Veritas Prep students get five additional computer-adaptive tests, for a total of 12.)

The whole time, we kept evaluating the current bank questions (aka “items” in testing parlance), adding new ones, and measuring the ability levels of tens thousands of GMAT students. To date, we have gathered more than 12 million responses from students, and put all of that data to work to keep making our tests better and better. And we keep doing this every week.

Earlier this year, we embarked on a new chapter in the development of our computer-adaptive testing system: We began working with Dr. Larry Rudner, the former Chief Psychometrician at the Graduate Management Admission Council (GMAC), and the definitive authority on the GMAT examination. Dr. Rudner took a look at every aspect of our system, from how we manage our items, to how good each item is at helping our system measure ability levels, to how we employ Item Response Theory to produce an accurate ability level for each test taker. In the end, not only did Dr. Rudner provide us with a roadmap for how to make our tests even better, but he also gave us a great deal of praise for the system that we have now.

What exactly did he say about our GMAT practice tests? See for yourself:

After months spent evaluating every aspect of their GMAT practice exams, it’s clear that Veritas Prep has mastered the science of test simulation. They offer thousands of realistic questions that have been validated using Item Response Theory and a powerful computer adaptive testing algorithm that closely matches that of the real GMAT® exam. Simply stated, Veritas Prep gives students a remarkably accurate measure of how they will perform on the Official GMAT.”

– Lawrence M. Rudner, PhD, MBA. Former Chief Psychometrician at GMAC and the definitive authority on the GMAT exam

Our work on our practice tests will never stop — after all, every month we add new items to our GMAT Question Bank, and many of these questions eventually make it into our computer-adaptive tests — but Dr. Rudner’s endorsement is particularly satisfying given the thousands of hours that have gone into building a testing system as robust as ours. When you take this or any practice test (even the official ones from GMAC), keep in mind that it never can perfectly predict how you will perform on test day. But, with Veritas Prep’s own practice tests, you have the confidence of knowing that more than three years of hard work and over 12 million responses from other students have gone into giving you as authentic a practice experience as possible.

We plan on putting this system to use in even more places, and helping even more students prepare for a wide variety of exams… That’s how powerful Item Response Theory is. Stay tuned!

Finally, we love talking and writing about this stuff. If you’re relatively new to studying for the GMAT or understanding how these tests work, check out some of our previous articles on computer-adaptive testing:

By Scott Shrum

3 Important Concepts for Statistics Questions on the GMAT

Quarter Wit, Quarter WisdomWe have discussed these three concepts of statistics in detail:

– Arithmetic mean is the number that can represent/replace all the numbers of the sequence. It lies somewhere in between the smallest and the largest values.

– Median is the middle number (in case the total number of numbers is odd) or the average of two middle numbers (in case the total number of numbers is even).

– Standard deviation is a measure of the dispersion of the values around the mean.

A conceptual question is how these three measures change when all the numbers of the set are varied is a similar fashion.

For example, how does the mean of a set change when all the numbers are increased by say, 10? How does the median change? And what about the standard deviation? What happens when you multiply each element of a set by the same number?

Let’s discuss all these cases in detail but before we start, we would like to point out that the discussion will be conceptual. We will not get into formulas though you can arrive at the answer by manipulating the respective formulas.

When you talk about mean or median or standard deviation of a list of numbers, imagine the numbers lying on the number line. They would be spread on the number line in a certain way. For example,

——0—a———b—c———————d———e————————f—g———————

Case I:

When you add the same positive number (say x) to all the elements, the entire bunch of numbers moves ahead together on the number line. The new numbers a’, b’, c’, d’, e’, f’ and g’ would look like this

——0——————a’———b’—c’———————d’———e’————————f’—g’——————

The relative placement of the numbers does not change. They are still at the same distance from each other. Note that the numbers have moved further to the right of 0 now to show that they have moved ahead on the number line.

The mean lies somewhere in the middle of the bunch and will move forward by the added number. Say, if the mean was d, the new mean will be d’ = d + x.

So when you add the same number to each element of a list, 

New mean = Old mean + Added number.

On similar lines, the median is the middle number (d in this case) and will move ahead by the added number. The new median will be d’ = d + x

So when you add the same number to each element of a list, 

New median = Old median + Added number

Standard deviation is a measure of dispersion of the numbers around the mean and this dispersion does not change when the whole bunch moves ahead as it is. Standard deviation does not depend on where the numbers lie on the number line. It depends on how far the numbers are from the mean. So standard deviation of 3, 5, 7 and 9 is the same as the standard deviation of 13, 15, 17 and 19. The relative placement of the numbers in both the cases will be the same. Hence, if you add the same number to each element of a list, the standard deviation will stay the same.

Case II:

Let’s now move on to the discussion of multiplying each element by the same positive number.

The original placing of the numbers on the number line looked like this:

——0—a———b—c———————d———e————————f—g———————

The new placing of the numbers on the  number line will look something like this:

——0———a’——————b’———c’————————————d’—————————e—- etc

The numbers spread out. To understand this, take an example. Say, the initial numbers were 10, 20 and 30. If you multiply each number by 2, the new numbers are 20, 40 and 60. The difference between them has increased from 10 to 20.

If you multiply each number by x, the mean also gets multiplied by x. So, if d was the mean initially, d’ will be the new mean which is x*d.

New mean = Old mean * Multiplied number

Similarly, the median will also get multiplied by x.

New median = Old median * Multiplied number

What happens to standard deviation in this case? It changes! Since the numbers are now further apart from the mean, their dispersion increases and hence the standard deviation also increases. The new standard deviation will be x times the old standard deviation. You can also establish this using the standard deviation formula.

New standard deviation = Old standard deviation * Multiplied number

The same concept is applicable when you increase each number by the same percentage. It is akin to multiplying each element by the same number. Say, if you increase each number by 20%, you are, in effect, multiplying each number by 1.2. So our case II applies here.

Now, think about what happens when you subtract/divide each element by the same number.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Behind the Scenes of Your GMAT Score

GMAT Tip of the WeekAmong the most frequent questions we receive here at Veritas Prep headquarters (sadly, “How much am I allowed to tip my instructor?” is not one of them!) is the genre of “On my most recent practice test, I got X right and Y wrong and only Z wrong in a row… Why was my score higher/lower than my other test with A right and B wrong and C wrong in a row?” inquiries from students desperately trying to understand the GMAT scoring algorithm. We’ve talked previously in this space about why simply counting rights and wrongs isn’t all that great a predictor of your score. And perhaps the best advice possible relates to our Sentence Correction advice here a few months ago: Accept that there are some things you can’t change and focus on making a difference where you can.

But we also support everyone’s desire to leave no stone unturned in pursuit of a high GMAT score and everyone’s intellectual curiosity with regard to computer-adaptive testing. So with the full disclosure that these items won’t help you game the system and that your best move is to turn that intellectual curiosity toward mastering GMAT concepts and strategies, here are four major reasons that your response pattern — did you miss more questions early in the test vs. late in the test; did you miss consecutive questions or more sporadic questions, etc. — won’t help you predict your score:

1) The all-important A-parameter.

Item Response Theory incorporates three metrics for each “item” (or “question” or “problem”): the B parameter is the closest measurement to pure “difficulty”. The C parameter is essentially a measure of likelihood that a correct answer can be guessed. And the A parameter tells the scoring system how much to weight that item. Yes, some problems “count” more than others do (and not because of position on the test).

Why is that? Think of your own life; if you were going to, say, buy a condo in your city, you’d probably ask several people for their opinion on things like the real estate market in that area, mortgage rates, the additional costs of home ownership, the potential for renting it if you were to move, etc. And you’d value each opinion differently. Your very risk-loving friend may not have the opinion to value highest on “Will I be able to sell this at a profit if I get transferred to a new city?” (his answer is “The market always goes up!”) whereas his opinion on the neighborhood itself might be very valuable (“Don’t underestimate how nice it will be to live within a block of the blue line train”). Well, GMAT questions are similar: Some are extremely predictive (e.g. 90% of those scoring over 700 get it right, and only 10% of those scoring 690 or worse do) and others are only somewhat predictive (60% of those 700+ get this right, but only 45% of those below 700 do; here getting it right whispers “above 700” whereas before it screams it).

So while you may want to look at your practice test and try to determine where it’s better to position your “misses,” you’ll never know the A-values of any of the questions, so you just can’t tell which problems impacted your score the most.

2) Content balancing.

OK, you might then say, the test should theoretically always be trying to serve the highest value questions, so shouldn’t the larger A-parameters come out first? Not necessarily. The GMAT values balanced content to a very high degree: It’s not fair if you see a dozen geometry problems and your friend only sees two, or if you see the less time-consuming Data Sufficiency questions early in the test while someone else budgets their early time on problem solving and gets a break when the last ten are all shorter problems. So the test forces certain content to be delivered at certain times, regardless of whether the A-parameter for those problems is high or low. By the end of the test you’ll have seen various content areas and A-parameters… You just won’t know where the highest value questions took place.

3) Experimental items.

In order to know what those A, B, and C parameters are, the GMAT has to test its questions on a variety of users. So on each section, several problems just won’t count — they’re only there for research. And this can be true of practice tests, too (the Veritas Prep tests, for example, do contain experimental questions). So although your analysis of your response pattern may say that you missed three in a row on this test and gotten eight right in a row on the other, in reality those streaks could be a lot shorter if one or more of those questions didn’t count. And, again, you just won’t know whether a problem counted or not, so you can’t fully read into your response pattern to determine how the test should have been scored.

4) Item delivery vs. Score calculation.

One common prediction people make about GMAT scoring is that missing multiple problems in a row hurts your score substantially more than missing problems scattered throughout the test. The thinking goes that after one question wrong the system has to reconsider how smart it thought you were; then after two it knows for sure that you’re not as smart as advertised; and by the third it’s in just asking “How bad is he?” In reality, however, as you’ve read above, the “get it right –> harder question; get it wrong –> easier question” delivery system is a bit more nuanced and inclusive of experimentals and content balancing than people think. So it doesn’t work quite like the conventional wisdom suggests.

What’s more, even when the test delivers you an easier question and then an even easier question, it’s not directly calculating your score question by question. It’s estimating your score question-by-question in order to serve you the most meaningful questions it can, but it calculates your score by running its algorithm across all questions you’ve seen. So while missing three questions in a row might lower the current estimate of your ability and mean that you’ll get served a slightly easier question next, you can also recover over the next handful of questions. And then when the system runs your score factoring in the A, B, and C parameters of all of your responses to “live” (not experimental) questions, it doesn’t factor in the order in which those questions were presented — it only cares about the statistics. So while it’s certainly a good idea to get off to a good start in the first handful of problems and to avoid streaks of several consecutive misses, the rationale for that is more that avoiding early or prolonged droughts just raises your degree of difficulty. If you get 5 in a row wrong, you need to get several in a row right to even that out, and you can’t afford the kinds of mental errors that tend to be common and natural on a high-stakes exam. If you do manage to get the next several right, however, you can certainly overcome that dry spell.

In summary, it’s only natural to look at your practice tests and try to determine how the score was calculated and how you can use that system to your advantage. In reality, however, there are several unseen factors that affect your score that you just won’t ever see or know, so the best use of that curiosity and energy is learning from your mistakes so that the computer — however it’s programmed — has no choice but to give you the score that you want.

Getting ready to take 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

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.

What to Do When Math Fails You on the GMAT!

Quarter Wit, Quarter WisdomThey say Mathematics is a perfect Science. There is a debate over this among scientists but we can definitely say that Mathematical methods are not perfect so we cannot use them blindly. We could very well use the standard method for some given numbers and get stranded with “no solution.” The issue is what do we do when that happens?

For example, review this post on averages.

Here we saw that:

Average Speed = 2ab/(a + b)

Applicable when one travels at speed a for half the distance and speed b for other half of the distance. In this case, average speed is the harmonic mean of the two speeds.

So now, say if we have a question which looks like this:

Question: In the morning, Chris drives from Toronto to Oakville and in the evening he drives back from Oakville to Toronto on the same road. Was his average speed for the entire round trip less than 100 miles per hour?

Statement 1: In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.

Statement 2: In the evening, Chris drove at an average speed which was no more than 50 miles per hour while travelling from Oakville to Toronto.

Solution: We know that the question involves average speed. The case involves travelling at a particular average speed for one half of the journey and at another average speed for the other half of the journey.

So average speed of the entire trip will be given by 2ab/(a+b)

But the first problem is that we are given a range of speeds. How do we handle ‘at least 10’ and ‘no more than 50’ in equation form? We have learnt that we should focus on the extremities so let’s analyse the problem by taking the numbers are the extremities:10 and 50

Statement 1: In the morning, Chris drove at an average speed of at least 10 miles per hour while travelling from Toronto to Oakville.

What if Chris drives at an average speed of 10 mph in the morning and averages 100 mph for the entire journey? What will be his average speed in the evening? Perhaps around 200, right? Let’s see.

100 = 2*10*b/(10 + b)

1000 + 100b = 20b

1000 = -80b

b = – 1000/80

How can speed be negative?

Let’s hold on here and try the same calculation for statement 2 too.

Statement 2: In the evening, Chris drove at an average speed which no more than 50 miles per hour while travelling from Oakville to Toronto.

If Chris drives at an average speed of 50 mph in the evening, and averages 100 mph, let’s find his average speed in the morning.

100 = 2a*50/(a + 50)

100a + 5000 = 100a

5000 = 0

This doesn’t make any sense either!

What is going wrong? Look at it conceptually:

Say, Toronto is 100 miles away from Oakville. If Chris wants his average speed to be 100 mph over the entire trip, he should cover 100+100 = 200 miles in 2 hrs.

What happens when he travels at 10 mph in the morning? He takes 100/10 = 10 hrs to reach Oakville in the morning. He has already taken more time than what he had allotted for the entire round trip. Now, no matter what his speed in the evening, his average speed cannot be 100mph. Even if he reaches Oakville to Toronto in the blink of an eye, he would have taken 10 hours and then some time to cover the total 200 miles distance. So his average speed cannot be equal to or more than 200/10 = 20 mph.

Similarly, if he travels at 50 mph in the evening, he takes 2 full hours to travel 100 miles (one side distance). In the morning, he would have taken some time to travel 100 miles from Toronto to Oakville. Even if that time is just a few seconds, his average speed cannot be 100 mph under any circumstances.

But statement 1 says that his speed in morning was at least 10 mph which means that he could have traveled at 10 mph in the morning or at 100 mph. In one case, his average speed for the round trip cannot be 100 mph and in the other case, it can very well be. Hence statement 1 alone is not sufficient.

On the other hand, statement 2 says that his speed in the evening was 50 mph or less. This means he would have taken AT LEAST 2 hours in the morning. So his average speed for the round trip cannot be 100 mph under any circumstances. So statement 2 alone is sufficient to answer this question with ‘No’.

Answer (B)

Takeaway: If your average speed is s for a certain trip, your average speed for half the distance must be more than s/2.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Kanye West’s Everything I Am Teaches Critical Reasoning

GMAT Tip of the Week“Everything I’m not made me everything I am,” says Kanye West in his surprisingly-humble track Everything I Am. And while, unsurprisingly, much of what he’s talking about is silencing his critics, he might as well be rapping about making you an elite critic on Critical Reasoning problems. Because when it comes to some of the most challenging Critical Reasoning problems on the GMAT, everything they’re not makes them everything they are. Which is a convoluted way of saying this:

On challenging Strengthen and Assumption questions, the correct answer often tells you that a potential flaw with the argument is not true.

Everything that’s not true in that answer choice, then, makes the conclusion substantially more valid.

Consider this argument, for example:

Kanye received the most votes for the “Best Hip Hop Artist” award at the upcoming MTV Video Music Awards, so Kanye will be awarded the trophy for Best Hip Hop Artist.

If this were the prompt for a question that asked “Which of the following is an assumption required by the argument above?” a correct answer might read:

A) The Video Music Award for “Best Hip Hop Artist” is not decided by a method other than voting.

And the function of that answer choice is to tell you what’s not true (“everything I’m not”), removing a flaw that allows the conclusion to be much more logically sound (“…made me everything I am.”) These answer choices can be challenging in context, largely because:

1) Answer choices that remove a flaw can be difficult to anticipate, because those flaws are usually subtle.

2) Answer choices that remove a flaw tend to include a good amount of negation, making them a bit more convoluted.

In order to counteract these difficulties, it can be helpful to use “Everything I’m not made me everything I am” to your advantage. If what’s NOT true is essential to the conclusion’s truth, then if you consider the opposite – what if it WERE true – you can turn that question into a Weaken question. For example, if you took the opposite of the choice above, it would read:

The VMA for “Best Hip Hop Artist” is decided by a method other than voting.

If that were true, the conclusion is then wholly unsupported. So what if Kanye got the most votes, if votes aren’t how the award is determined? At that point the argument has no leg to stand on, so since the opposite of the answer directly weakens the argument, then you know that the answer itself strengthens it. And since we’re typically all much more effective as critics than we are as defenders, taking the opposite helps you to do what you’re best at. So consider the full-length problem:

Editor of an automobile magazine: The materials used to make older model cars (those built before 1980) are clearly superior to those used to make late model cars (those built since 1980). For instance, all the 1960’s and 1970’s cars that I routinely inspect are in surprisingly good condition: they run well, all components work perfectly, and they have very little rust, even though many are over 50 years old. However, almost all of the late model cars I inspect that are over 10 years old run poorly, have lots of rust, and are barely fit to be on the road.

Which of the following is an assumption required by the argument above?

A) The quality of materials used in older model cars is not superior to those used to make other types of vehicles produced in the same time period.

B) Cars built before 1980 are not used for shorter trips than cars built since then.

C) Manufacturing techniques used in modern automobile plants are not superior to those used in plants before 1980.

D) Well-maintained and seldom-used older model vehicles are not the only ones still on the road.

E) Owners of older model vehicles take particularly good care of those vehicles.

First notice that several of the answer choices (A, B, C, and D) include “is not” or “are not” and that the question stem asks for an assumption. These are clues that you’re dealing with a “removes the flaw” kind of problem, in which what is not true (in the answer choices) is essential to making the conclusion of the argument true. Because of that, it’s a good idea to take the opposites of those answer choices so that instead of removing the flaw in a Strengthen/Assumption question, you’re introducing the flaw and making it a Weaken. When you do that, you should see that choice D becomes:

D) Well-maintained and seldom-used older model vehicles ARE the only ones still on the road.

If that’s the case, the conclusion – “the materials used to make older cars are clearly superior to those used in newer ones” – is proven to be flawed. All the junkers are now off the road, so the evidence no longer holds up; you’re only seeing well-working old cars because they’re the most cared-for, not because they were better made in the first place.

And in a larger context, look at what D does ‘reading forward’: if it’s not only well-maintained and seldom-driven older cars on the road, then you have a better comparison point. So what’s not true here makes the argument everything it is. But dealing in “what’s not true” can be a challenge, so remember that you can take the opposite of each answer choice and make this “Everything I’m Not” assumption question into a much-clearer “Everything I Am” Weaken question.

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

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.

Expression vs Equation on GMAT

Quarter Wit, Quarter WisdomToday, we want to take up a conceptual discussion on expressions and equations and the differences between them. The concept is quite simple but a discussion on these is warranted because of the similarity between the two.

An expression contains numbers, variables and operators.

For example

x + 4

2x – 4x^2

5x^2 + 4x -18

and so on…

These are all expressions. We CANNOT equate these expressions to 0 by default. We cannot solve for x in these cases. As the value of x changes, the value of the expression changes.

For example, given x + 4, if x is 1, value of the expression is 5. If x is 2, value of the expression is 6. If value of the expression is given to be 10, x is 6 and so on.

We cannot say, “Solve x + 4.”

If we set an algebraic expression equal to something, with an “=“ sign, we have an equation.

So here are some ways of converting the above expressions into equations:

I. x + 4 = -3

II. 2x – 4x^2 = 0

III. 5x^2 + 4x -18 = 3x

Now the equation can be solved. Note that the right hand side of the equation needn’t always be 0. It might be something other than 0 and you might need to make it 0 by bringing whatever is on the right hand side to the left hand side or by segregating the variable if possible:

I. x + 4 = -3

x + 7 = 0

x = -7

II. 2x – 4x^2 = 0

2x(1 – 2x) = 0

x = 0 or 1/2

III. 5x^2 + 4x -18 – 3x = 0

5x^2 + x – 18 = 0

5x^2 + 10x – 9x – 18 = 0

5x(x + 2) -9(x + 2) = 0

(x + 2)(5x – 9) = 0

x = -2, 9/5

In each of these cases, we get only a few values for x because we were given equations.

Think about what you mean by “solving an equation”. Let’s take a particular type of equation – a quadratic.

This is how you usually depict a quadratic:

f(x) = ax^2 + bx + c

or

y = ax^2 + bx + c

This is a parabola – upward facing if a is positive and downward facing if a is negative.

When we solve ax^2 + bx + c = 0 for x, it means, when y = 0, what is the value of x? So you are looking for x intercepts.

When we solve ax^2 + bx + c = d for x, it means, when y = d, what is the value of x? Depending on the values of a, b, c and d, you may or may not get values for x.

Let’s take an example:

x^2 – 2x – 3 = 0

(x + 1)(x – 3) = 0

x = -1 or 3

This is what it looks like:

images

When y is 0, x can take two values: -1 and 3.

So what do we do when we have x^2 – 2x -3 = -3?

We solve it in the same way:

x^2 – 2x -3 + 3 = 0

x(x – 2) = 0

x = 0 or 2

So when y is -3, x is 0 or 2. It has 2 values for y = -3 as is apparent from the graph too.

Similarly, you can solve for it when y = 5 and get two values for x.

What happens when you put y = -5? x will have no value for y = -5 so the equation x^2 – 2x – 3 = – 5 has no real solutions (so ‘no solutions’ as far as we are concerned).

We hope you understand the difference between an expression and an equation now and also that you cannot equate any given expression to 0 and solve it.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Shake & Bake Your Way To Function Success

GMAT Tip of the WeekFor many of us, cooking a delicious homemade meal and solving a challenge-level GMAT math problem are equally daunting challenges. So many steps, so many places to make a mistake…why can’t there be an easier way? Well, the fine folks at Kraft foods solved your first problem years ago with a product called “Shake and Bake.” You take a piece of chicken (your input), stick in the bag of seasoning, shake it up, bake it, and voila – you have yourself a delicious meal with minimal effort. So gourmet level cooking is now nothing to fear…but what about those challenging GMAT quant problems?

You’re in luck. Function problems on the GMAT are essentially Shake and Bake recipes. Consider the example:

f(x) = x^2 – 80

If that gets your heart rate and stress level up, you’re not alone. Function notation just looks challenging. But it’s essentially Shake and Bake if you dissect what a function looks like.

The f(x) portion tells you about your input. f(x) = ________ means that, for the rest of that problem, whatever you see in parentheses is your “input” (just like the chicken in your Shake and Bake).

What comes after the equals sign is the recipe. It tells you what to do to your input to get the result. Here f(x) = x^2 – 80 is telling you that whatever your input, you square it and then subtract 80 and that’s your output. …And that’s it.

So if they ask you for:

What is f(9)? (your input is 9), then f(9) = 9^2 – 80, so you square 9 to get 81, then you subtract 80 and you have your answer: 1.

what is f(-4)? (your input is -4), then f(4) = 4^2 – 80, which is 16 – 80 = -64.

What is f(y^2)? (your input is y^2), then f(y^2) = (y^2)^2 – 80, which is y^4 – 80.

What is f(Rick Astley), then your input is Rick Astley and f(Rick Astley) = (Rick Astley)^2 – 80.

It really doesn’t matter what your input is. Whatever the test puts in the parentheses, you just use that as your input and do whatever the recipe says to do with it. So for example:

f(x) = x^2 – x. For which of the following values of a is f(a) > f(8)?

I. a = -8
II. a = -9
III a = 9

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

While this may look fairly abstract, just consider the inputs they’ve given you. For f(8), just put 8 wherever that x goes in the “recipe” f(x) = x^2 – x:

f(8) = 8^2 – 8 = 64 – 8 = 56

And then do the same for the three other possible values:

I. f(-8) means put -8 wherever you see the x: (-8)^2 – (-8) = 64 + 8 = 72, so f(-8) > f(8).
II. f(-9) means put -9 wherever you see the x: (-9)^2 – (-9) = 81 + 9 = 90, so f(-9) > f(8)
III. f(9) means put a 9 wherever you see the x: 9^2 – 9 = 81 – 9 = 72, so f(9) > f(8), and the answer is E.

Ultimately with functions, the notation (like the Shake and Bake ingredients) is messy, but with practice the recipes become easy to follow. What goes in the parentheses is your input, and what comes after the equals sign is your recipe. Follow the steps, and you’ll end up with a delicious GMAT quant score.

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

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.

When Not to Use Number Plugging on the GMAT

Quarter Wit, Quarter WisdomA few weeks back we discussed the kind of questions which beg you to think of the process of elimination – a strategy probably next only to number plugging in popularity.

Today we discuss the kind of questions which beg you to stay away from number plugging (but somehow, people still insist on using it because they see variables).

Not every question with variables is suitable for number plugging. If there are too many variables, it can be confusing and error prone. Then there are some other cases where number plugging is not suitable. Today we discuss an official question where you face two of these problems.

Question: If m, p , s and v are positive, and m/p < s/v, which of the following must be between m/p and s/v?

I. (m+s)/(p+v)

II. ms/pv

III. s/v – m/p

(A) None

(B) I only

(C) II only

(D) III only

(E) I and II both

Solution: The moment people see m, p, s and v variables, they jump to m = 1, p = 2 etc.

But two things should put you off number plugging here:

– There are four variables – just too many to plug in and manage.

– The question is a “must be true” question. Plugging in numbers is not the best strategy for ‘must be true’ questions. If you know that say, statement 1 holds for some particular values of m, p, s and v (say, 1, 2, 3 and 4), that’s fine but how do you know that it will be true for every set of valid values of m, p, s and v? You cannot try every set because the variables can take an infinite variety of values. If you find a set of values for the variables such that statement 1 does not hold, then you know for sure that it may not be true. In this case, number plugging does have some use but it may be a while before you can arrive at values which do not satisfy the conditions. In such questions, it is far better to take the conceptual approach.

We can solve this question using some number line and averaging concepts.

We are given that m/p < s/v

This means, this is how they look on the number line:

…………. 0 ……………….. m/p …………………… s/v ……………..

(since m, p, s and v are all positive (not necessarily integers though) so m/p and s/v are to the right of 0)

Let’s look at statement II and III first since they look relatively easy.

II. ms/pv

Think of the case when m/p and s/v are both less than 1. When you multiply them, they will become even smaller. Say .2*.3 = .06. So the product ms/pv may not lie between m/p and s/v.

Tip: When working with number properties, you should imagine the number line split into four parts:

  • less than -1
  • between -1 and 0
  • between 0 and 1
  • greater than 1

Numbers lying in these different parts behave differently. You should have a good idea about how they behave.

III. s/v – m/p

Think of a case such as this:

…………. 0 ………………………… m/p … s/v ……….

s/v – m/p will be much smaller than both m/p and s/v and will lie somewhere “here”:

…………. 0 ……… here ………………… m/p … s/v ……….

So the difference between them needn’t actually lie between them on the number line.

Hence s/v – m/p may not be between m/p and s/v.

I. (m+s)/(p+v)

This is a little tricky. Think of the four numbers as N1, N2, D1, D2 for ease and given fractions as N1/D1 and N2/D2.

(m+s)/(p+v)

= [(m+s)/2]/[(p+v)/2]

= (Average of N1 and N2)/(Average of D1 and D2)

Now average of the numerators will lie between N1 and N2 and average of the denominators will lie between D1 and D2. So (Average of N1 and N2)/(Average of D1 and D2) will lie between N1/D1 and N2/D2. Try to think this through.

We will try to explain this but you must take some examples to ensure that you understand it fully. When is one fraction smaller than another fraction?

When N1/D1 < N2/D2, one of these five cases will hold:

  • N1 < N2 and D1 = D2 . For example: 2/9 and 4/9

Average of numerators/Average of denominators = 3/9 (between N1/D1 and N2/D2)

  • N1 < N2 and D1 > D2. For example: 2/11 and 4/9

Average of numerators/Average of denominators = 3/10 (between N1/D1 and N2/D2)

  • N1 << N2 and D1 < D2. For example: 2/9 and 20/19 i.e. N1 is much smaller than N2 as compared with D1 to D2.

Average of numerators/Average of denominators = 11/14 (between N1/D1 and N2/D2)

  • N1 = N2 but D1 > D2. For example: 2/9 and 2/7

Average of numerators/Average of denominators = 2/8 (between N1/D1 and N2/D2)

  • N1 > N2 but D1 >> D2. For example: 4/9 and 2/1

Average of numerators/Average of denominators = 3/5 (between N1/D1 and N2/D2)

In each of these cases, (average of N1 and N2)/(average of D1 and D2) will be greater than N1/D1 but smaller than N2/D2. Take some more numbers to understand why this makes sense. Note that you are not expected to conduct this analysis during the test. The following should be your takeaway from this question:

Takeaway: (Average of N1 and N2)/(Average of D1 and D2) will lie somewhere in between N1/D1 and N2/D2 (provided N1. N2, D1 and D2 are positive)

(m+s)/(p+v) must lie between m/p and s/v.

Answer (B)

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!

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Oh Thank Heaven For Seven-Eleven

GMAT Tip of the WeekA week after the Fourth of July, a lesser-known but certainly-important holiday occurs each year. Tomorrow, friends, is 7-11, a day to enjoy free Slurpees at 7-11 stores, to roll some dice at the craps table, and to honor your favorite prime numbers. So to celebrate 7-11, let’s talk about these two important prime numbers.

Checking Whether A Number Is Prime

Consider a number like 133. Is that number prime? The first three prime numbers (2, 3, and 5) are easy to check to see whether they are factors (if any are, then the number is clearly not prime):

2 – this number is not even, so it’s not divisible by 2.
3 – the sum of the digits (an important rule for divisibility by three!) is 7, which is not a multiple of 3 so this number is not divisible by 3.
5 – the number doesn’t end in 5 or 0, so it’s not divisible by 5

But now things get a bit trickier. There are, in fact, (separate) divisibility “tricks” for 7 and 11. But they’re relatively inefficient compared with a universal strategy. Find a nearby multiple of the target number, then add or subtract multiples of that target number. If we want to test 133 to see whether it’s divisible by 7, we can quickly go to 140 (you know this is a multiple of 7) and then subtract by 7. That’s 133, so you know that 133 is a multiple of 7. (Doing the same for 11, you know that 121 is a multiple of 11 – it’s 11-squared – so add 11 more and you’re at 132, so 133 is not a multiple of 11)

This is even more helpful when, for example, a question asks something like “how many prime numbers exist between 202 and 218?”. By finding nearby multiples of 7 and 11:

210 is a multiple of 7, so 203 and 217 are also multiples of 7
220 is a multiple of 11, so 209 is a multiple of 11

You can very quickly eliminate numbers in that range that are not prime. And since none of the even numbers are prime and neither are 205 and 215 (the ends-in-5 rule), you’re left only having to check 207 (which has digits that sum to a multiple of 3, so that’s not prime), 211 (more on that in a second), and 213 (which has digits that sum to 6, so it’s out).

So that leaves the process of testing 211 to see if it has any other prime factors than 2, 3, 5, 7, and 11. Which may seem like a pretty tall order. But here’s an important concept to keep in mind: you only have to test prime factors up to the square root of the number in question. So for 211, that means that because you should know that 15 is the square root of 225, you only have to test primes up to 15.

Why is that? Remember that factors come in pairs. For 217, for example, you know it’s divisible by 7, but 7 has to have a pair to multiply it by to get to 217. That number is 31 (31 * 7 = 217). So whatever factor you find for a number, it has to multiply with another number to get there.

Well, consider again the number 211. Since 15 * 15 is already bigger than 211, you should see that for any number bigger than 15 to be a factor of 211, it has to pair with a number smaller than 15. And as you consider the primes up to 15, you’re already checking all those smaller possibilities. That allows you to quickly test 211 for divisibility by 13 and then you’re done. And since 211 is not divisible by 13 (you could do the long division or you could test 260 – a relatively clear multiple of 13 – and subtract 13s until you get to or past 211: 247, 234, 221, and 208, so 211 is not a multiple of 13. Therefore 211 is prime.

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

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.

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

Solving Inference-Based 700+ Level Official GMAT Questions

Quarter Wit, Quarter WisdomSometimes, to solve some tough questions, we need to make inferences. Those inferences may not be apparent at first but once you practice, they do become intuitive. Today we will discuss one such inference based high level question of an official GMAT practice test.

Question: In a village of 100 households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:

(A) 65

(B) 55

(C) 45

(D) 35

(E) 25

Solution: We need to find the value of x – y

What is x? It is the greatest possible number of households that have all three devices

What is y? It is the lowest possible number of households that have all three devices

Say there are 100 households and we have three sets:

Set DVD including 75 households

Set Cell including 80 households

Set MP3 including 55 households

We need to find the values of x and y to get x – y.

We need to maximise the overlap of all three sets to get the value of x and we need to minimise the overlap of all three sets to get the value of y.

Maximum number of households that have all three devices:

We want to bring the circles to overlap as much as possible.

The smallest set is the MP3 set which has 55 households. Let’s make it overlap with both DVD set and Cell set. These 55 households are the maximum that can have all 3 things. The rest of the 45 households will definitely not have an MP3 player. Hence the value of x must be 55.

Sets Min Max Inference Im1

Note here that the number of households having no device may or may not be 0 (it doesn’t concern us anyway but confuses people sometimes). There are 75 – 55 = 20 households that have DVD but no MP3 player. There are 80 – 55 = 25 households that have Cell phone but no MP3 player. So they could make up the rest of the 45 households (20 + 25) such that these 45 households have exactly one device or there could be an overlap in them and hence there may be some households with no device. In the figure we show the case where none = 0.

Now, let’s focus on the value of y i.e. minimum number of households with all three devices:

How will we do that? Before we delve into it, let us consider a simpler example:

Say you have 3 siblings (A,B and C) and 5 chocolates which you want to distribute among them in any way you wish. Now you want to minimise the number of your siblings who get 3 chocolates. No one gets more than 3. What do you do?

Will you leave out one sibling without any chocolates (even if he did rat you out to your folks!)? No. Because if one sibling gets no chocolates, the other siblings get more chocolates and then more of them will get 3 chocolates. So instead you give 1 to each and then give the leftover 2 to 2 of them (one each). This way, no sibling gets 3 chocolates and you have successfully minimised the number of siblings who get 3 chocolates. Basically, you spread out the goodies to ensure that minimum people get too many of them.

This is the same concept.

When you want to minimise the overlap, you basically want to spread the goodies around. You want minimum people to have all three. So you give at least one to all of them. Here there will be no household which has no device. Every household will have at least one device.

So you have 80 households which have cell phone. The rest of the 20 households say, have a DVD player so the leftover 55 households (75 – 20) with DVD player will have both a cell phone and a DVD player. There are 55 households who already have two devices and 45 households with just one device.

Now how will you distribute the MP3 players such that the overlap between all three is minimum? Give the MP3 players to the households which have just one device so 45 MP3 player households are accounted for. But we still need to distribute 10 more MP3 players. These 10 will fall on the 55 overlap of the previous two sets. Hence there are a minimum of 10 households which will have all three devices. This means y = 10

Sets Min Max Inference Im2

x – y = 55 – 10 = 45

Answer (C)

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Raising Your Data Sufficiency Accuracy From 33% To 99%

GMAT Tip of the WeekYou’re looking at a Data Sufficiency problem and you’re feeling the pressure. You’re midway through the GMAT Quantitative section and your mind is spinning from the array of concepts and questions that have been thrown at you. You know you nailed that tricky probability question a few problems earlier and you hope you got that last crazy geometry question right. When you look at Statement 1 your mind draws a blank: whether it’s too many variables or too many numbers or too tricky a concept, you just can’t process it. So you look at Statement 2 and feel relief. It’s nowhere near sufficient, as just about anyone even considering graduate school would know immediately. So you smile as you cross off choices A and D on your noteboard, saying to yourself: “Good, at least I have a 33% chance now.”

You’re better than that.

Too often on Data Sufficiency problems, people are impressed by giving themselves a 33% or even 50% chance of success. Keep in mind that guessing one of three remaining choices means you’re probably going to get that problem wrong! And of more strategic importance is this: if one statement is dead obvious, you haven’t just raised your probability of guessing correctly – you should have just learned what the question is all about!

If a Data Sufficiency statement is clearly insufficient, it’s arguably the most important part of the problem.

Consider this example:

What is the value of integer z?

(1) z represents the remainder when positive integer x is divided by positive integer (x – 1)

(2) x is not a prime number

Many examinees will be thrilled here to see that statement 2 is nowhere near sufficient, therefore meaning that the answer must be A, C, or E – a 33% chance of success! But a more astute test-taker will look closer at statement 2 and think “this problem is likely going to come down to whether it matters that x is prime or not” and then use that information to hold Statement 2 up to that light.

For statement 1, many will test x = 5 and (x – 1) = 4 or x = 10 and (x – 1) = 9 and other combinations of that ilk, and see that the result is usually (always?) 1 remainder 1. But a more astute test-taker will see that word “prime” and ask themselves why a prime would matter. And in listing a few interesting primes, they’ll undoubtedly check 2 and realize that if x = 2 and (x – 1) = 1, the result is 1 with a remainder of 0 – a different answer than the 1, remainder 1 that usually results from testing values for x. So in this case statement 2 DOES matter, and the answer has to be C.

Try this other example:

What is the value of x?

(1) x(x + 1) = 2450

(2) x is odd

Again, someone can easily skip ahead to statement 2 and be thrilled that they’re down to three options, but it pays to take that statement and file it as a consideration for later: when I get my answer for statement 1, is there a reason that even vs. odd would matter? If I get an odd solution, is there a possible even one?

Factoring 2450 leaves you with consecutive integers 49 and 50, so x could be 49 and therefore odd. But is there any possible even value for x, a number exactly one smaller than (x + 1) where the product of the two is still 2450? There is: -50 and -49 give you the same product, and in that case x is even. So statement 2 again is critical to get the answer C.

And the lesson? A ridiculously easy statement typically holds much more value than “oh this is easy to eliminate.” So when you can quickly and effortlessly make your decision on a Data Sufficiency statement, don’t be too happy to take your slightly-increased odds of a correct answer and move on. Use that statement to give you insight into how to attack the other statement, and take your probability of a correct answer all the way up to “certain.”

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

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

When to Make Assumptions on GMAT Problem Solving Questions

Quarter Wit, Quarter WisdomToday we will discuss the flip side of “do not assume anything in Data Sufficiency” i.e. we will discuss “go ahead and assume in Problem Solving!”

Problem solving questions have five definite options, that is, “cannot be determined” and “data not sufficient” are not given as options. So this means that in all cases, data is sufficient for us to answer the question. So as long as the data we assume conforms to all the data given in the question, we are free to assume and make the problem simpler for ourselves. The concept is not new – you have been already doing it all along – every time you assume the total to be 100 in percentage questions or the value of n to be 0 or 1, you are assuming that as long as your assumed data conforms to the data given, the relation should hold for every value of the unknown. So the relation should be the same when n is 0 and also the same when n is 1.

Now all you have to do is go a step further and, using the same concept, assume that the given figure is more symmetrical than may seem. The reason is that say, you want to find the value of x. Since in problem solving questions, you are required to find a single unique value of x, the value will stay the same even if you make the figure more symmetrical – provided it conforms to the given data.

Let us give an example from Official Guide 13th edition to show you what we mean:

Question: In the figure shown, what is the value of v+x+y+z+w?

Star

(A) 45

(B) 90

(C) 180

(D) 270

(E) 360

We see that the leg with the angle w seems a bit narrower – i.e. the star does not look symmetrical. But the good news is that we can assume it to be symmetrical because we are not given that angle w is smaller than the other angles.  We can do this because the value of v+x+y+z+w would be unique. So whether w is much smaller than the other angles or almost the same, it doesn’t matter to us. The total sum will remain the same. Whatever is the total sum when w is very close to the other angles, will also be the sum when w is much smaller. So for our convenience, we can assume that all the angles are the same.

Now it is very simple to solve. Imagine that the star is inscribed in a circle.

Star in a circle

Now, arc MN subtends the angle w at the circumference of the circle; this angle w will be half of the central angle subtended by MN (by the central angle theorem discussed in your book).

Arc NP subtends angle v at the circumference of the circle; this angle v will be half of the central angle subtended by NP and so on for all the arcs which form the full circle i.e. PQ, QR and RM.

All the central angles combined measure 360 degrees so all the subtended angles w + v + x + y + z will add up to half of it i.e. 360/2 = 180.

Answer (C)

There are many other ways of solving this question including long winded algebraic methods but this is the best method, in my opinion.

This was possible because we assumed that the figure is symmetrical, which we can in problem solving questions!

But beware of question prompts which look like this:

– Which of the following cannot be the value of x?

– Which of the following must be true?

You cannot assume anything here since we are not looking for a unique value that exists. If a bunch of values are possible for x, then x will take different values in different circumstances.

If we know that the unknown has a unique value, then we are free to assume as long as we are working under the constraints of the question. Finally, we would like to mention here that this is a relatively advanced technique. Use it only if you understand fully when and what you can assume.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Talking About Equality

cupid-gmat-tipIf you’ve ever struggled with algebra, wondered which operations you were allowed to perform, or been upset when you were told that the operation you just performed was incorrect, this post is for you. Algebra is all about equality.

What does that mean?

Consider the statement:

8 = 8

That’s obviously not groundbreaking news, but it does show the underpinnings of what makes algebra “work.” When you use that equals sign, =, you’re saying that what’s on the left of that sign is the exact same value as what’s on the right hand side of that sign. 8 = 8 means “8 is the same exact value as 8.” And then as long as you do the same thing to both 8s, you’ll preserve that equality. So you could subtract 2 from both sides:

8 – 2 = 8 – 2

And you’ll arrive at another definitely-true statement:

6 = 6

And then you could divide both sides by 3:

6/3 = 6/3

And again you’ve created another true statement:

2 = 2

Because you start with a true statement, as proven by that equals sign, as long as you do the exact same thing to what’s on either side of that equals sign, the statement will remain true. So when you replace that with a different equation:

3x + 2 = 8

That’s when the equals sign really helps you. It’s saying that “3x + 2” is the exact same value as 8. So whatever you do to that 8, as long as you do the same exact thing to the other side, the equation will remain true. Following the same steps, you can:

Subtract two from both sides:

3x = 6

Divide both sides by 3:

x = 2

And you’ve now solved for x. That’s what you’re doing with algebra. You’re taking advantage of that equality: the equals sign guarantees a true statement and allows you to do the exact same thing on either side of that sign to create additional true statements. And your goal then is to use that equals sign to strategically create a true statement that helps you to answer the question that you’re given.

Equality applies to all terms; it cannot single out just one individual term.

Now, where do people go wrong? The most common mistake that people make is that they don’t do the same thing to both SIDES of the inequality. Instead they do the same thing to a term on each side, but they miss a term. For example:

(3x + 5)/7 = x – 9

In order to preserve this equation and eliminate the denominator, you must multiply both SIDES by 7. You cannot multiply just the x on the right by 7 (a common mistake); instead you have to multiply everything on the right by 7 (and of course everything on the left by 7 too):

7(3x + 5)/7 = 7(x – 9)

3x + 5 = 7x – 63

Then subtract 3x from both sides to preserve the equation:

5 = 4x – 63

Then add 63 to both sides to preserve the equation:

68 = 4x

Then divide both sides by 4:

17 = x

The point being: preserving equality is what makes algebra work. When you’re multiplying or dividing in order to preserve that equality, you have to be completely equitable to both sides of the equation: you can’t single out any one term or group. If you’re multiplying both sides by 7, you have to distribute that 7 to both the x and the -9. So when you take the GMAT, do so with equality in mind. The equals sign is what allows you to solve for variables, but remember that you have to do the exact same thing to both sides.

Inequalities? Well those will just have to wait for another day.

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

GMAT or GRE: How Will MBA Admissions Officers View My GRE Score?

GRE vs. GMATOver the past five years or so, more business schools have been jumping on the GRE bandwagon by accepting either a GMAT or a GRE score. The percentage of candidates to top MBA programs who apply with only a GRE score is growing, but it’s still very small — less than 5% at most schools.

This leads many candidates to wonder how applying with a GRE score may be viewed by MBA admissions committees.

After speaking with dozens of admissions officers, I have a few insights that may be helpful:

  1. Feelings have changed over the past five years, so be careful that you don’t use outdated information. Countless blogs have been written over the years about whether to take the GRE. If they were not written in the past year, I would not put any stock in them. Attitudes have changed dramatically at many business schools over just the past year or two as they have greater experience in handling applicants with a GRE score in lieu of a GMAT score.
  1. Unless stated otherwise, almost all business schools genuinely do not have a preference between the GMAT and the GRE. While Veritas Prep believes that the GMAT exam offers a more accurate and nuanced assessment of the skills that business schools are looking for, according to feedback from admissions officers across the board and our independent analysis, the two exams are treated equally. Using data published by the business schools, trends clearly show that average GMAT scores and average GRE scores are nearly identical across the board. There is no inherent advantage or disadvantage to applying with a GRE score.
  1. Across the board, admissions officers use the official ETS score conversion tool to translate GRE scores into equivalent GMAT scores. Because so few candidates apply with a GRE score, the admissions committees don’t have a really strong grasp of the scoring scale. Every school we’ve spoken to uses ETS’ score conversion tool to convert GRE scores to GMAT scores so they may compare applicants fairly. You can use the same tool to see how your scores stack up.
  1. The GRE is not a differentiator. I get a lot of “traditional” MBA applicants with a management consulting or investment banking background who ask if they should take the GRE. They’re often nervous that their GMAT score won’t stack up against the stiff competition in their fields and hope that the GRE will differentiate them. Unfortunately, it doesn’t. If anything, admissions officers may wonder why they chose to take the GRE even though all factors in their career path point toward applying to MBA programs and not any other graduate programs. There’s no need to raise any questions in the mind of the admissions reader when the GMAT is a clear option.
  1. The GRE isn’t easier, but it’s different. I also see a lot of applicants who struggle with standardized tests who seek to “hide” behind a GRE score because they believe that it’s easier than the GMAT. Even if the content may seem more basic to you, what matters is how you stack up against the competition. Remember that every Masters in Engineering and Mathematics PhD candidate will be taking the GRE, focused solely on the Quant sections. They’re going to knock these sections out of the park without even breaking a sweat. On the other side, English Lit majors and other candidates for humanities-related degrees will be focused exclusively on the Verbal sections, and their grammar abilities are likely to be much better than yours. This means that getting a strong balanced score (which is what MBA admissions officers are looking for) becomes extremely difficult on the GRE. Even if the content feels easier to you, remember that the competition will tough. That said, if you’re struggling with the way the GMAT asks questions, you might find the GRE to be a more straightforward way of assessing your abilities. This can be an advantage to some applicants based on their unique thought process and learning style, but it shouldn’t be seen as a panacea for all test-takers.
  1. Some schools are GMAT-preferred. For example, Columbia Business School now accepts the GRE, but its website and admissions officers clearly state that they prefer the GMAT. If you’re applying to any business schools that fall into this category, we highly recommend that you take the GMAT unless there’s a very compelling argument for the GRE. One compelling argument might be that you have already scored well on the GRE to attend a master’s program directly out of undergrad and you would prefer not to take another standardized test to now get your MBA. Or perhaps you’re applying to a dual-degree program where the other program requires the GRE. Without a compelling reason otherwise, you should definitely plan to take the GMAT.

Bottom line: We recommend that the GMAT remain your default test if you’re planning to apply to exclusively to business schools. If you really struggle with the style of questions on the GMAT, you might want to explore the GRE as a backup option. In the end, you should simply take the test on which you can get the best score and not worry about trying to game the system.

If you have questions about whether the GMAT or the GRE would be a better option for your individual circumstances, please don’t hesitate to reach out to us at 1-800-925-7737 or submit your profile information on our website for a free admissions evaluation. And, as always, be sure to find us on Facebook and Google+, and follow us on Twitter!

Travis Morgan is the Director of Admissions Consulting for Veritas Prep and earned his MBA with distinction from the Kellogg School of Management at Northwestern University. He served in the Kellogg Student Admissions Office, Alumni Admissions Organization and Diversity & Inclusion Council, among several other posts. Travis joined Veritas Prep as an admissions consultant and GMAT instructor, and he was named Worldwide Instructor of the Year in 2011. 

GMAC Announces Two New GMAT Policies, Both In Your Favor!

GMAT Cancel ScoresMBA applicants, your path to submitting a score report that you can be proud of just got a bit smoother. In an announcement to test-takers today, GMAC revealed two new policies that each stand out as particularly student-friendly:

1) As of July 19, 2015, the designation “C” will no longer appear on score reports to designate a cancelled score. This couples nicely with the recent change to the GMAT’s cancellation policy allowing you to preview your score before you decide whether to “keep” or cancel it. So as of July 19, there is zero risk that anyone but you will ever notice that you had a bad test day (unless, of course, you decide to publish that score). Even better, this policy also applies to previously cancelled scores (not just to tests taken after July 19). If you submit a score report to a school now, and you have multiple test sittings in which you cancelled your score, business schools will never know it.

What does this policy mean for you? For one, you can feel markedly less pressure when you take the GMAT, as a bad score only has to be your business. There is no downside! Furthermore, you can feel confident selecting an aggressive timeline for your GMAT test date, as even if you do not perform to your goals at worst-case that attempt is “an expensive but very authentic practice test.” While in the vast majority of cases, that C never felt to schools like a Scarlet Letter, the stigma in students’ minds was often enough to inspire fear on test day and anxiety in the admissions process. Fear no more!

2) Effective immediately, you only need to wait 16 days (as opposed to 31) before retaking the GMAT. With that waiting period now cut just about in half, you have a few terrific advantages:

  • If you decide you need to retake the exam, you can stick on your study regiment just 2.5 more weeks to polish up those last few concepts and you’ll take the test while everything is still fresh and you’re still in “game shape.”
  • You’re significantly less likely to end up in limbo between “set the test date that maximizes your chance for success on THAT test” and “set the test date that gives you the safety net of one more try if the first one doesn’t go so well.” That month-plus between administrations made for tricky decisions for applicants in the past. Now you have that much more flexibility when choosing a date to get the test and a backup plan in before your applications are due.

Is there a downside? GMAC wouldn’t likely be as aggressive with the 16-day waiting period if it didn’t have the capacity to allow more GMAT administrations in the busy season, but there is a chance that the ~3 weeks leading up to the major application deadlines could get crowded at test centers. To have your pick of test dates for both your first shot and your backup, you may want to consider taking the GMAT 6 (and maybe 3) weeks before you and others need the score as opposed to 3 weeks and “immediately” before you need it.

Are you getting ready 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

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.

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

Advanced Applications of Common Factors on the GMAT – Part II

Quarter Wit, Quarter WisdomThere is something about factors and divisibility that people find hard to wrap their heads around. Every advanced application of a basic concept knocks people out of their seats! Needless to say, that the topic is quite important so we are trying to cover the ground for you. Here is another post on the topic discussing another important concept.

In a previous post, we saw that

“Two consecutive integers can have only 1 common factor and that is 1.”

This implies that N and N+1 have no common factor other than 1. (N is an integer)

Similarly,

N + 5 and N + 6 have no common factor other than 1. (N is an integer)

N – 3 and N – 2 have no common factor other than 1. (N is an integer)

2N and 2N + 1 have no common factor other than 1. (N is an integer)

We are sure you have no problem up until now.

How about:

N and 2N+1 have no common factor other than 1. (N is an integer)

It is a simple application of the same concept but makes for a 700 level question!

2N and 2N+1 have no common factor other than 1 – we know

The factors of N will be a subset of the factors of 2N. It will not have any factors which are not there in the list of factors of 2N. So if 2N and another number have no common factors other than 1, N and the same other number can certainly not have any common factor other than 1.

Taking an example, say N = 6

Factors of 2N (which is 12) are 1, 2, 3, 4, 6, 12.

Factors of 2N + 1 (which is 13) are 1, 13.

2N and 2N + 1 can have no common factors.

Now think, what are the factors of N? They are 1, 2, 3, 6 (a subset of the factors of 2N)

They will obviously not have any factor in common with 2N+1 (except 1) since these are the same factors as those of 2N except that these are fewer.

So we can deduce the following (N and M are integers):

M and NM +1 will have no common factor other than 1.

8 and 8M + 1 will have no common factor other than 1.

M and NM – 1 will have no common factor other than 1.

and so on…

Here is the 700 level official question of this concept:

Question: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

Statement 1: x = 12u, where u is an integer.

Statement 2: y = 12z, where z is an integer.

Solution:

x = 8y + 12

We need to find the greatest common divisor of x and y. We have 8y in the equation. A couple of immediate deductions:

The factors of y will be a subset of the factors of 8y.

The difference between x and 8y is 12 so the greatest common divisor of x and 8y will be a factor of 12 (discussed in this post a few weeks back).

This implies that the greatest factor that x and y can have must be a factor of 12.

Looking at the statements now:

Statement 1: x = 12u, where u is an integer.

Now we know that x has 12 as a factor. The problem is that we don’t know whether y has 12 as a factor.

y could be 3 —> x = 8*3 + 12 = 36 (a multiple of 12). Here greatest common divisor of x and y will be 3.

or y could be 12 —> x = 8*12 + 12 = 108 (a multiple 12). Here greatest common divisor of x and y will be 12.

So this statement alone is not sufficient.

Statement 2: y = 12z, where z is an integer.

This statement tells us that y also has 12 as a factor. So now do we just mark (C) as the answer and move on? Well no! It seems like an easy (C) now, doesn’t it? We must analyse this statement alone.

Substituting y = 12z in the given equation:

x = 8*12z + 12

x = 12*(8z + 1)

So this already gives us that x has 12 as a factor. We don’t really need statement 1.

Since both x and y have 12 as a factor and the highest common factor they can have is 12, greatest common divisor of x and y must be 12.

This statement alone is sufficient to find the greatest common divisor of x and y.

Answer (B)

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Dave Chappelle’s Friend Chip Teaches Data Sufficiency Strategy

Chappelle GMAT Tip“Officer, I didn’t know I couldn’t do that,” Dave Chappelle’s friend, Chip, told a police officer after being pulled over for any number of reckless driving infractions. In Chappelle’s famous stand-up comedy routine, he mocks the audacity of his (privileged) friend for even thinking of saying that to a police officer. But that’s the exact type of audacity that gets rewarded on Data Sufficiency problems, and a powerful lesson for those who, like Dave in the story, seem more resigned to their plight of being rejected at the mercy of the GMAT yet again.

How does Chip’s mentality help you on the GMAT? Consider this Data Sufficiency fragment:

Is the product of integers j, k, m, and n equal to 1?

(1) (jk)/mn = 1

The approach that most students take here involves plugging in numbers for j, k, m, and n and seeing what answer they get. Knowing that jk = mn (by manipulating the algebra in statement 1) they may pick combinations:

1 * 8 = 2 * 4, in which case the product is 64 and the answer is no

2 * 5 = 1 * 10, in which case the product is 100 and the answer is no

And so some will, after picking a series of arbitrary number choices, claim that the answer must be no. But in doing so, they’re leaving out the possibilities:

1 * 1 = 1 * 1, in which case the product jkmn = 1*1*1*1 = 1, so the answer is yes

-1 * 1 = -1 * 1, in which case the product is also 1, and the answer is yes

And here’s where Chip Logic comes into play: in any given classroom, when the two latter sets of numbers are demonstrated, at least a few students will say “How are we allowed to use the same number twice? No one told us we could do that?”. And the best response to that is Chip’s very own: “I didn’t know I COULDN’T do that.” Since the problem didn’t restrict the use of the same number twice (to do so they might say “unique integers j, k, m, and n”), it’s on you to consider all possible combinations, including “they all equal 1.” Data Sufficiency tends to reward those who consider the edge cases: the highest or lowest possible number allowed, or fractions/decimals, or negative numbers, or zero. If you’re going to pick numbers on Data Sufficiency questions, you have to think like Chip: if you weren’t explicitly told that you couldn’t, you have to assume that you can.

So on Data Sufficiency problems, when you pick numbers, do so with a sense of entitlement and audacity. Number-picking is no place for the timid – your job is to “break” the obvious answer by finding allowable combinations that give you a different answer; in doing so, you can prove a statement to be insufficient. So as you chip away at your goal of a 700+ score, summon your inner Chip. When it comes to picking numbers, “I didn’t know I couldn’t do that” is the mentality you need to know you can use.

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

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.

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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.

Set Up a Consistent and Manageable Study Schedule to Succeed on Test Day

procrastinationWhen I ask my students how their studying is going, the response is often to give an embarrassed smile, and admit that they just haven’t found as much time as they would have liked to devote to GMAT problems. This is understandable. Most of them have full-time jobs. Many serve on the boards of non-profit organizations. Others have young families. Preparing for a test as challenging as the GMAT can often feel like taking on a part-time job, and when piled on top of an already burdensome schedule, the demands can feel overwhelming and unreasonable.

Consequently, whenever they do find time to study, they tend to cram in as much work as they can, forsaking little things like socializing, exercise, and sleep. In an earlier post, I discussed why it can be counterproductive to engage in marathon study sessions, so in this one, I want to explore strategies for consistently finding small blocks of time so that our study regimens will be less painful and more productive.

The good news is that while we all feel incredibly busy, research shows that, in actuality, we’re a good deal less saturated with responsibilities than we think we are. In Overwhelmed: Work, Love, and Play When No Has the Time, Brigid Schulte discusses how our sense of having too much to do is, in a sense, a self-fulfilling prophesy. When we feel as though there’s too much to do, we tend to procrastinate, and part of this procrastination involves lamenting to others about how overwhelmed we are. Of course, while we’re complaining about our busy schedules, we’re not exactly models of productivity, and so we fall even further behind, which compounds our overriding sense of helplessness, compelling us to complain even more, a cycle that deepens as it perpetuates itself.

So then, how do we break this cycle?

First, we need to identify the biggest productivity-killers that trigger our procrastination tendencies in the first place. It will surprise no one to hear that email is a major culprit. What is surprising, at least to me, is how much of our idea was devoted to responding to emails. According to a study conducted by Mckinsey, we spend, on average, 28% of our workdays on email.

If you’re working a 10-hour day, as many of my students are, that’s nearly three hours of pure email time. If they can cut this down to 2 hours, well, that’s an hour of potential GMAT study time.  A few simple strategies can accomplish this. This Forbes article offers some excellent advice.

The most salient recommendations are pretty simple. First, set up an auto-responder. Unless an email is urgent, the sender will not expect to hear back from you right away. Second, get in the habit of sending shorter emails. If complicated logistics are involved, make a phone call rather than going back and forth over email. Also, make judicious use of folders to prioritize which messages are most important. And last, do not, under any circumstances, send an email that is mostly about how you don’t have any time to do things like, well, sending recreational emails.

Next, during those times when we’d otherwise have been on our phones complaining how much we have to do, we can instead use our phones to sneak in a bit of extra study time. Many of my students take the subway or commuter rail to work. While I don’t expect anyone to crack open their GMAT books in this environment, there’s no reason why they can’t use a good app on their phones to sneak in a good 20-minute session each day. And if you were wondering, yes, Veritas Prep has an excellent app for precisely such occasions.

The hope is that simple strategies, like the ones outlined above, will allow you to make your study regimen both consistent and manageable, diminishing the need to over-study when you finally have a block of free time on the weekend. If you’re able to do something more restorative on the weekend and feel refreshed when you begin the following work week, you’ll find you’ll be more productive that week and more inclined to stick with your study plan without running the risk of burnout. In time, you’ll feel less busy, and paradoxically, will be able to get more done.

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

Are Brain Training Exercises Helpful When Studying for Standardized Tests?

StudentIn the last two classes I’ve taught, I’ve had students come up to me after a session to ask about the value of brain-training exercises. The brain-training industry has been getting more attention recently as neuroscience sheds new light on how the brain works, baby-boomers worry about cognitive decline, and companies offering brain-improvement software expand. It’s impossible to listen to NPR without hearing an advertisement for Lumosity, a brain-training website that now boasts 70 million subscribers.  The site claims that the benefits of a regular practice range from adolescents improving their academic performance to the elderly staving off dementia.

The truth is, I never know quite what to tell these students. The research in this field, so far as I can tell is in its infancy. For years, the conventional wisdom regarding claims about brain-improvement exercises had been somewhat paradoxical. No one really believed that there was any magic regimen that would improve intelligence, and yet, most people accepted that there were tangible benefits to pursuing advanced degrees, learning another language, and generally trying to keep our brains active. In other words, we accepted that there were things we could do to improve our minds, but that such endeavors would never be a quick fix. The explanation for this disconnect is that there are two different kinds of intelligence. There is crystalized intelligence, the store of knowledge that we accumulate over a lifetime. And then there is fluid intelligence, our ability to quickly process novel stimuli. The assumption had been that crystallized intelligence could be improved, but fluid intelligence was a genetic endowment.

Things changed in 2008 with the release of a paper written by the researchers Susanne Jaeggi, martin Buschkuehl, John Jonides, and Walter Perrig. In this paper, the researches claimed to have shown that when subjects regularly played a memory game called Dual N-Back, which involved having to internalize two streams of data simultaneously, their fluid intelligence improved. This was ground-breaking.

This research has played an integral in role in facilitating the growth of the brain-training industry. Some estimates put industry revenue at over a billion dollars. There have been articles about the brain-training revolution in publications as wide-ranging as The New York Times and Wired. This cultural saturation has made it inevitable that those studying for standardized tests occasionally wonder if they’re shortchanging themselves by not doing these exercises.

Unfortunately, not much research has been performed to assess the value of these brain-training exercises on standardized tests. (A few smaller studies suggest promise, but the challenge of creating a true control group makes such studies extraordinarily difficult to evaluate). Moreover, there’s still debate about whether these brain-training exercises confer any benefit at all beyond helping the person training to improve his particular facility with the game he’s using to train.  Put another way, some say that games like Dual N-Back will improve your fluid intelligence, and this improvement translates into improvements in other domains. Others say that training with Dual N-Back will do little aside from making you unusually proficient at Dual N-Back.

It’s hard to arrive at any conclusion aside from this: the debate is seriously muddled. There are claims that the research has been poorly done. There are claims that the research is so persuasive that the question has been definitively answered. Obviously, both cannot be true. My suspicion is that the better-researched exercises, such as Dual N-Back, confer some modest benefit, but that this benefit is likely to be most conspicuous in populations that are starting from an unusually low baseline.

This brings us to the relevant question: is it worth it to incorporate these brain-exercise programs into a GMAT preparation regime? The answer is a qualified ‘maybe.’ If you’re very busy, there is no scenario in which it is worthwhile to sacrifice GMAT study time to play brain-training games that may or may not benefit you. Secondly, the research regarding the cognitive benefits of aerobic exercise, mindfulness meditation, and social interaction is far more persuasive than anything I’ve seen about brain-training games.

However, if you’re already studying hard, working out regularly, and finding time for family and friends, and you think can sneak in another 20 minutes a day for brain-training without negatively impacting the other more important facets of your life, it can’t hurt. Just know that, as with most challenging things in life, the shortcuts and hacks should always be subordinated to good, old-fashioned hard work and patience.

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

Important Caveat on Joint Variation GMAT Questions

Quarter Wit, Quarter WisdomBefore we start today’s discussion, recall a previous post on joint variation. A question arose some days back on the applicability of this concept. This official question was the case in point:

Question: In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment i. What is p if i = 70?

Statement I: e = 0.5 whenever i = 60

Statement II: p = 2.0 whenever i = 50

This was the issue that was raised:

If one were to follow the method given in the post on joint variation, one would arrive at this solution:

p/e = k (a constant)

e/i = m (another constant)

Hence, p*i/e = n is the joint variation expression

(where k, m and n are constants)

So we get that p is inversely proportional to i, that is, p*i = Constant 

Statement II gives us the values of p and i which can help us get the value of the Constant.

2*50 = Constant 

The question asks us the value of p given the value of i = 70. If Constant = 100, 

p = 100/70.

But actually, this is wrong and the value that you get for p in this question is different.

The question is “why is it wrong?”

Valid question, right? It certainly seems like a joint variation scenario – relation between three variables. Then why does’t it work in this case?

The takeaway from this question is very important and before you proceed, we would like you to think about it on your own for a while and then proceed to the the rest of the discussion.

Here is how this question is actually done:

Taking one statement at a time:

“production index p is directly proportional to efficiency index e,”

implies p = ke (k is the constant of proportionality)

“e is in turn directly proportional to investment i”

implies e = mi (m is the constant of proportionality. Note here that we haven’t taken the constant of proportionality as k since the constant above and this constant could be different)

Then, p = kmi (km is the constant of proportionality here. It doesn’t matter that we depict it using two variables. It is still just a number)

Here, p seems to be directly proportional to i!

So if you have i and need p, you either need this constant directly (as you can find from statement II) or you need both k and m (statement I only gives you m).

So the issue now is that is p inversely proportional to i or is it directly proportional to i?

Review the joint variation post – In it we discussed that joint variation gives you the relation between 2 quantities keeping the third (or more) constant.

p will vary inversely with i if and only if e is kept constant.

Think of it this way: if p increases, e increases. But we need to keep e constant, we will have to decrease i to decrease e back to original value. So an increase in p leads to a decrease in i to keep e constant.

But if we don’t have to keep e constant, an increase in p will lead to an increase in e which will increase i.

It is all about the sequence of increases/decreases

Here, we are not given that e needs to be kept constant. So we will not use the joint variation approach.

Note how the independent question is framed in the joint variation post:

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical M present and inversely proportional to the concentration of chemical N present. If the concentration of chemical N is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical M required to keep the reaction rate unchanged?

You need relation between N and M when reaction rate is constant.

You are given no such constraint here. So an increase in p leads to an increase in e which in turn, increases i.

So let’s complete the solution to our original question:

p = ke

e = mi

p = kmi

Statement I: e = 0.5 whenever i = 60

0.5 = m * 60

m = 0.5/60

We do not know k so we cannot find p given i and m.

This statement alone is not sufficient.

Statement II: p = 2.0 whenever i = 50

2 = km * 50

km = 1/25

If i = 70, p = (1/25)*70 = 14/5

This statement alone is sufficient.

Answer (B)

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: Making the Most of Your Mental Stamina

GMAT Tip of the WeekOne of the most fascinating storylines during the current 2015 NBA Finals is that of LeBron James’ workload and stamina. Responsible for such a huge percentage of Cleveland’s offense and a key component of the team’s necessarily suffocating defense, James needs to parcel out his energy usage much like an endurance athlete does in the Tour de France or Ironman World Championships. And it’s fascinating to watch as he slowly walks the ball up the court (killing time to shorten the game and also buying valuable seconds of rest before initiating the offense) and nervously watches his teammates lose ground while he takes his ~2 minute beginning-of-the-4th rest on the bench. At the final buzzer of each game he looks exhausted but thus far has been exhaustedly-triumphant twice. And watching how he handles his energy can teach you valuable lessons about how to manage the GMAT.

At the end of your GMAT exam you will be exhausted. But will you be exhaustedly triumphant? Here are 5 things you can do to help you tiredly walk out of the test center with a championship smile:

1) Practice The Way You’ll Play

The GMAT is a long test. You’ll be at the test center for about 4 hours by the time you’re done, and even during those 8-minute section breaks you’ll be hustling the whole time. Think of it this way: with a 30-minute essay, a 30-minute Integrated Reasoning section, a 75-minute Quant section and a 75-minute Verbal section, you’ll be actively answering questions for 3 hours and 30 minutes – a reasonable time for someone your age to complete a marathon (and well more than an hour off the world record). If you were training for a marathon, you wouldn’t stop your workouts after an hour or 90 minutes each time; at the very least you’d work up to where you’re training for over two hours at least once a week. And the same is true of the GMAT. To have that mental stamina to stay focused on a dense Reading Comprehension passage over 3 hours after you arrived at the test center, you need to have trained your mind to focus for 3+ hours at a time. To do so:

-Take full-length practice tests, including the AWA and IR sections.
-Practice verbal when you’re tired, after a long day of work or after you’ve done an hour or more of quant practice
-Make at least one 2-3 hour study session a part of your weekly routine and stick to it. Work can get tough, so whether it’s a Saturday morning or Sunday afternoon, pick a time that you know you can commit to and go somewhere (library, coffee shop) where you know you’ll be able to focus and get to work.

2) Be Ready For The 8-Minute Breaks

Like LeBron James, you’ll have precious few opportunity to rest during your “MBA Finals” date with the GMAT. You have an 8-minute break between the IR section and the Quant section and another 8-minute break between the Quant section and the Verbal section…and that’s it. And those breaks go quickly, as in that 8 minutes you need to check out with the exam proctor to leave the room and check back in to re-enter. A minute or more of your break will have elapsed by the time you reach your locker or the restroom…time flies when you’re on your short rest period! So be ready:

-Have a plan for your break, knowing exactly what you want to accomplish: restroom, water, snack. You shouldn’t have to make many energy-draining decisions during that time; your mind needs a break while you refresh your body, so do all of your decision-making before you even arrive at the test center.
-Practice taking 8-minute breaks when you study and take practice tests. Know how long 8 minutes will take and what you can reasonably accomplish in that time.

3) Use Energy Wisely

If you’re watching LeBron James during the Finals you’ll see him take certain situations (if not entire plays) off, conserving energy for when he has the opportunity to sprint downcourt on a fast break or when he absolutely has to get out on a ready-to-shoot Steph Curry. For you on the GMAT, this means knowing when to stress over calculations on quant or details on reading comprehension. Most students simply can’t give 100% effort for the full test, so you may need to consider:

-On this Data Sufficiency problem, do you need to finish the calculations or can you stop early knowing that the calculations will lead to a sufficient answer?
-As you read this Reading Comp passage, do you need to sweat the scientific details or should you get the gist of it and deal with details later if a question specifically asks for them?
-With this Geometry problem, is it worth doing all the quadratic math or can you estimate using the answer choices? If you do do the math, are you sure that it will get you to an answer in a reasonable amount of time?

Sometimes the answer is “yes” – if it’s a problem that you know you can get right, but only if you grind through some ugly math, that’s a good place to invest that energy. And other times the answer is “no” – you could do the work, but you’re not so sure you even set it up right and the numbers are starting to look ugly and you usually get these problems wrong, anyway. Practice is the key, and diagnosing how those efforts have gone on your practice tests. You might not have enough mental energy to give all the focus you’d like all day, so have a few triggers in there that will help you figure out which battles you can lose in an effort to win the war.

4) Master The “Give Your Mind A Break” Problems

Some GMAT problems are extremely abstract and require a lot of focus and ingenuity. Others are very process-driven if you know the process – among those are the common word problems (weighted averages, rate problems, Venn diagram problems, etc.) and straightforward “solve for this variable” algebra problem solving problems. If you’ve put in the work to master those content-driven problems, they can be a great opportunity to turn your brain off for a few minutes while you just grind out the necessary steps, turning your mind back on at the last second to double check for common mistakes.

This comes down to practice. If you recognize the common types of “just set it up and do the work” problems, you’ll know them when you see them and can relax to an extent as you perform the same steps you have dozens of times. If you recognize the testmaker’s intent on certain problems – in an “either/or” SC structure, for example, you know that they’re testing parallelism and can quickly eliminate answers that don’t have it; if a DS problem includes >0 or <0, you can quickly look for positive/negative number properties with the “usual suspects” that indicate those things – you can again perform rote steps that don’t require much mental heavy lifting. The test is challenging, but if you put in the work in practice you’ll find where you can take some mental breaks without getting punished.

5) Minimize What You Read

The verbal section comes last, and that’s where focus can be the hardest as you face a barrage of problems on a variety of topics – astronomy, an election in a fake country, a discovery about Druid ruins, comparative GDP between various countries, etc. A verbal section will include thousands of words, but only a couple hundred are really operative words upon which correct answers hinge. So be proactive as you read verbal problems. That means:

-Scan the answer choices for obvious decision points in SC problems. If you know they’re testing verb tense, for example, then you’re looking at the original sentence for timeline and you don’t have to immediately focus on any other details. On many questions you can get an idea of what you’re reading for before you even start reading.

-Let details go on RC passages. Your job is to know the general author’s point, and to have a good idea of where to find any details that they might ask about. But in an RC passage that includes a dozen or more details, they may only ask you about one or two. Worry about those details when you’re asked for them, saving mental energy by never really stressing the ones that end up not mattering at all.

-Read the question stem first on CR problems. Before you read the prompt, know your job so that you know what to look for. If you need to weaken it, then look for the flaw in the argument and focus specifically on the key words in the conclusion. If you need to draw a conclusion, your energy needs to be highest on process-of-elimination at the answers, and you don’t have to stress the initial read of the prompt nearly as much.

Know that the GMAT is a long, exhausting day, and you won’t likely get out of the test center without feeling completely wiped out. But if you manage your energy efficiently, you can use whatever energy you have left to triumphantly raise that winning score report over your head as you walk out.

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

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

When Not to Use Parallelism on the GMAT

Quarter Wit, Quarter WisdomWe know that we are often tested on parallelism on the GMAT. The logically parallel entities should be grammatically parallel. But today, we need to talk about circumstances where you might be tempted to employ parallelism but it would be incorrect to do so.

For example, look at this sentence:

A New York City ordinance of 1897 regulated the use of bicycles, mandated a maximum speed of eight miles an hour, required cyclists to keep feet on pedals and hands on handlebars at all times, and granted pedestrians right-of-way.

Is everything ok here? Well, it certainly seems so. We have four elements in parallel:

regulated …

mandated …

required …

granted …

But actually, there is a problem in this sentence:

‘regulated…’ will not be parallel to the rest of the three elements. The rest of the three elements will be in parallel.

Before we explain why, let’s take a simpler example:

The girl sitting next to me wears blue everyday, eats only waffles, and listens to music in office.

The sentence will not be ‘The girl sits next to me…’ because ‘sit’ is not parallel to other verbs. “sit” modifies the girl and is not used as a verb here. It is a present participle modifier modifying ‘girl’. It specifies the girl about whom we are talking.

Similarly, in the original sentence, ‘regulate’ is modifying ‘ordinance of 1897’. It is telling you which ordinance of 1897.

The other verbs ‘mandated’, ‘required’ and ‘granted’ are used as verbs and are parallel. They are assimilated under ‘regulate’. They tell you how the ordinance regulated.

How did it regulate?

mandated …

required …

granted …

Hence, you cannot use ‘regulated’ here. You must use ‘regulating’  – the present participle modifier to modify the ordinance. So you have to think logically – are the items in the given list actually parallel? Are they equal elements? If yes, then they need to be grammatically parallel too; else not.

Here is the complete official question:

Question: A New York City ordinance of 1897 regulated the use of bicycles, mandated a maximum speed of eight miles an hour, required of cyclists to keep feet on pedals and hands on handlebars at all times, and it granted pedestrians right-of-way.

(A) regulated the use of bicycles, mandated a maximum speed of eight miles an

hour, required of cyclists to keep feet on pedals and hands on handlebars at all

times, and it granted

(B) regulated the use of bicycles, mandated a maximum speed of eight miles an

hour, required cyclists to keep feet on pedals and hands on handlebars at all

times, granting

(C) regulating the use of bicycles mandated a maximum speed of eight miles an

hour, required cyclists that they keep feet on pedals and hands on handlebars

at all times, and it granted

(D) regulating the use of bicycles, mandating a maximum speed of eight miles an

hour, requiring of cyclists that they keep feet on pedals and hands on

handlebars at all times, and granted

(E) regulating the use of bicycles mandated a maximum speed of eight miles an

hour, required cyclists to keep feet on pedals and hands on handlebars at all

times, and granted

Solution:

From our above discussion, we know that we have choose one of (C), and (E).

(A), (B) and (D) put regulate parallel to the other verbs.

Still, let’s point out all the errors of these options:

(A) regulated the use of bicycles, mandated a maximum speed of eight miles an

hour, required of cyclists to keep feet on pedals and hands on handlebars at all

times, and it granted

Parallelism problem – regulated cannot be parallel to mandated and other verbs. Also, ‘mandated’ is not parallel to ‘it granted’. Besides, ‘required of X to do Y’ is unidiomatic.

(B) regulated the use of bicycles, mandated a maximum speed of eight miles an

hour, required cyclists to keep feet on pedals and hands on handlebars at all

times, granting

Parallelism problem – ‘regulated’ is parallel to ‘mandated’ though it should not be.

‘granting’ is not parallel to ‘mandated’ and ‘required’ though it needs to be parallel.

You also need an ‘and’ before the last element of the list ‘and granted …’

(D) regulating the use of bicycles, mandating a maximum speed of eight miles an

hour, requiring of cyclists that they keep feet on pedals and hands on

handlebars at all times, and granted

This is not a valid sentence because the main clause does not have a verb. ‘regulating…’, ‘mandating…’ and ‘requiring…’ are the present participle modifiers.

‘granted…’ is not parallel to the other elements. Besides, ‘requiring of X that they do Y’ is unidiomatic.

Now let’s look at the leftover options:

(C) regulating the use of bicycles mandated a maximum speed of eight miles an

hour, required cyclists that they keep feet on pedals and hands on handlebars

at all times, and it granted

‘it granted’ is not parallel to the other verbs. Besides, ‘required X that they do Y’ is unidiomatic.

(E) regulating the use of bicycles mandated a maximum speed of eight miles an

hour, required cyclists to keep feet on pedals and hands on handlebars at all

times, and granted

Perfect! All issues sorted out!

Answer (E)

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Tip of the Week: No Calculator? No Problem.

GMAT Tip of the WeekFor many GMAT examinees, the realization that they cannot use a calculator on the GMAT quantitative section is cause for despair. For most of your high school career, calculators were a featured part of the math curriculum (what TI are we up to now?); nowadays you almost always have Microsoft Excel a click away to perform those calculations for you.

But remember: it’s not that YOU don’t get to use a calculator on the GMAT quant section. It’s that NO ONE gets to use a calculator. And that creates the opportunity for a competitive advantage. If you know that the GMAT doesn’t include “calculator problems” – the testmakers know that you don’t get a calculator, too, so they create questions that savvy examinees can find efficient ways to solve by hand (or head) or estimate – then you can use that to your advantage, looking for “clean” numbers to calculate and saving calculations until they’re truly necessary. As an example, consider the problem:

A certain box contains 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?

(A) 3
(B) 6
(C) 14
(D) 17
(E) 20

If you’re well-versed in “non-calculator” math, you should recognize a couple things as you scan the problem:

1) The 23 oranges represent a prime number. That’s an ugly number to calculate with in a non-calculator problem.
2) 70% is a very clean number, which reduces to 7/10. Numbers that end in 0 don’t tend to play well with or come from double-digit prime numbers, so in this problem you’ll need to “clean up” that 23.
3) The 14 apples are pretty nicely related to the 70%. 14*5 = 70, and 14 = 7 * 2, where 70% is 7/10. So in sum, the 14 is a pretty “clean” number you’re working with to find a relationship that includes that also “clean” 70%. And the 23 is ugly.

So if you wanted to plug in numbers here to see how many oranges should be removed, keep in mind that your job is to get that 23 to look a lot cleaner. So while the Goldilocksian conventional methodology for backsolving is to “start with the middle number, then determine whether it’s correct, too big, or too small,” if you’re preparing for non-calculator math you should quickly see that with answer choice C of 14, that would give you 14 apples and 9 (which is 23-14) oranges), and you’re stuck at that ugly number of 23 as your total number of pieces of fruit. So your goal should be to find cleaner numbers to calculate.

You might try choice A, 3, which is very easy to calculate (23 oranges minus 3 = 20 oranges left), but a quick scan there would show that that’s way too many oranges (still more oranges than apples). So the other number that can clean up the 23 oranges is 17 (choice D), which would at least give you an even number (23 – 17 = 6). Because you’re now dealing with clean numbers (14, 6, and 70%) it’s worth doing the full calculation to see if choice D is really correct. And since 14 apples out of 20 total pieces of fruit is, indeed, 70%, you know that D is correct.

Now, if you follow these preceding paragraphs step-by-step, they should look just as long and unwieldy as the algebra or some traditional backsolving. But to an examinee seasoned in non-calculator math, finding “clean numbers worth testing” is more about the scan than the process. You should know that Odd + or – Odd = Even, but that Odd + or – Even is Odd. So with an even “fixed” number of 14 apples and an odd “changeable” number of 23 oranges, an astute GMAT test-taker looking to save time would probably eschew plugging in C first and realize that it’s just not going to be correct. Then another scan of numbers shows that only 3 and 17 are odd and prone to becoming “clean” when subtracted from the prime 23, so D should start looking tempting within seconds.

Note: this strategy isn’t for everyone or for every problem, but for those shooting for the 700s it can be extremely helpful to develop enough “number fluency” that you can save time not-testing numbers that you can see don’t have a real chance. On a non-calculator test that typically involves “clean” (even, divisible by 10, etc.) numbers, quickly recognizing which numbers will result in good, clean, non-calculator math is a very helpful skill.

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

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.

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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.

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.

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