GMAT Tip of the Week: Trick or Treat

ZombieinsteinOne of the most dreaded things about the GMAT is the time-honored “Testmaker Trick” – the device that the GMAT question author uses to sucker you into a trap answer on a question. You’ve done all the math right, but forgot to consider negative numbers or submitted the answer for x when the question really asks for y. The “Testmaker Tricks” are enough to make you resent the test and to see it in a derogatory light. This is a grad school test, not Simon Says! Why should it matter that Simon didn’t say “positive”?

But as we head into Halloween weekend, it’s an appropriate time for you to think back to the phrase that earned you pounds and pounds of candy (and maybe tons if you followed Jim Harbaugh’s double-costume strategy): Trick or Treat.

In a GMAT context, that means that on these challenging questions, what tricks one examinee is the “treat” or reward for those who buy into the critical thinking mindset that the GMAT is set up to reward. The GMAT testmakers themselves are defensive about the idea of the “trap” answer, preferring to see it as a reward system; the intent isn’t to “trick” people as much as it is to “treat” higher-order thinking and critical reasoning. Consider the Data Sufficiency example:

Is x > 3z?

(1) x/z > 3

(2) z > 0

Here the “trick” that the testmaker employs is that of negative numbers. Many people will say that Statement 1 is sufficient (just multiply both sides by z and Statement 1 directly answers the questions, x > 3z), but it’s important to remember that z could be negative, and if it were negative you’d have to flip the sign, as you do in an inequality problem when you multiply or divide by a negative. In that case x < 3z and the answer is an emphatic no.

Now, those test takers who lament the trick after getting it wrong are somewhat justified in their complaint that “you forgot about negatives!” is a pretty cheap trick. But that’s not the entire question: Statement 2 exists, too, and it’s a total throwaway when you consider it alone. Why is it there? It’s there to “treat” those who are able to leverage that hint: why would it matter if z is greater than 0? That statement provides a very important clue as to how you should have been thinking when you looked at Statement 1.

If your initial read of Statement 1 – under timed pressure in the middle of a test, mind you – had you doing that quick algebra and making the mistake of saying that it’s sufficient, that’s understandable. But if you blew right past the clear hint in the second statement, you missed a very important opportunity to seize the treat. To some degree this problem is about the math, but the GMAT often adds that larger degree of leveraging hints – after all, much of business success comes down to your ability to find an asset that others have overlooked, or to get more value out of an asset than anyone else could.

So as you study for the GMAT, keep that Halloween spirit close by. When you miss a problem because of a dirty “trick,” take a second to also go back and see if you missed a potential treat – a reward that the GMAT was dangling just out of reach so that only the most critical thinkers could find it and take advantage. GMAT problems aren’t all ghosts, goblins, and ghouls out to frighten and trick you; often they include very friendly pieces of information just disguised or camouflaged enough that you have to train yourself to spot the treat.

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

By Brian Galvin.

Does the GMAT Even Really Measure Anything?

SAT/ACTAt some point, in pretty much every class I teach, a student will ask me what the GMAT really measures. The tone of the question invariably suggests that the student doesn’t believe that the test accurately assesses anything of real significance, that the frustrations and anxieties we endure when preparing for the exam are little more than a form of admissions sadism.

When it comes to standardized testing, a certain amount of cynicism is understandable – if person A has a better grasp on the fundamentals of geometry and algebra than person B, why on earth would we conclude on that basis that person A will be more likely to have a successful career in a field totally unrelated to geometry and algebra?

Of course, I have my stock answer: the test is designed to reward flexible thinking, to provide feedback on our ability to make good decisions under pressure. And though I do believe this, I’m also well aware that tests have their limitations. There are many incredibly talented and intelligent people who struggle in the artificial conditions of a testing environment, and no 3.5 hour exam will be able to fully capture an individual’s potential. At some level, we all know this. It’s why the admissions process is holistic. Still, your GMAT score is important, so I thought it worthwhile to do a bit of research about what the data says regarding how well the test predicts future success.

In 2005, GMAC issued a report in which it examined data from 1997-2004 about the correlation between GMAT scores and graduate school grades. The report summarizes a regression analysis in which researchers generated what they term a “validity coefficient.” A coefficient of “1” would mean that the correlation between the GMAT and graduate school grades was perfect – the two variables would move in lockstep. According to this report, any coefficient between .3 and .4 is considered useful for admissions.

The GMAT’s validity coefficient came out to .459, suggesting that the test does, in fact, have some predictive value, and this predictive value seems to be superior to other variables that admissions committees consider. The validity coefficient for undergraduate grades, for example, was .283. (And when the variables are combined, the validity coefficient is higher any individual coefficient.) So is that the end of the story? Can I rebuff my students’ complaints about standardized testing by sending them an abstract of this report? It’s not quite that simple.

In the conclusion section of the paper, we’re offered the following: “When examining the validity data in this study, one should recognize that there is a great deal of variability across programs and that the relative importance for each of the investigated variables differs for each program. This is to be expected.”

So one interpretation of the data is that the GMAT does a pretty good job of predicting how well students will do in their MBA programs. But if you’ve been studying for the GMAT for any length of time, hopefully your “correlation is not causation” reflex was triggered. What if students with higher GMAT scores attend more selective schools and then it turns out that those selective schools have more lenient grading policies because they figure that the necessary vetting has already been performed? In this case, the correlation between GMAT score and grades wouldn’t be shedding much light on how well the test-takers would perform academically, but rather, would be providing information about what kinds of programs test-takers would eventually attend.

Moreover, one could argue that looking at the correlation between GMAT scores and grad school grades is of limited usefulness. Schools no doubt hope their students do well in their classes, but it stands to reason that admissions decisions are also informed by predictions about what prospective students can contribute to the school’s community, as well as what kind of future career success these students can expect after they graduate. What, then, is the correlation between graduate grades and career success beyond the classroom? And how would we even begin to measure or define “success”? These are complex questions with no good answer.

Furthermore, while the paper appeared statistically rigorous to me, amateur that I am, we still have to consider that it was commissioned by GMAC, the company that administers the test, so there is a conflict of interest to bear in mind.  A recent article by the Journal of Education for Business questioned the results of the earlier research and insisted that the section of the GMAT that best predicted conventional managerial qualities, such as leadership initiative and communication skill, was the Analytical Writing section, the component of the test that admissions committees care about least and that had the lowest validity coefficient, according to the earlier paper.

Needless to say, though I found these papers interesting, they provided me with no definitive answers to offer my students when they ask about what the GMAT really measures. And, paradoxically enough, this is something we should find encouraging. If the GMAT were measuring any kind of fixed inherent quality, there’d be little point in prepping for the test. But if the test requires a unique skillset, that skillset can be mastered, irrespective of how directly applicable that skillset will be to future endeavors. Pragmatically speaking, the thing that matters most is that admissions committees do care about the GMAT score. So my ultimate message to my students is this: stop worrying about what the GMAT measures, and instead, harness that energy to focus on what you need to do to maximize your score.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

How to Solve Tough GMAT Quant Problems by Blending Strategies

victorinox_mountaineer_lgI wrote a post a few weeks ago in which I discussed the importance of blending strategies on certain questions. It’s a mistake to pigeonhole a complex problem as one in which a single tool will be most effective. By test day you will have cultivated a veritable Swiss army knife of strategies and you want to be able to switch from one to another seamlessly.

This philosophy came to mind the other day when a student sent me the following official problem:

For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as man regular admissions tickets were sold as student tickets, was the total revenue from ticket sales that day?

A) 24,960

B) 25,920

C) 28,080

D) 28,500

E) 29,160

Oh boy. There’s a lot going on here. So let’s start by simply finding the total number of tickets sold. We know that every 5 minutes, 30 tickets are sold. We know that there are twelve 5-minute increments each hour, so 12*30 = 360 tickets are sold each hour. We see that the museum will be open for a total of 9 hours, so a total of 9*360 = 3240 tickets are sold during that time.

We’ve got two different kinds of tickets – general and student. The general tickets were $10 and the student tickets were $6. And we know that 3 times as many general tickets were sold as student tickets. So the tickets were overwhelmingly for general admission. If they were all for general admissions tickets, we know that the revenue would have been 3240*10 = 32,400. Because 25% of the tickets were sold for $6, we know that the correct answer will be a bit below this value. If we were short on time, E would be a pretty reasonable guess.

But say we’ve achieved a level of mastery where we don’t need to guess. Hopefully, you recognized that if the ratio of general tickets to student tickets is 3:1, we’re dealing with a kind of weighted average, meaning we can use a number line to find the average overall ticket price, which will be much closer to $10 than to $6. So we know the average price is greater than $8, as this would be the average price if the same number of both kinds of tickets were sold. What about $9? On the number line, we’ll have the following: 6——–9—-10.

9 is three units away from 6 and one unit away from 10, thus yielding our desired 3:1 ratio. Now we know that the average price is $9 per ticket.

So all we have to do is calculate 3240 * 9, as 3240 tickets were sold for an average of $9 each, and we have our answer. That math isn’t too bad, but we can incorporate a couple more useful strategies to save some time. We know that 3000*9 = 27,000, so clearly 3240*9 is greater than 27,000. Now we can eliminate A and B from contention.  Next, we can see that going from right to left, the first non-zero digit of 3240*9 will be 6, as 4*9 = 36. Among C, D, and E, the only answer choice that has a 6 in the tens place is E, which is our answer.

Takeaway: In a single question, we ended up doing a bit of estimation, using the answer choices, employing some rudimentary logic, and using the number line to simplify a weighted average. Just as important as what we did do, is what we avoided doing – a lot of grinding calculation.

We cannot emphasize this enough: the Quant section is not a math test. It’s an opportunity to demonstrate fluid thinking under pressure. So when you’re doing practice questions, work on employing every tool in your Swiss army knife of strategies. By the day of the test, the more fluidly you can switch from one tool to another, the better you’ll be able to handle even the most challenging problems.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

Complicated GMAT Work-Rate Questions Made Easy!

Quarter Wit, Quarter WisdomToday, we will take up a gem of a work-rate question from our own curriculum. Its basics lie in a post on joint variation that we discussed many weeks ago. Here is a quick recap of the actual methodology:

If 10 workers complete a work in 5 days working 8 hours a day, how much work will be done by 6 workers in 10 days working 2 hours a day?

Here is what it looks like:

 

10 workers……………..5 days …………….. 8 hours ……………1 work

6 workers………………10 days …………… 2 hours …………… ? work

We need to find the amount of work done, so we start with the work done in the first case and then multiply it by the respective ratios:

Work done = 1 * (6/10) * (10/5) * (2/8) = 3/10

We multiply by 6/10 because number of men decreases from 10 to 6. The work done will reduce, so we multiply by 6/10 (the fraction less than 1).

We also multiply by 10/5 because number of days increases from 5 to 10. Because of this, the work done will increase, so we multiply by 10/5 (the fraction more than 1).

We also multiply by 2/8 because number of hours decreases from 8 to 2. Because of this, the work done will decrease, hence, we multiply by 2/8 (the fraction less than 1).

So the process is super simple – start with what you need to find out, say x, and multiply it by the ratio of each thing that changes from A to B. Whether you multiply by A/B or B/A depends on whether with this change increases or reduces x. If x increases, you will multiply by the fraction that is greater than 1, however if x decreases, you will multiply by the fraction that is less than 1.

On this same concept, let’s look at the question:

16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

Statement 1: Mules work more slowly than horses.

Statement 2: 48 mules can haul the same load of lumber in 16 minutes.

Let’s see what data we have in the question stem:

16 horses …….. 24 mins ………. 1 work

12 horses …….. 14 mins ………. ? work

Work done = 1*(14/24)*(12/16) = (7/16)th of the work

We multiply by 14/24 because if the time taken to do the work decreases, the work done will also decrease. 14/24 is less than 1 so it will decrease the work done.

We also multiply by 12/16 because if the number of horses decreases, the work done will also decrease. 12/16 is less than 1 so it will decrease the work done.

All in all, we now know that 12 horses complete 7/16th of the work in 14 mins. So there is still 1 – 7/16 = 9/16 of the work left to do.

Now let’s review the two statements.

Statement 1: Mules work more slowly than horses.

This statement doesn’t give us any figures, so how can we analyse it mathematically? What we can do is find the range in which the time taken by all the horses and mules together will lie according to this statement.

Case 1: When mules work at a rate that is infinitesimally smaller than the rate of horses.

In this case, 12 mules are equivalent to 12 horses. So we have a total of 12 + 12 = 24 horses working together to complete (9/16)th of the work.

16 horses …….. 24 mins ………. 1 work

24 horses ……… ? mins ………. 9/16 work

Time taken = 24*(16/24)*(9/16) = 9 mins

Since the mules are slower than the horses, the time taken to complete the work will be more than 9 minutes. How much more than 9 minutes, we do not know. Now look at the flip side:

Case 2: When the mules work at a rate close to 0.

If the mules work slower, time taken will be more till the point when mules work so slowly that they do almost no work.

16 horses …….. 24 mins ………. 1 work

12 horses ……… ? mins ………. 9/16 work

Time taken = 24*(16/12)*(9/16) = 18 minutes

Therefore, depending on how fast/slow the mules are, the time taken to do the rest of the work could be anywhere from 9 minutes to 18 minutes. Therefore the time taken could be either less or more than 15 minutes – this statement alone is not sufficient.

Statement 2: 48 mules can haul the same load of lumber in 16 minutes.

We now know exactly how fast the mules are, so this must be sufficient to say whether the time taken to do the rest of the work was less or more than 15 minutes – we don’t need to actually find the time taken here – therefore, the answer is B, Statement 2 alone is sufficient.

However, if you would like to find out for practice, just find the equivalence between the horses and the mules first.

To haul the load in 16 minutes, we need 48 mules

To haul the load in 24 minutes, we need 48 * (16/24) = 32 mules

So 32 mules are equivalent to 16 horses (because 16 horses haul the load in 24 minutes). This means that 2 mules are equivalent to 1 horse, and 12 mules are, therefore, equivalent to 6 horses.

So now, in effect we have a total of 12 + 6 = 18 horses, and the situation now becomes this:

16 horses …….. 24 mins ………. 1 work

18 horses ……… ? mins ………. 9/16 work

Time taken = 24*(16/18)*(9/16) = 12 minute – less than a quarter-hour to finish the work.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube and Google+, and 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: Percents Are Easy, Words Are Hard

GMAT Tip of the WeekPop quiz: 1) Your restaurant bill came to exactly $64.00 and you want to leave a 20% tip. How much do you leave? 2) You’re running a charity half-marathon and your fundraising goal is $6000. You’ve raised $3300. What percent of your goal have you reached? 3) Your $20,000 investment is now worth $35,000. By what percent has your investment increased in value?

[Answers: $12.80; 55%; 75%]

 

If that was easy for you, good. It better have been. After all, you’re applying to graduate school and that’s maybe 6th grade math in three real-life contexts. Percents are not hard! But percent problems can be. And that’s what savvy GMAT test-takers need to learn:

On the GMAT, percent problems aren’t hard because of the numbers. They’re hard because of the words.

Consider two situations:

1) A band sells concert t-shirts online for $20 each, and in California, web-based sales are subject to a 10% sales tax. How much does a California-based purchaser pay in sales tax after buying a t-shirt?

2) At a concert in California, a band wants to sell t-shirts for $20. For simplicity’s sake at a cash-only kiosk, the band wants patrons to be able to pay $20 even – hopefully paying with a single $20 bill – rather than having to pay sales tax on top. If t-shirts are subject to a 10% tax on the sale price, and the shirts are priced so that the after-tax price comes to $20, how much will a patron pay in sales tax after buying a t-shirt?

So what are the answers?

The first, quite clearly, should be $2. Take 10% of the $20 price and there’s your answer. And taking 10% is easy – just divide by 10, which functionally means moving the decimal point one place to the left and keeping the digits the same.

The second is not $2, however, and the reason is critical to your preparation for percent questions above the 600 level on the GMAT: the percent has to be taken OF the proper value. Patrons will pay 10% OF the before-tax price, not 10% of the after-tax price. $20 is the after-tax price (just as $22 is the after-tax price in the first example…note that there you definitely did not take the 10% of the $22 after-tax price!). So the proper calculation is:

Price + 10% of the Price = $20

1.1(P) = 20

P = 20/1.1 = 18.18

So the price comes out to $18.18, meaning that $1.82 is the amount paid in tax.

While the calculation of 20/1.1 may have been annoying, it’s not “clever” or “hard” – the reason that many people will just say $2.00 to both isn’t that they screwed up dividing $20 by 1.1, but instead because they saw a percent problem with two numbers (10% and $20) and just “calculated a percent.” That’s what makes the majority of GMAT percent problems tricky – they require an attention to detail, to precision in wording, for examinees to ensure that the (generally pretty darned easy) percent calculations are taking the percent of the proper value.

They’re logic puzzles that require a bit of of arithmetic, not simple arithmetic problems that just test your ability to divide by 10 absent critical thought. So as you approach GMAT percent problems, remember that the math should be the easy part. GMAT percent problems are often more about reading comprehension and logic than they are about multiplication and division.

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

By Brian Galvin.

How “Back to the Future” Can Help Your GMAT Score!

Back to the FutureAs a social media user, you’re probably very away that today – October 21, 2015 – is “The Future,” the day from Back to the Future II when Marty McFly and Doc Brown (along with a sleeping Jennifer) visit Hill Valley 30 years in the future. And while we don’t yet have hoverboards and while the bold prediction that the Cubs will have just won the World Series seems to be slipping away, the Back to the Future trilogy does offer some incredibly valuable GMAT lessons. How can Marty McFly help you better understand the GMAT and increase your score?

1) The Space-Time Continuum

Throughout the Back to the Future series, Doc Brown was keenly aware of the impacts that any slight alteration to the past would have on the future (as it turns out, stopping your parents from meeting or allowing the scores of all future sporting events to fall into the hands of your family’s mortal enemy could have disastrous results!). The GMAT works on a similar premise: because the GMAT is adaptive, each question impacts the future questions you will see – the events are connected and sequential. Which means:

A) You can’t go back and change your answers. That would violate the “Space-Time Continuum” nature of the GMAT (changing #5 would mean that questions 6-37 would all be different, so it’s just not an option). And THAT means that you have to make good decisions in real-time – you need to double-check for careless errors before you submit, because if you realize later that you blew it, that question is gone.

B) You can’t afford a disastrous start. It’s not that the first 10 questions matter exponentially more (as the old myth goes), but they are slightly more important if only for this reason: a strong early performance means that you’re seeing harder questions once you’re in your groove, and a poor early performance means that you’re seeing easier questions and have a much lower margin for error. Throughout each section you’ll make a few mistakes and you’ll hit a lucky guess or two.

If you’ve done well and avoided careless mistakes early, then your mistakes and lucky guesses will be on harder questions. If you haven’t, then those mistakes come on easier questions and pull down your score all the more. It *is* possible to recover from a poor start…it just requires you to be a lot closer to perfect and that can be hard to do on test day. Please note: you don’t need to get all 10 right to consider it a good start!  6 or 7 will probably put you on a track you’re happy with; the key is to just make sure you’re not making too many silly mistakes early and missing the questions that you should get right.

2) Save the Clock Tower! 

Back to the Future taught a generation the importance of timeline, and that’s critical on the GMAT. You need to be mindful of time and ensure that you have enough to finish each section. Just like in the movies, where mismanagement of time and unforeseen events created precarious situations (would Doc get the wire connected before lightning struck? Would Marty get to that point at the proper time? Would Doc reach Clara before the train tumbled off the cliff?), the GMAT offers you plenty of opportunities to waste time and get off schedule (and maybe your score falls off a cliff, or you’re the one stuck in the past…an era when master’s degrees were far from the norm).

You need to conserve time on the test so that you don’t find a catastrophe waiting at the end. Which means that sometimes you have to let a hard problem go so that it doesn’t suck up several minutes of your time (even if the hard problem seems to be calling you “chicken”!). Like Marty should have done in most time-travel situations, have a plan for how you’ll address events in a timely fashion and stick to it. If you want to have 53 minutes left after 10 questions and you have 51, know that you’ll probably have to guess soon to get back on track.

3) Find Your Skateboard

1985 was easy for Marty, like a 400-500 level GMAT problem. If he needed to quickly get from one place to another, he’d hop on his skateboard and grab the back of a truck. But 1955 and 2015 were quite different – there weren’t conventional skateboards for him to use, so he had to improvise either by breaking a scooter in two or learning how to handle a hoverboard.

The GMAT is similar: the tools you’ll use to solve problems (find skateboard, let a Tannen chase you, veer off at the last second leaving him to crash into a pile of manure) are extremely similar, but just different enough that it may not be obvious what to do at first. Your job as you study is to learn how to look for that “skateboard.”

On exponent problems, for example, the key is almost always getting the given information to a point where you can perform the rules you know. And since those rules are almost always requiring you to deal with exponents with the same base and that the terms are being multiplied or divided, your “finding the skateboard” process usually involves factoring non-prime bases into prime factors and factoring addition and subtraction into multiplication. Much like Marty McFly in a new decade, you’ll find yourself seeing slightly-familiar, but yet totally different situations on the test – your job is to focus more on the similarity and seek out a couple steps to get it to where the rest is rote.

4) Be a Man (or Woman) of Action

In the original Back to the Future, you saw how the entire future changed with just one action: the ever analytical and incredibly intelligent George McFly just wasn’t a confident or action-oriented man, and so despite Marty’s best efforts to talk him up to Lorraine and to get him to be a bit more debonair, the McFly family future was fading quickly. Until…George had the opportunity to stop analyzing and just “do,” telling Biff to “get your damn hands off” Lorraine and ultimately punching Biff in the mouth. From that point on, the George-and-Lorraine romance was on (again?) and the future was just a matter of density. I mean…destiny.

If you’re reading a blog post about the GMAT you’re certainly not the type that Principal Strickland would call a slacker, but there’s a good likelihood that you’ll perform on test day like the “old” George McFly: intelligent and capable, but timid and over-analytical. Particularly with the timed nature of the GMAT, you often just have to go with an instinct and try it out, whether that means writing down an equation and then double checking that you like your math (as opposed to reading the question again and again) or testing your theory that you’re allowed to cross-multiply there (test it with small numbers and see if you get the answer you should).

The biggest mistake that the truly-capable make on the GMAT is one of paralysis by analysis; they’re afraid to put pen to paper to “try something” and then they become acutely aware of the time ticking past them and panic all the more. Avoid that trap! Be willing to try, to take action, and you’ll find that – like the owner of  DeLorean time machine – you have plenty of time.

On this 30th anniversary of Marty’s journey to the future, plan for your future 30 years down the road. The way you study for the GMAT, the way you manage your time and confidence on the test – they could have a major impact on what your future looks like. Heed the lessons that Doc and Marty taught you, and you could leave the test center saying, “Roads? Where I’m going, we don’t need roads,” of course because most elite b-school campuses are all about sidewalks.

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

By Brian Galvin.

7 Formulas for Tackling Three Overlapping Sets on the GMAT

Quarter Wit, Quarter WisdomIn a previous post, we saw how to solve three overlapping sets questions using venn diagrams. Today, we will look at all of the various formulas floating around on three overlapping sets. Most of these are self explanatory but we will look into the details of some of them.

 

 

 

There are two basic formulas that we already know:

1) Total = n(No Set) + n(Exactly one set) + n(Exactly two sets) + n(Exactly three sets)

2) Total = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C) + n(No Set)

From these two formulas, we can derive all others.

n(Exactly one set) + n(Exactly two sets) + n(Exactly three sets) gives us n(At least one set). So we get:

3) Total = n(No Set) + n(At least one set)

From (3), we get n(At least one set) = Total – n(No Set)

Plugging this into (2), we then get:

4) n(At least one set) = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C)

Now let’s see how we can calculate the number of people in exactly two sets. There is a reason we jumped to n(Exactly two sets) instead of following the more logical next step of figuring out n(At least two sets) – it will be more intuitive to get n(At least two sets) after we find n(Exactly two sets).

n(A and B) includes people who are in both A and B and it also includes people who are in A, B and C. Because of this, we should remove n(A and B and C) from n(A and B) to get n(A and B only). Similarly, you get n(B and C only) and n(C and A only), so adding all these three will give us number of people in exactly 2 sets.

n(Exactly two sets) = n(A and B) – n(A and B and C) + n(B and C) – n(A and B and C) + n(C and A) – n(A and B and C). Therefore:

5) n(Exactly two sets) = n(A and B) + n(B and C) + n(C and A) – 3*n(A and B and C)

Now we can easily get n(At least two sets):

6) n(At least two sets) = n(A and B) + n(B and C) + n(C and A) – 2*n(A and B and C)

This is just n(A and B and C) more than n(Exactly two sets). That makes sense, doesn’t it? Here, you include the people who are in all three sets once and n(Exactly two sets) converts to n(At least two sets)!

Now, we go on to find n(Exactly one set). From n(At least one set), let’s subtract n(At least two sets); i.e. we subtract (6) from (4)

n(Exactly one set) = n(At least one set) – n(At least two sets), therefore:

7) n(Exactly one set) = n(A) + n(B) + n(C) – 2*n(A and B) – 2*n(B and C) – 2*n(C and A) + 3*n(A and B and C)

You don’t need to learn all these formulas. Just focus on first two and know how you can arrive at the others if required. Let’s try this in an example problem:

Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

(A) 185

(B) 180

(C) 175

(D) 190

(E) 195

You are given that:

n(At least one channel) = 250

n(Exactly two channels) = 50

So we know that n(At least one channel) = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels) = 250

250 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)

Let’s find the value of n(Exactly 3 channels) = x

We also know that n(At least one channel) = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C) = 250

Also, n(Exactly two channels) = n(A and B) + n(B and C) + n(C and A) – 3*n(A and B and C)

So n(A and B) + n(B and C) + n(C and A) = n(Exactly two channels) + 3*n(A and B and C)

Plugging this into the equation above:

250 = n(A) + n(B) + n(C) – n(Exactly two channels) – 3*x + x

250 = 116 + 127 + 107 – 50 – 2x

x = 25

250 = n(Exactly 1 channel) + 50 + 25

n(Exactly 1 channel) = 175, so your answer is C.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube and Google+, and 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: Your GMAT Verbal (Donald) Trump Card

GMAT Tip of the WeekThe general consensus coming out of this week’s Democratic debate for the 2016 U.S. Presidency was this: the Democrats were quick to defend and agree with each other, particularly in contrast to the recent Republican debates in which the candidates were much more apt to attack each other.

The Democrats discussed, but the Republicans DEBATED, fiercely and critically. And – putting politics aside – one of the main issues on which those Republican candidates have attacked each other is “who is the more successful CEO/entrepreneur?” (And the answer to that? Likely Wharton’s finest: Donald “You’re Fired” Trump.)

So as you watch the political debates in between GMAT study sessions, keep this in mind: on the GMAT verbal section, you want to think more like a Republican candidate, and if possible you want to think like The Donald. Trump thinking is your Trump card: on GMAT verbal, you should attack, not defend.

Why?

Because incorrect answers are very easy to defend if that’s your mindset. They’re wrong because of a small (but significant) technicality, but to the “I see the good in all answer choices” eye, they’ll often look correct. You want to be in attack mode, critically eliminating answer choices and enjoying the process of doing so. Consider an example:

From 1998 to 2008, the amount of oil exported from the nation of Livonia increased by nearly 20% as the world’s demand soared. Yet over the same period, Livonia lost over 8,000 jobs in oil drilling and refinement, representing a 25% increase in the nation’s unemployment rate.

Which of the following, if true, would best explain the discrepancy outlined above?

A) Because of a slumping local economy, Livonia also lost 5,000 service jobs and 7,500 manufacturing jobs.

B) Several other countries in the region reported similar percentages of jobs lost in the oil industry over the same period.

C) Because of Livonia’s overvalued currency, most of the nation’s crude oil is now being refined after it has been exported.

D) Technological advancements in oil drilling techniques have allowed for a greater percentage of the world’s oil to be obtained from underneath the ocean floor.

E) Many former oil employees have found more lucrative work in the Livonia’s burgeoning precious metals mining industry.

The paradox/discrepancy here is that oil exports are up, but that jobs in oil drilling and refinement are down. What’s a Wharton-bound Trump to do here? Donald certainly wouldn’t overlook the word “Critical” in “Critical Reasoning.” Almost immediately, he’d be attacking the two-part job loss – it’s not that “oil jobs” are down, it’s that oil jobs in “drilling AND refinement” are down. Divide and conquer, he’d think, one of those items (either drilling or refinement) is bound to be a “lightweight” ready to be attacked.

Choice A is something that you could talk yourself into. “Hey, the economy overall is down, so it only makes sense that oil jobs would be down, too.” But think critically – you ALREADY know that the oil sector is not down. Oil exports are up 20% and global demand is soaring, so these oil jobs should be different. Critical thinking shows you that the general economy and this particular segment are on different tracks. Choice A does not explain the discrepancy.

Choice B is similar: if you’re looking for a reason to make it right, you might think, “See, it’s just part of what’s going on in the world.” But again, be critical. This is a bad answer, because it overlooks information you already have. Livonia’s oil exports are up, so absent a major reason that those exports are occurring without human labor, we don’t have a sound explanation.

Choice C hits on Trump’s “divide and conquer” attack strategy outlined above: if a conclusion to a Critical Reasoning problem includes the word “AND” there’s a very high likelihood that one of the two portions is the weak link. So fixate on that “and” and try to find which is the lightweight. Here you see that the oil is being exported from Livonia, but no longer being REFINED there. Those are the jobs that are leaving the country, and that explains why exports could be up with employment going down.

Choice D is tempting (statistically the most popular incorrect answer choice to this problem, with Trump-like polling numbers in the ~25% range). Why? Because you’re conditioned to think, “Oh, they’re losing jobs to technology.” So if you’re looking to find a correct answer without much critical thought and effort, this one shines like a beacon. But get more critical on the second half of the sentence: it’s not that technology makes it easier to obtain oil without human labor, it’s that technology is allowing for more drilling from the ocean. But that’s irrelevant, because, again, Livonia’s exports are up! So whether it’s Livonia getting that seafloor oil or other countries doing so, the fact remains that with oil exports up, you’d think that Livonia would have more jobs in oil, and this answer doesn’t explain why that’s not the case.

Here it pays to be critical all the way through the sentence: just because the first few words match what you think you might want to hear, that doesn’t mean that the entire statement is true. Think of this in Trump terms: Megyn Kelly might start a sentence with, “Mr. Trump, you’re arguably the most successful businessman of your generation,” (and you know Trump will love that) but if she follows that with, “But many would argue that your success was largely a result of your father’s money and that your manipulation of bankruptcy laws is unbefitting of an American president,” you know he’d be in attack mode immediately thereafter. Don’t fall in love with the first few words of an answer choice – stay ready to attack at a moment’s notice!

And choice E is similarly vulnerable to attack: yes some oil employees may have taken other jobs, but someone has to be doing the oil work. And if unemployment is up overall (as you know from the stimulus) then people are waiting to take those jobs, so the fact that some employees have left doesn’t explain why no one has filled those spots. When Donald Trump had to surrender his post as the star of The Apprentice, Arnold Schwarzenegger was ready to take his place; so, too, should unemployed members of the labor pool in Livonia be ready to take those oil jobs, absent a major reason why they wouldn’t, and choice E fails to present one.

Overall, your job on GMAT Verbal is to be as critical as possible. You’re there to debate the answer choices, not to defend or discuss them. As you read the conclusion of a Critical Reasoning problem, you want to be scanning for a “lightweight” word or phrase that makes it all the more vulnerable to attack. And as you read each answer choice, you shouldn’t be quick to see the good in the sentence, but instead you should be probing it to see where it’s weak and vulnerable to attack.

Let the answer choices view you as a bully – you’re not at the GMAT test center to make friends. Always be attacking, always be looking for words, phrases, or ideas that are an answer choice’s undoing. Trump logic is your Trump card, take joy from telling four of five answer choices “You’re Fired.”

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

By Brian Galvin.

The Importance of Catching Details on the GMAT

Magnifying GlassIn our everyday lives, we all understand that attention to linguistic detail is important. When my wife tells me I need to pick up my daughter, I don’t unconsciously filter out minor elements like where my daughter is or what time I’m supposed to get her. Similarly, if you were on the phone making plans with a friend, you’d never hang up before knowing what you’d made plans to do.

Details aren’t just important – almost every conversation we have would be totally incoherent if we didn’t pay attention to them. And yet, for whatever reason, on the GMAT, we have a tendency to skim over these very same details without absorbing them. This tendency, I find, is particularly pronounced on Critical Reasoning questions. Take this question, which I reviewed with a student the other day:

Citizens of Parktown are worried by the increased frequency of serious crimes committed by local teenagers. In response the city government has instituted a series of measures designed to keep teenagers at home in the late evening. Even if the measures succeeded in keeping teenagers at home, however, they are unlikely to affect the problem that concerns citizens, since more crimes committed by local teenagers take place between 3p.m. and 6p.m. 

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

A) Similar measures adopted in other places have failed to reduce the number of teenagers on the streets in the late evening. 

B) The crimes committed by teenagers in the afternoon are mostly small thefts and inconsequential vandalism 

C) Teenagers are much less likely to commit serious crimes when they are at home than when they are not at home 

D) Any decrease in the need for police patrols in the late evening would not mean that there could be more intensive patrolling in the afternoon 

E) The schools in Parktown have introduced a number of after-school programs that will be available to teenagers until 6 p.m. on weekday afternoons.

My student broke down the argument quickly. He saw that the conclusion was that the city’s plan to keep teenagers at home in the late evening was unlikely to be successful because most teenage crimes were committed earlier in the day.

When I asked him to reiterate what the fine citizens of Parktown were concerned about, he shrugged and said ‘crime.’ Of course, this wasn’t wrong, per se, but it was incomplete. When I followed up and asked what kind of crime they were worried about, he was puzzled at first. It wasn’t until I asked him to reread the first sentence of the argument and to pay very close attention to adjectives that it clicked.

The citizens were worried about serious crime. And this makes sense. If someone told you that the neighborhood you were about to move in to had a very high crime rate, your reaction would not be the same if those crimes consisted largely of jay-walking as it would if you discovered that those crimes were more serious offenses. I then asked him to reread the sentence at the very end of the passage. This time, he got it.

While it’s true that the majority of crimes were committed between 3 and 6 pm, the argument doesn’t specify what kinds of crimes were committed during these hours. It’s this gap between the crimes that the citizens were concerned about – serious ones – and the crimes we’re given evidence about – all crimes – that is the key to this question. If the teenagers are jay-walking in the early afternoon, but engaging in far more damaging behavior in the evening, the plan to impose the curfew still makes sense, even if, technically, those jay-walking offenses constitute a majority of the crimes committed.

Now let’s go to the answer choices:

A: We’re trying to weaken the idea that the plan won’t work. If the plan didn’t work in other places, that certainly doesn’t weaken the idea that the plan won’t work in Parktown. A is out.

B: This looks good. Even though the crimes committed between 3 and 6 constitute a majority of the total crimes, these crimes are trivial. The citizens of Parktown are worried about serious crimes, which, if they’re committed at night, the curfew would help prevent. B is the correct answer.

C: This does nothing to address the core issue of the argument, which is that the plan won’t work because most crimes are committed before the curfew takes effect.

D: While decreasing the need for police patrols is a laudable objective, this isn’t relevant to the argument. Moreover, if the police patrols weren’t more available in the afternoon, when most crimes are committed, there’s certainly no reason to have more confidence that the curfew would be effective.

E: I am a fan of after-school programs, but the availability of such activities sheds little light on whether the curfew will work. After all, if teenagers are determined to commit crimes in the afternoon, the fact that they could join the Glee Club if they want to is unlikely to serve as an effective deterrent to whatever mischief they had planned.

Takeaway: Typically, when we talk about modifiers, we’re doing so in the context of Sentence Correction, but modifiers are no less important in Critical Reasoning. Information about “what kind,” “where,” and “when,” will be absolutely crucial to assessing any argument we encounter. If a modifier is present in the argument’s conclusion, but not in the argument’s premises, that is something we want to note. We make the effort to pay attention to these details when dealing with the mundane activities of our everyday lives, so let’s not neglect those same details on the GMAT.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

Manipulating Standard Formulas on the GMAT

Quarter Wit, Quarter WisdomWe know the formula we need to use to find the sum of n consecutive positive integers starting from 1. The formula is given as n(n+1)/2.

So the sum of first four positive integers is 4 * (4 + 1)/2 = 10.

This might seem a bit cumbersome, since it is easy to see that 1 + 2 + 3 + 4 = 10, but we know that the formula comes in very handy when n is a large number. For example, the sum of first 50 positive integers = 50 * 51/2 = 1275. Obviously, this will be a lot harder when done the “1 + 2 + 3 + 4 … + 49 + 50” way.

Now the question is, how do we adjust the same formula to find the sum of consecutive integers which do not start from 1?

Say, how do we find the sum of all positive integers from 8 to 20? The formula assumes a starting point of 1, so then we insert only the last number, n. How do we manage the 8? Let’s try to figure it out

Say the sum of first 20 positive integers = 1 + 2 + 3 + 4 + …. + 19 + 20 = 20 * 21/2

(1 + 2 + 3 +… + 7) + (8 + 9 +10 + … + 19 + 20) = 20 * 21/2

We need the value of the part in red, let’s call it the required sum.

(1 + 2 + 3 +… + 7) + The Required Sum = 20 * 21/2

Note here that we know the sum of 1 + 2 + 3 + … + 7 = 7 * 8/2

So, 7*8/2 + The Required Sum = 20 * 21/2, therefore the Required Sum = 20*21/2 – 7*8/2

To get the sum of consecutive integers from 8 to 20, we find the sum of all integers from 1 to 20 (using the formula we know) and subtract the sum of integers from 1 to 7 out of it (using the same formula).

To generalize, the sum of all positive integers from m to n is given as:

n(n+1)/2 – (m-1)*m/2

Let’s look at a question based on this concept:

If the sum of the consecutive integers from –40 to n inclusive is 356, what is the value of n?

(A) 47

(B) 48

(C) 49

(D) 50

(E) 51

If you are thinking that we haven’t gone over how to adjust the formula for negative numbers, you are right, but what we have discussed is enough to solve this question.

Numbers around 0 are symmetrical. So 1 and -1 add up to equal 0. Similarly, 2 and -2 add up to equal 0, and so on…

-40, -39 … 0 … 39, 40, 41, 42, 43, 44, 45 …

The sum of all numbers from -40 to 40 will be 0. Or another way to look at it is that 0 is the mean of all numbers from -40 to 40. So the total sum of these numbers will also be 0.

The given sum is actually the sum of numbers from 41 to n only.

We know how to calculate that:

n(n+1)/2 – 40*41/2 = 356

n(n+1) = 2352

From the options, we see that n cannot be 49 or 50 because the product of 49*50 or 50*51 will end in 0, so plug in n = 48 to check whether 48*49 is equal to 2352. It is, therefore our answer is B

(Had we obtained a lower product than required, we could have said that n must be 51. Had we obtained a higher product than was required, we could have said that n is 47.)

Another method:

Use the concept of arithmetic mean and ballpark. The mean of numbers from 41 to 47 or 48 or 49… will be somewhere between 44 and 46.

Let’s estimate the number of integers we need to get the sum of about 356. Each additional integer is quite large (more than 45) therefore, a difference of about 10-15 in the sum due to the various possible values of the mean will be immaterial.

45*7 = 315

45*8 = 360

This brings us very close to the value of 356.

Assuming there are 8 integers, their values will be from 41 to 48. The average of these 8 numbers will be 44.5. The total sum will be 44.5 * 8 = 356. It matches, so our answer is still B.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on FacebookYouTube 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: What To Do When The GMAT Gets All Netflix On You

GMAT Tip of the WeekPicture this: a friend texts you and asks, “Do you want to get a pizza and watch a movie after work?”. Do you find that odd at all?

But now picture this: that same friend asks, instead, “Do you want to get a pepperoni, mushroom and olive pizza with white sauce on thin crust from Domino’s and watch a Critically-Acclaimed Inspiring Underdog movie on Neflix after work?”. That’s strange, right? And why is that? Because it’s so specific.

Well, on the GMAT you’ll often see questions that ask for something oddly specific; “What is the value of x?” is pretty normal, but “What is the value of 6x – y?” is the equivalent of the specific pizza and odd Netflix category question. Why did they ask that? Often that’s a clue, and if you notice that clue it will help you better set up the problem. Consider this example:

Specific Question

 

 

 

 

Reflect on what this question is asking about. Not x. Not y. But to paraphrase Netflix, “a partially coefficiented combination of additive variables with a strong horizontal lead.” 6x – y. That’s oddly specific, so your first inclination should be, “Is there an easy way to get 6x – y?” as opposed to, “Let’s start solving for x” (which of course you can’t do here…that’s why E is a trap answer choice).

With that in mind, even if you’ve forgotten (or temporarily blanked on) some exponent rules, you should immediately be thinking, “I have 2x – how does that become 6x,” and, “Where does the subtraction come from?”.

The 6x, of course, comes from breaking 27 down into 3^3, so that you have (3^3)^2x, which then becomes 3^6x. And then with that, you have a fraction:

Exponent

 

 

 

And that’s where the subtraction comes from. When you divide two exponents of the same base, you subtract the exponents, so now you have your 6x – y ready to go. Of course, from there, you need to get a base of 3 on the other side of the equation, so you can express 81 as 3^4, and now you know that 6x – y = 4, answer choice B.

Most importantly here, when the GMAT asks you an oddly-specific question in the vein of the oddly-specific Netflix category, you should seize on that specificity. Very frequently on the GMAT, it’s easier to solve for that oddly-specific combination of variables than it is to solve for any of the individual variables themselves!

On Problem Solving questions this can save you plenty of time, taking that extra few seconds to ask yourself how you’d arrive at that specific combination. On Data Sufficiency, this practice can be even more a matter of correct or incorrect. Data Sufficiency problems often give you sufficient information to arrive at the oddly-specific combination from the question stem, but insufficient information to determine any of the individual components. Imagine this problem as a Data Sufficiency problem:

Data Sufficiency 1

 

 

 

 

Here, as you know from above, Statement 1 is sufficient, but if you go into the problem trying to solve for the variables individually, you’ll likely think that you need Statement 2 so that you can plug the value of y back into Statement 1 to supply the value of x. That way you’ll have the entire picture filled in: x = 1, y = 2, and 6x – y = 4.

But you don’t NEED Statement 2, so on a question like this the GMAT will punish you for not seeing that Statement 1 alone is sufficient. And it’s only sufficient because of that oddly-specific question stem. Check out this follow-up question (with a similar setup, but variables changed to a and b since the actual numbers will change):

Data Sufficiency 2

 

 

 

 

Here you cannot use Statement 1 to get directly to the oddly-specific question stem. You can get to 4a – b = 4, but that doesn’t tell you about 6a – b. So here, the answer is C because you need Statement 2 so that you can solve for each variable individually.

More often than not, when the GMAT asks for an oddly-specific combination of variables it provides a way to arrive at it. So pay attention to the question itself: if it’s asking for something out of the ordinary or oddly specific, see that as a thinly-veiled clue that allows you to be the Confident GMAT Problem Solver With Excellent Think Like The Testmaker Skills En Route To A 700+ that you know you can be.

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

By Brian Galvin.

Read the Last Piece First on the GMAT!

Make Studying FunWhen I was in grad school, I had a writing teacher who insisted on reading the last page of a novel before she read the first. Her reasoning was that she was starting a kind of journey, and she was curious to know where she’d be going before she could decide whether she wished to embark. Now, as a devoted reader, I couldn’t find this strategy more abhorrent. Uncertainty and mystery are integral parts of the pleasure of reading fiction. Why ruin it?

However, when it comes to the GMAT, I am quite content to ruin the suspense of a question in favor of deriving a more convenient and efficient means of solving it. Interestingly, it turns out that when a question offers multiple bits of information, starting with the last piece can often be a way of dramatically simplifying the problem.

Take the following problem that a tutoring student of mine encountered on her GMATPrep test:

Mary’s income is 60 percent more than Tim’s income, and Tim’s income is 40% less than Juan’s income. What percent of Juan’s income is Mary’s income?

A) 124%

B) 120%

C) 96%

D) 80%

E) 64%

She approached the question like many test-takers would: she started with the first piece of information, and called Mary’s income $100. And then she got stuck. She realized that Tim’s income isn’t $40 here, as $100 is more than double $40, so clearly Mary’s income would not then be 60% greater than Tim’s (though Tim’s would have been 60% less than Mary’s.) So then, I suggested, why not start at the end?

The last person mentioned here is Juan, so let’s call Juan’s income $100. She then knocked out the remaining calculations in about 30 seconds. If Juan’s income is $100, and Tim’s income is 40% less than Juan’s, than Tim’s income would be $60. And if Tim’s income is $60, and Mary’s income is 60% more than Tim’s, Mary’s income would be 60 + 60% of 60 = 60 + 36 = 96. (Or 1.6 * 60 = 96.) If Mary’s income is $96 and Juan’s is $100, then clearly, Mary’s income is 96% of Juan’s, and the answer is C. Not bad.

Let’s try it again on another question:

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5000 have been vaccinated against both, how many have been vaccinated only against rubella?

A) 2500

B) 7500

C) 10000

D) 15000

E) 17500

First, note that this is a classic overlapping sets questions, so let’s set up a simple matrix:

DG Graph 1

 

 

 

 

 

But now, let’s start by inserting the last piece of information we’re given. 5000 have been vaccinated against both, so that goes in the Mumps/Rubella Vaccine cell. Now we’ve got:

DG Graph 2

 

 

 

 

 

Next, we’ll work backwards. We’re told that the number that have been vaccinated against both (5000) is twice the number that have been vaccinated against only mumps. So the number that have been vaccinated against only mumps must be 2500. Now our table looks like this:

DG Graph 3

 

 

 

 

 

Now we know that 7500 people have been vaccinated against Mumps. Last, we’re told that the number vaccinated against Rubella is twice the number that have been vaccinated against Mumps, which means that 15,000 people have been vaccinated against Rubella. If 15,000 total have been vaccinated against Rubella, and 5000 of those have been vaccinated against both, then, according to our table, 10,000 have been vaccinated against only Rubella. So C is our answer.


DG Graph 4

 

 

 

 

 

Takeaway: The GMAT question writer is going to provide information to you in a very strategic way. If the most useful piece of info comes at the end of a lengthier question, the question will be harder if you start at the beginning. So be like my zany grad school teacher and start at the end. It may ruin the suspense, but as a consolation, you’re more likely to get the question right, and I’m guessing that’s a trade-off most of us are more than happy to make.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

How Understanding Sampling Can Help You Conquer the GMAT

Quarter Wit, Quarter WisdomToday, we will discuss the concept of sampling. People with a statistics background will be very comfortable with it, but if you have not studied statistics, a little bit of knowledge will be helpful. You are not required to know this for the GMAT, however there could be questions framed on the sampling premise, and you will be far more comfortable solving them with some understanding in place. A sample is a selection made from a larger group (the “population”) which helps you examine certain characteristics of the larger group using limited resources.

For example:

In a large population, say all the people in a state, it is difficult to find the number of people with a certain trait, such as red hair. So you pick up 100 people at random (from different families, different areas, different backgrounds) and find the number of people who have red hair in this selection of 100.

Let’s say 12 have red hair. You can then generalize that approximately 12% of the whole population has red hair. The more unbiased your sample, the better the approximation.

In this example, you found something about the entire population (12% has red hair) based on a small sample and hence, using few resources. To find the actual percentage of people who have red hair in the entire population, you would need far more effort, time and money. Usually the use of fewer resources justifies the use of sampling even though it comes with some error.

So that is a bit of background on sampling. It will help you make sense of the  official question given below:

In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?

A) 400

B) 625

C) 1,250

D) 2,500

E) 10,000

This is what took place: From a pond, 50 fish were caught, tagged and returned to the pond. Then 50 were caught again and 2 of those were found to be tagged.

Why was this done?

The total number of fish in the pond is the population of the pond. It is unknown. Since counting the total number of fish in the pond was hard, they tagged 50 of them and let them disperse evenly in the population. This means they gave a certain trait to a known number of fish in the pond – they tagged 50 fish.

Then they caught 50 fish again and these fish became the sample. Out of these 50, 2 were found to be tagged. So 2 of the 50 fish caught were found to have the trait given (tagged) – 4% of our sample was tagged.

The question tells us that “… the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond …” that is, the question tells us that the sample is representative of the population. This implies that 50 (the number of fish we tagged) is 4% of the entire fish population of the pond.

50 = 4% of Total Fish Population, therefore, we can calculate that the Total Fish Population = 50 * 100/4 = 1250. Our answer is then C.

Using sampling, we were able to calculate the total population of the pond without actually counting each fish. For increased accuracy, often the exercise of taking samples is repeated many times and then some kind of average is used to get the best approximation.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on FacebookYouTube 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!

How to Solve Probability Problems on the GMAT

Roll the DiceAt some point in every class I teach, I’ll take a poll from my students about which topics they struggle with most. The answers will vary, but one topic that comes up over and over again is probability. Though I do recall finding probability somewhat vexing when I studied it as an undergraduate, I’ve always found it surprising that this is such an area of concern for GMAT test-takers, for the simple reason that probability questions, historically, have tended not to be very common on the test.

I suspect there are two reasons for the concern. First, is simply that the human brain isn’t naturally wired to do probability very well. Whereas many branches of mathematics are thousands of years old and have their roots in ancient civilizations, there was no working theory of probability until the 16th century.

This is pretty surprising. The ancient Greeks, for example, possessed the rudiments of integral calculus, but when it came to probability, they were clueless. Moreover, there is plenty of research demonstrating that, even now, well-educated adults struggle with probability even when the question touches on material within their field of expertise.

Secondly, GMAC seems to be realizing that probability is such an elastic concept that other question types can be incorporated into a probability question. Consequently, probability questions have been showing up a bit more frequently on some of the newer material released by GMAC. If we’re not wired to do probability very well, and these questions are showing up more frequently, some anxiety about the topic is inevitable.

The reason that probability can encompass other categories so easily is that the probability of an event occurring is, at heart, a simple ratio: the number of desired outcomes/the number of total possible outcomes. To simplify matters, it can be helpful to break this ratio into its component parts. First find the total possible number of outcomes. Then find the number of desired outcomes. When we think about the issue this way, it seems much more manageable. Take this newer official question, for example:

If an integer n to be chosen randomly between 1 and 96 inclusive, what is the probability that n(n+1)(n+2) is divisible by 8 ? 

A) 1/4 

B) 3/8

C) 1/2

D) 5/8

E) 3/4 

On the surface, this is a probability question, but because we’re talking about divisibility, it’s also testing our knowledge of number properties. So let’s start by thinking about our total possible outcomes. There are 96 numbers between 1 and 96 inclusive, so clearly, there are 96 total possible outcomes when we select a number at random. We have the denominator of our fraction.

Now we just have to figure out how many ways we can multiply three consecutive numbers, n(n+1)(n+2), to get a multiple of 8. Put another way, any multiple of 8, or 2^3, must contain three 2’s. One way this can happen is if the middle number, n+1, is odd, because every odd number must be sandwiched between a multiple of 2 and a multiple of 4.

If n+1 is 3, for example, you’d have 2*3*4, which is a multiple of 8. (We need three 2’s in all. The 2 gives us one, and the 4 donates the other 2’s.) If n+1 is 5, you’d have 4*5*6, which is also a multiple of 8. (The 4 donates two 2’s and the 6 donates one. So long as we have three 2’s, we have a multiple of 8.) Between 1 and 96, we’ve got 48 odd numbers.

The other way we can get a multiple of 8, when we multiply n(n+1)(n+2)  is if n + 1 is itself a multiple of 8. Clearly 7*8*9 will be a multiple of 8. As will 15*16*17. We can either count the multiples of 8 between 1 and 96, or we can use the trusty formula: [(High-Low)/Interval] + 1. The first multiple of 8 between 1 and 96 is 8. The largest is 96. And the interval will be 8. So we get [(96-8)/8] + 1 = 11 + 1 = 12 multiples of 8.

So we have two categories of desired outcomes: there are 48 ways that n+1 can be odd, and there are 12 ways that n+1 can be a multiple of 8, giving us a total of 48 + 12 = 60 desired outcomes.

We’re done! The number of desired outcomes/number of total possible outcomes is 60/96, which will reduce to 5/8. The correct answer is D.

Takeaway: There’s no reason to be intimidated by probability questions, particularly when we remember that a probability calculation can be viewed as a ratio of two numbers. If we break the problem into its constituent parts, the question is often revealed to be quite a bit easier than it seems at first glance, a realization that proves true for almost any challenging GMAT problem.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

Advanced Exponent Properties for the GMAT

Quarter Wit, Quarter WisdomToday, let’s discuss the relative placements of exponents on the number line.

We know what the graph of 2^x looks like:

 

 

 

 

Graph of 2^x

 

 

 

 

 

 

 

It shows that when x is positive, with increasing value of x, 2^x increases very quickly (look at the first quadrant), but we don’t know exactly how it increases.

It also shows that when x is negative, 2^x stays very close to 0. As x decreases, the value of 2^x decreases by a very small amount.

Now note the spacing of the powers of 2 on the number line:

Number line jpg

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

and so on…

2^1 = 2 * 2^0 = 2^0 + 2^0

2^2 = 2 * 2^1 = 2^1 + 2^1

2^3 = 2 * 2^2 = 2^2 + 2^2

2^4 = 2 * 2^3 = 2^3 + 2^3

So every power of 2 is equidistant from 0 and the next power. This means that a power of 2 would be much closer to 0 than the next higher powers. For example, 2^2 is at the same distance from 0 as it is from 2^3.

But 2^2 is much closer to 0 than it is to 2^4, 2^5 etc.

Let’s look at a question based on this concept. Most people find it a bit tough if they do not understand this concept:

Given that x = 2^b – (8^30 + 16^5), which of the following values for b yields the lowest value for |x|?

A) 35

B) 90

C) 91

D) 95

E) 105

We need the lowest value of |x|. We know that the smallest value any absolute value function can take is 0. So 2^b should be as close as possible to (8^30 + 16^5) to get the lowest value of |x|.

Let’s try to simplify:

(8^30 + 16^5)

= (2^3)^30 + (2^4)^5

= 2^90 + 2^20

Which value should b take such that 2^b is as close as possible to 2^90 + 2^20?

2^90 + 2^20 is obviously larger than 2^90. But is it closer to 2^90 or 2^91 or higher powers of 2?

Let’s use the concept we have learned today – let’s compare 2^90 + 2^20 with 2^90 and 2^91.

2^90 = 2^90 + 0

2^91 = 2^90 + 2^90

So now if we compare these two with 2^90 + 2^20, we need to know whether 2^20 is closer to 0 or closer to 2^90.

We already know that 2^20 is equidistant from 0 and 2^21, so obviously it will be much closer to 0 than it will be to 2^90.

Hence, 2^90 + 2^20 is much closer to 2^90 than it is to 2^91 or any other higher powers.

We should take the value 90 to minimize |x|, therefore the answer is B.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on FacebookYouTube 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!

5 Tips for Being Efficient with Data Sufficiency Problems

GoalsGMAT Data Sufficiency problems present test takers with several unique issues.  First, this type of problem has likely not been encountered before and thus, there is a learning curve for not only what the “rules” regarding such problems are, but also how to approach the various questions. Additionally, Data Sufficiency problems do not lend themselves to being solved through brute force – with Data Sufficiency questions you do not really need to answer the question in order to solve the problem.

Data Sufficiency questions are inherently more difficult than Problem Solving questions because they are more conceptual in nature.  Take for example the following problem:

Is xy > 0?

1) x < 6

2) 0 ≤ y < x

Right off the bat, we see that there are 2 variables, so to answer the question we need to know the values of x and y.  However, this problem is better viewed conceptually – instead of  determining the actual values of x and y, if we recognize that this problem is really testing us on the Properties of Numbers, we realize that what is actually being asked is if x and y are either both positive or both negative. Once we re-phrase the question this way, the problem is much easier to deal with.  Statement 1 says that x is less than 6, but this does not tell us definitively whether x is positive or negative. Nor, does Statement 1 give us any information about y.  Thus, Statement 1 is not sufficient.

Statement 2 gives us information about both x and y.  We now know that y is less than or equal to 0, and x is greater than y. This looks promising.  But, since y could be 0 (or greater than 0), we cannot say that xy is greater than 0.  Statement 2 is not sufficient.  Taking both Statements together provides no more information about y, so we still cannot answer the question (although some might be tempted to overlook the less than or equal to portion).

Here are some tips to efficiently and strategically approach these unique problems:

  • Memorize the answer choices! They are the same for every Data Sufficiency question on the GMAT, so you can save valuable time by knowing them and knowing that if Statement 1 is sufficient, your answer choices are either A or D.
  • Before reading the statements, try to verbalize what information you need to answer the question. This will help you to determine whether the statements provide the information you need.
  • Leverage as much information as you can from the prompt. Often times, important information is included in the prompt but not readily apparent.
  • Be very wary of statements that provide information that blatantly and obviously answers the question. If a question asks what the value of x is and one statement tells you x = 6, take a very close look at the other statement. Many times, the other statement will contain information that is difficult to decipher and the test makers are baiting you to select the obvious answer and move on.
  • Be on the lookout for statements that give no new information. The circumference of a circle, for instance, contains just as much information as the length of the radius. If you know the circumference, you can find the radius; conversely, if you know the radius, you can find the circumference. Often on Data Sufficiency questions, Statement 2 will just be a repackaging of the same information provided by Statement 1.

Even though GMAT Data Sufficiency problems require some different thinking, with some strategic practice, you will master them. Start with becoming familiar with the structure of the questions and the concepts they most commonly test.

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

By Dennis Cashion, a Veritas Prep instructor based in Denver.

The GMAT Quant Decimal Trend You NEED to Know

Pi to the 36th digitWhenever GMAC releases new material, I’m always on the lookout for conspicuous trends – esoteric or little known rules that end up being applicable in multiple questions. One type of question that has recently shown up with greater frequency involves terminating decimals. The concept isn’t, in the abstract, a terribly hard one. ½, for example, is .5, and so this is a terminating decimal. It ends. 1/3, on the other hand is .33333…, and continues indefinitely, so it’s not a terminating decimal. That’s not so hard. So, you say to yourself: all I have to do is perform a little division, and then I can see for myself if the decimal terminates or not, right?

But then you see a question like this:

Which of the following fractions has a decimal equivalent that is a terminating decimal?

A) 10/189

B) 15/196

C) 16/225

D) 25/144

E) 39/128

Once you spend a little time trying to divide 10 by 189, you realize that the question is going to be incredibly painful and time-consuming if you have to keep applying this approach until you find a fraction that results in a terminating decimal. So let’s be mindful of the fact that the purpose of the GMAT is not to test one’s facility for engaging in tedious arithmetic, but rather to assess our ability to recognize patterns under pressure.

Generally speaking, the best way to uncover a pattern is to use simple numbers first and then extrapolate our results to the more complex scenario we’re tasked with evaluating. We already established above that ½ is a terminating decimal and 1/3 is not. Let’s continue in that vein and see what we find (terminating decimals are in bold):

½ = .5

1/3 = .3333…

¼ = .25

1/5 = .2

1/6 = .166666…

1/7= .142857…

1/8 = .125

1/9 = .1111

1/10 = .1

Next, let’s examine our terminating decimal expressions and see if these numbers have any elements in common. Each of these fractions, it turns out, has a denominator whose prime factorization is composed solely of two prime bases, 2 or 5 or both. This turns out to be a general principle: if a fraction has been simplified, and the prime factorization of the denominator can be expressed in the form of 2^x * 5^y where x and y are non-negative integers, the fraction can be expressed as a terminating decimal.

Now back to our question. We can rephrase the question to be, “Which of the following denominators has a prime factorization that consists solely of 2’s or 5’s or both?”

Not bad. That certainly makes life a little easier. But before we dive in and begin taking prime factorizations with reckless abandon, let’s think like the test-maker. There is no way to do this question without working with the answer choices. Most test-takers will begin with A and work their way down. If you’re trying to create a difficult time-consuming question, where would you bury the correct answer? Probably towards D or E. So when we encounter this kind of scenario, we’re better off if we start at the bottom and work our way up.

E) 39/128. The denominator is 128, which has a prime factorization of 2^7. Because the denominator consists solely of 2’s, this fraction, when expressed as a decimal, must terminate. We’re done. E is the answer. (Intuitively, this makes sense, as all we’re really doing is cutting our numerator in half seven times.) Much easier than doing long division.

Before we commit this principle to memory, let’s make sure that it will be helpful in other contexts. After all, the rule that unlocks a single question won’t be terribly useful to us. So here is the same concept utilized in a Data Sufficiency question:

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal? 

(1) 90 < r < 100 

(2) s = 4 

Notice how much easier this question is if we rephrase it as “if r/s is in its most simplified form, does the prime factorization of the denominator consist entirely of 2’s or 5’s?”

Statement 1 can’t be sufficient on its own, as it tells us nothing about the denominator. 91/2 is a terminating decimal, for example, but 91/3 is not.

Statement 2 tells us that the denominator is 4, or 2^2. If we’ve internalized our terminating decimal rule, we see right away that this must be sufficient, as anything dividing by 4 will result in a terminating decimal. The answer is B, Statement 2 alone is sufficient to answer the question.

Takeaway: When studying for the GMAT, it can feel as though there are an infinite number of rules, axioms, and formulas to memorize. Our job, when preparing, is to find the rules that are applicable in multiple contexts and internalize those. If we encounter a problem that seems unusually time-consuming, and no rule springs to mind, we can derive the necessary pattern on the spot by working with simple numbers.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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

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

GMAT Tip of the Week: Yogi Berra Teaches GMAT Sentence Correction

GMAT Tip of the WeekThe world lost a legend this week with the passing of Yogi Berra, a New York Yankee and World War II hero. Yogi was universally famous – his name was, of course, the inspiration for beloved cartoon character Yogi Bear’s – but to paraphrase the man himself, those who knew him didn’t really know him.

As news of his passing turned into news reports summarizing his life, many were stunned by just how illustrious his career was: 18 All-Star game appearances (in 19 pro seasons), 10 World Series championships as a player, 3 American League MVP awards, part of the Normandy campaign on D-Day… To much of the world, he was “the quote guy” who also had been a really good baseball player. His wordsmithery is what we all remembered:

  • Never answer an anonymous letter.
  • It ain’t over ’til it’s over.
  • It gets late early out here.
  • Pair up in threes.

And his command (or butchering) of the English language is what you should remember as you take the GMAT. Yogi Berra famously “didn’t say some of the things I said” but he did, however inadvertently, have a lot to say about GMAT Sentence Correction:

Pronouns Matter

What’s funny about his quote, “Always go to other people’s funerals, otherwise they won’t come to yours”?

It’s the pronoun “they.” You know what Yogi means – go to other people’s funerals so that other people will come to yours. But in that sentence, the logical referent for “they” is “other people(‘s)”, and those other people have already been designated in the sentence as people who have already died. So the meaning is illogical: those same people cannot logically attend a funeral in the future. When you use a pronoun, it has to refer back to a specific noun. If that noun cannot logically do what the pronoun is said to be doing, that’s a Sentence Correction, illogical meaning problem.

What’s funny about his quote, “When you come to a fork in the road, take it”?

Again, it’s the pronoun, this time “it.” Since a fork in the road is a place where the road diverges into two paths, you can’t take “it” – you have to pick one path. And this is a good example of another sentence correction theme. In order to fix this thought (and the one above), there’s really not a pronoun that will work. “Them” has no logical referent (there’s only one fork) so the meaning is extremely important.

The only way to fix it is to change something prior in the sentence. Perhaps, “When you come to a turnoff on the road, take it,” or, “when the road presents a turn, take it.” On the GMAT, a pronoun error isn’t always fixed by fixing the pronoun – often the correct answer will change the logic that precedes the pronoun so that in the correct answer the previously-incorrect pronoun is correct.

Modifiers Matter

What’s funny about his quote, “Congratulations. I knew the record would stand until it was broken”?

Of course records stand until they’re broken, but in a grammatical sense Yogi’s primary mistake was his placement of the modifier “until it was broken.” What he likely meant to say is, “Until the record was broken, I thought it might stand forever.” That’s a perfectly logical thought, but we all laugh at the statement he actually made because the placement of the modifier creates a laughable meaning. So learn to spot similarly-misplaced modifiers by checking to make sure the language means exactly what it should.

Redundancy Is Funny (but sometimes has its place)

What’s funny about, “We made too many wrong mistakes,” and “It’s like déjà vu all over again”?

They’re redundant. A mistake is, by nature, something that went wrong. And déjà vu is the feeling that something happened before, so of course it’s “all over again.” Redundancy does come up on the GMAT, but as Yogi himself would point out, there’s a fine line between “redundant (and wrong)” and “a useful literary device”.

Take, for example, his famed, “It ain’t over ’til it’s over” quote. In a sports context, even though the word “over” is repeated, that sentence carries a lot of useful meaning: “when someone might say that the game is over, if there is still time (or outs) remaining there’s always a chance to change the result.” The world chuckles at this particular Yogi quote, but in actuality it’s arguably his most famous because, in its own way, it’s quite poignant.

What does that mean for you on the GMAT? Don’t prioritize redundancy as a primary decision point! GMAT Sentence Correction, by nature, involves plenty of different literary devices and sentence structures, and it’s extremely unlikely that you’ll feel like an expert on all of them.

Students often eliminate correct answers because they perceive redundancy, but a phrase like “not unlike” (a “not” next to an “un-“? That’s a redundant double-negative!) actually has a logical and important meaning (“not unlike” means “it’s not totally different from…there are at least some similarities,” whereas “like” conveys significantly more similarity). Rules for modifiers and pronouns are much more absolute, and you can get plenty of practice with those. Be careful with redundancy because, as Yogi might say, sometimes saying it twice is twice as good as saying it once.

It’s all in your head.

“Baseball is ninety percent mental and the other half is physical.”

To paraphrase the great Yogi Berra, 90% of Sentence Correction is mental and the other half is grammatical. When he talked about baseball, he was talking about the physical tools – the ability to hit, run, throw, catch –  as meaning substantially less than people thought, but the mental part of the game – strategy, mental toughness, stamina, etc. – being more important than people thought. The exact percentages, as his quote so ineloquently suggests, are harder to pin down and less important than the takeaway.

So heed Yogi’s advice as it pertains to Sentence Correction. Memorizing and knowing hundreds of grammar rules is “the other half” (or maybe 10%) of the game – employing good strategy (prioritizing primary Decision Points, paying attention to logical meaning, etc.) is the more-important-but-often-overlooked part of success. However eloquently or inelegantly Yogi Berra may have articulated his lessons, at least he made them memorable.

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

By Brian Galvin.

6 Simple Steps to Attack Critical Reasoning Questions on the GMAT

GMAT ReasoningThe first step in attacking any Critical Reasoning question on the GMAT is to identify the premises and conclusions of the argument being presented. While Strengthen, Weaken, Assumption and Resolve the Paradox questions include a conclusion in the stimulus, Inference questions require you to select the conclusion (answer choice) that directly follows from the information presented in the stimulus.

This can be difficult because several of the answers can appear attractive. Keep in mind, however, that for Inference questions, the correct answer must be true. Answers that are “likely to be true” or “could be true” based on the information provided in the stimulus seem attractive at first, but if they are not true 100% of the time, in every situation, then they are not the correct answer.

Another difficulty in approaching Inference questions is that with the many of the other question types (Strengthen, Weaken, etc.), your job is to select the answer that includes new information that either undermines or supports the conclusion. For Inference questions, you do not want to bring in information that is not in the stimulus. All of the information required to answer the question will be included in the stimulus.

Here is a 6-step approach that can help you to efficiently attack GMAT Critical Reasoning Inference questions:

1) Read the question stem first.

This will allow you quickly categorize the type of Critical Reasoning question (Strengthen, Weaken, Inference, etc.) and let you focus on identifying the premises in the stimulus. Questions such as, “Which of the following can be correctly inferred from the statements above?” and, “If the statements above are true, which of the following must also be true?” signify that you are dealing with an Inference question.

2) Speculate what you think the correct conclusion is.

Sometimes this may be difficult to verbalize, but having an outline or framework of what the “must be true” answer should include will help to eliminate some answer choices.

3) Evaluate the answer choices using your speculated answer.

You want to carefully read all 5 answer choices. As you read the answers, compare them to the answer, or the outline of the answer, you speculated. Some answers are obviously incorrect – either they are too narrow in scope, too extreme to be always be true, or do not follow the criteria laid out in the stimulus. Eliminate these answers. For other answer choices that seem attractive, keep them as possibilities. Once you have read all of the answer choices, you can then compare your list of possible answers using the criteria that the correct answer must be always be true.

4) Become a Defense Lawyer.

When comparing your list of possible answers, try to come up with plausible scenarios that would prove the answer being considered not true. Just because the stimulus says that “everyone sitting in the dentist’s office waiting room at 9:00 a.m. was a patient” does not necessarily mean that they were waiting for an appointment. Some could have already finished their appointment, and some could have been there dropping off another patient. Like a defense lawyer, you need to find every every scenario in which an answer choice might not be true in order to eliminate it from your options.

5) Be aware of exaggerated or extreme answers.

Because the correct answer must always be true, modifiers that exaggerate an element of the premise or make an extreme claim usually signify an incorrect answer. If the stimulus says, “Some of the widgets produced by Company X were defective,” an attractive, yet incorrect answer choice may exaggerate this statement with a modifier such as “most” by claiming, “Most of Company X’s widgets were found to be defective.” Furthermore, answers that include the terms “always”, “never”, “none” and the like are good indicators that the answer will not be true 100% of the time.

6) Be aware of answers that change the scope of the stimulus.

On more difficult Inference questions (as if they were not difficult enough), the test makers will tempt you to select an answer choice that slightly changes an element of the facts laid out in the stimulus. For example, the stimulus might discuss the decrease in the violent crime rate in City A over a certain time period.

The attractive answer that follows all of the elements of having to be true 100% of the time, but is still incorrect might discuss decrease in the murder rate of City A over that time period. While the answer would seem to fit the bill, the murder rate is not the same as the rate of violent crime – this changes the scope of the initial stimulus and we can therefore rule that answer out.

The correct inference or conclusion on Critical Reasoning Inference questions is very close to what is stated explicitly in the stimulus. Remember, the right answer choice on these question types must be true 100% of the time.

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

By Dennis Cashion, a Veritas Prep instructor based in Denver.

How to Use the Answer Choices to Solve GMAT Quant Problems

EssayIn your approach to solving Quantitative problems on the GMAT, do not forget that the answers are part of the problem and often provide valuable information.

Take for example, the following question:

 

 

 

If 3x4y = 177,147 and x – y = 11, then x =?

A) Undefined

B) 0

C) 11

D) 177,136

E) 177,158

Where do we begin here? 177,147 is a large (not familiar) number and there are not one, but two exponents in the equation.  Looking at the answer choices, we can see that D and E cannot be the answer as they are too large, so at least now we have a starting point.  Additionally, we can see that our choices come down to some mixture of x and y, all y, or all x.

If x = 0, then we can say that 177, 147 is not divisible by 3 and is divisible by 4, so checking the divisibility rule is the ticket! Knowing that to be divisible by 4, the last two digits must be divisible by 4, we can see that 177,147 is not divisible by 4, so 4y becomes irrelevant and we realize y must equal 0.  The sum of the digits of 177, 147 is 27, which is divisible by 3, so we can see that the 3portion of the equation is relevant. We can now (correctly) conclude that the correct answer is answer choice C, x = 11.

Answer choices are little used resources by GMAT test takers.  In the heat of battle, we become so focused on solving the problems in front of us that we forget to utilize all of the information at our disposal.  Another way the answer choices can help you is by plugging them back into the problem to see if they work.

This “back-plugging” is useful when the problem to be solved is algebraic in nature and the answer choices are numbers (not variables). You may find it is easier on a certain problem to arithmetically calculate 2, 3 or even 5 answers by plugging in the answer choices, than in creating and manipulating a complex algebraic equation.  In these cases, plugging in answer choice C first will help you to eliminate up to 60% of the answers on the first calculation.

Many times, just understanding what the correct answer should “look like” by employing some reasoning on the front end will allow you to eliminate some, if not all of the incorrect answers.  Consider this problem:

((-1.9)(o.6) – (2.6)(1.2))/6.0 = ?

A) -0.71

B) 1.00

C) 1.07

D) 1.71

E) 2.71

This is not a difficult problem by any measure, and some test takers will not hesitate to jump in and begin multiplying and dividing decimals.  However, by spending a little bit of time looking at the big picture of this problem, an astute test taker would see that the answer must be negative.  The first term is negative and we are subtracting a larger number from it.  Therefore, the correct answer must be A.

So, instead of jumping in and crunching numbers on the GMAT, you can save yourself some time and brain power by using the answer choices to assist you in reasoning your way to the correct answer – or at least in eliminating several of the incorrect answers.

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

By Dennis Cashion, a Veritas Prep instructor based in Denver.

99th GMAT Score or Bust! Lesson 9: Talk Like a Lawyer

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 99thpercentile with the proper techniques and preparation. In this “9 for 99th” video seriesRavi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

First, take a look at the previous lessons in this series: 1, 2, 3, 4, 5, 6, 7 and 8!

Lesson Nine: 

Talk Like a Lawyer. When you click “Agree” on a user contract (think iTunes) or read through a GMAT question, you may just see an overkill of words. But thanks to lawyers, every word on that user agreement is carefully chosen – and that GMAT question is written the same exact way. In this final “9 for 99th” video, Ravi (a member of the bar himself) shows you how to talk and read like a lawyer, noticing those subtle word choices that can make or break your answer to those carefully-written GMAT problems you see on test 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, YouTube 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

Beat the GMAT Verbal Section by Personalizing Questions

Integrated Reasoning GMATMy students often ask why the verbal section has to come at the very end of the GMAT. When they’re fresh, they complain, they’re able to answer a much higher percentage of questions correctly. Of course, this is precisely the point. Part of what the GMAT is assessing is your stamina and focus, both of which will certainly be flagging by the time you’ve been in the testing facility for over three hours.

Moreover, the questions themselves aren’t exactly known for their dazzling wit and soaring narrative verve. They’re boring. Reading Comp. passages are often tedious and technical, while Critical Reasoning arguments can feel so abstract as to be ungraspable. So how do we, as test-takers, combat this?

One answer, when it comes to those abstract Critical Reasoning questions, is to personalize the argument. I’ve blogged in the past about how our reading comprehension improves dramatically when we’re emotionally invested in what we’re reading, so why not attempt to trick ourselves into this state of heightened concentration?

If the CR question is about the impact of pesticide use on crop yields, I imagine I’m the farmer, and the well-being of my family is at stake. If the question is about how overtime pay will impact employee incentives, I imagine I own the business and that the consequence of my company’s compensation structure will impact not only me, but dozens of workers whose livelihood I’m responsible for. By creating these artificial stakes, I find that my brain is able to lock in on the minutia of the question in a way it can’t if the question is about some airy fictional farmer, whom I know exists only in the mind of some bureaucratic question writer.

Take an official question, for example:

In the past the country of Malvernia has relied heavily on imported oil. Malvernia recently implemented a program to convert heating systems from oil to natural gas. Malvernia currently produces more natural gas each year than it uses, and oil production in Malvernian oil fields is increasing at a steady pace. If these trends in fuel production and usage continue, therefore, Malvernian reliance on foreign sources for fuel is likely to decline soon. 

Which of the following would it be most useful to establish in evaluating the argument?

(A) When, if ever, will production of oil in Malvernia outstrip production of natural gas?

(B) Is Malvernia among the countries that rely most on imported oil?

(C) What proportion of Malvernia’s total energy needs is met by hydroelectric, solar, and nuclear power?

(D) Is the amount of oil used each year in Malvernia for generating electricity and fuel for transportation increasing?

(E) Have any existing oil-burning heating systems in Malvernia already been converted to natural-gas-burning heating systems?

If you’re anything like most test-takers, your eyes glaze over a bit. You know that Malvernia is not a real country, that it’s been invented for the sake of the problem. Consequently, the details of energy consumption in this non-existent country are not going to be terribly compelling to, well, anyone. This is by design. So let’s create some artificial stakes. Let’s say you’re the President of Malvernia. The economic well-being of your country, and, therefore, the prospects of your reelection, are going to be impacted by your country’s energy policy. Now let’s break down the facts:

  • Historically, you’ve relied on oil imports.
  • A new program converts heating systems from oil to gas.
  • You produce more gas than you use.
  • Oil production is increasing.

Based on this, you’ve concluded that your reliance on foreign oil will soon decrease. The question is what do you, as President, need to know to determine whether this prediction is valid?

Let’s break down each answer choice:

(A) The question of when production of oil will outstrip production of gas isn’t really relevant. In fact, if you’re using less oil as a result of the change in heating systems, and oil production is up, it’s possible that you can reduce your dependence on foreign oil without having to produce more oil than gas. A is out.

(B) Whether you are among the most dependent countries on foreign oil doesn’t matter. You are now, and we’re trying to determine if you will be in the future. This doesn’t help. Eliminate B.

(C) Hydroelectric, solar, and nuclear power aren’t relevant for this argument. We know that you’re dependent on foreign oil now, irrespective of other energy sources. It’s increased oil production and switching to gas that will, according to the argument, reduce this dependence. C is out of scope.

(D) Let’s say your oil consumption for electricity and transportation is increasing. Suddenly, the fact that you’re switching heating systems from oil to gas might not help – if your oil needs are going up in other areas, you may remain dependent on foreign oil. But if your oil consumption in these other areas is not increasing, that would reduce your dependence on foreign oil because your heating systems are switching to gas. D looks good.

(E) This doesn’t matter at all. We know that the systems are going to switch from oil to gas, so the question of whether some systems have already made the switch sheds no light on whether you will remain dependent on foreign oil.

D is the answer. Once you have the answer to whether your oil consumption for electricity and transportation is increasing, you’ll be better able to assess whether you will remain dependent on foreign oil, and, consequently, whether your reign as supreme ruler of Malvernia will continue.

Takeaway: There is plenty of research indicating that our comprehension improves drastically when we’re reading something we care about. When we put ourselves into the position of the agents having to make decisions in these arguments, we can transform a tedious abstraction into something that has a bit of emotional resonance, which will, in turn, result in a higher GMAT score.

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

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

3 Ways to Improve Brain Function for Better Studying

SATI recently read The Organized Mind by Daniel Levitin, a book teeming with insights about simple adjustments we can make in our daily routines to improve our productivity. I’ve written about this topic in the past, but it can’t be emphasized enough – the primary problem most test-takers encounter is that they struggle to find enough time to study consistently.

According to GMAC, test-takers who score 700 or above spend, on average, 114 hours preparing for the exam. There’s nothing magic about that number, but it does reveal that getting ready for the GMAT is an intensive ordeal. As technologies improve and our focus becomes increasingly fragmented by our proliferating gadgets, the challenge, whether we’re studying for the GMAT or trying to complete a project at work, is how we can be productive and still have enough time and energy to enjoy some semblance of a personal life.

1) Sleep

First, Levitin emphasizes the importance of sleep. When we’re feeling overwhelmed, our instinct is to work more and sleep less – we feel as though we need more waking hours to complete whatever tasks we have to perform. The problem with this approach is that sleep deprivation causes us to be significantly less effective and productive, so much so that the additional time we gain is more than offset by the diminished performance that results from a sleep-debt.

The statistics on the subject are nothing short of astonishing. According to economists, sleep deprivation costs U.S. businesses more than $150 billion dollars a year from accidents and lost productivity. It is also associated with increased risk for heart disease, obesity, suicide, and cancer. This is an easy fix.

Levitin recommends going to bed at the same time each night (preferably an hour earlier than you’re accustomed to) and waking at the same time each morning. If it isn’t possible to sleep more at night, a nap as short as 15 minutes can serve the same refreshing function. Napping has been shown to reduce our risk of developing a host of medical conditions, and the beneficial effects are so striking that many companies have designated nap rooms filled with cots.

2) Stop Multi-Tasking

Next, Levitin discusses the cognitive impact of multi-tasking. We all know that it isn’t a great idea to try to study while texting or answering emails, etc., but what’s striking is that the impact of allowing other activities to siphon our attention is actually quantifiable. Glenn Wilson, a British researcher from Gresham College, conducted a study in which he found that when participants were informed that they had an unread email in their inbox, their effective IQ decreased by 10 points. Moreover, he documented that the cognitive-blunting effects of multi-tasking are more pronounced than the effects of smoking marijuana.

Other studies have revealed that task-switching, in general, heightens the brain’s glucose demands and amplifies anxiety, and the resulting discomfort ratchets up the desire to find some kind of distraction, such as, checking email again. Experts recommend designating two or three blocks of time a day for responding to email, and beyond that, strictly forbidding yourself to check for new messages.

A more ingenious idea comes from Lawrence Lessig, a Harvard Law professor. Lessig recommends declaring email bankruptcy, which would involve composing an automatic reply that informs whoever has contacted you that if this email requires an immediate response, they should call you, and if not, they should resend the email in a week if they haven’t heard from you. This technique will allow you greater latitude in structuring your day in terms of when you respond to emails, and will, hopefully, negate the multi-tasking concerns that lead to the aforementioned IQ drop. And when you’re studying for the GMAT, have a strict policy of not checking your phone or opening a new browser window.

3) Don’t Procrastinate

Last, and perhaps most importantly, the book addresses the problem of procrastination. Procrastination is a universal problem and likely results from the basic architecture of the human brain, wired as it is to seek pleasure and avoid pain. Jake Eberts, a Harvard MBA and successful film producer, offers a bit of very simple but compelling advice: just get in the habit of always doing the most unpleasant thing on your agenda first. There is evidence that our willpower is gradually depleted throughout the day, so it’s best to tackle the most dreaded elements of our to-do list first thing in the morning.

Takeaway: Here are three very easy things you can do, starting today, if you’re having difficulty finding the time/energy to study:

1) First, sleep more. If that means a 15-minute midday nap, so be it – you will gain in productivity far more than you lose in time sacrificed.

2) Second, declare email bankruptcy and put away your phone. Multi-tasking produces a scientifically documented brain drain.

3) Last, do the most unpleasant thing first. Whether that unpleasant thing is 25 Data Sufficiency questions, or some work-related activity, your resilience will be greatest first thing in the morning, so that’s the time to tackle the task you want to do least.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

Min/Max Questions on the GMAT are a Piece of Cake (or Pie)!

Pie ChartWhen I was a child, dessert was serious business. If my family were having pie, that pie had to be evenly distributed among family members, or violence would ensue. Portion size was something we understood at a primal, instinctive level. A larger piece for my brother meant a smaller piece for me. If I wanted to be generous, I could cut myself a smaller piece, thus providing one of my fortunate brothers with a larger dessert share. Every child knows this. But somehow what a child knows intuitively about pie, an adult can forget when dealing with a GMAT question.

I’m talking specifically about min/max questions. For these problems, there are only two things we need to do. First, we need to determine the size of the pie. Then, if we’re trying to maximize one slice, we need to minimize the size of all the other slices and see what’s left over. Similarly, if we’re trying to minimize one slice, we need to maximize all the other slices. Let’s see this principle in action with an official question:

Five pieces of wood have an average length (arithmetic mean) of 124 centimeters and a median length of 140 centimeters. What is the maximum length, in centimeters, of the shortest piece of wood? 

A) 90 

B) 100 

C) 110 

D) 130 

E) 140

First, let’s determine the size of the pie. If the average is 124 centimeters, and there are five pieces of wood, we know that the total sum of all the pieces of wood would be 5*124 = 620. Let’s call the smallest piece, ’s.’ So far, we have the following:

s ___, 140, ___, ___

Next, we want to maximize the smallest piece. Think pie. If I want to maximize the size of one piece, in this case ‘s,’ I want to minimize the size of all the other slices. The minimum size for the second smallest slice is ‘s.’ (If it were any smaller, it would be the smallest slice.) The minimum size for our two larges slices is 140. (If those were any smaller, the median would change.)

Now, we’re left with the following set:

s, s, 140, 140, 140.

Well, we already know that the sum is 620, so now we have the following equation:

s + s + 140 + 140 + 140 = 620.

2s + 420 = 620

2s = 200

s = 100. The answer is B.

Let’s try a tougher one:

For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.

There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?

A) 0

B) 1

C) 2

D) 3

E) 4

We know it’s a min/max question, so first we need to determine the size of the pie. We’re told that a team will earn 6 – n points whenever one of its members finishes in nth place. The team that has the first place finisher (n = 1) will earn 6 – 1 = 5 points. The second place finisher (n =2) will earn 6 – 2 = 4 points. The trend quickly becomes clear:

First place: 5 points

Second place: 4 points

Third place: 3 points

Fourth place: 2 points

Fifth place: 1 point

One of the conditions of the problem is that ‘n’ cannot be any larger than 5, so at this point, there are no more points to earn. Summing all the available points, we get 1 + 2 + 3 + 4 + 5 = 15. So there are 15 points total for the three teams to divvy up.

Now we’re trying to minimize the number of points one team earned. What did we do in the Goldstein household when we were feeling particularly sadistic and wished to stick my youngest brother with the smallest possible piece of pie? We’d maximize the size of all the other pieces, leaving the youngest, most vulnerable Goldstein with a sad pile of unpalatable mush. Let’s do the same here.

We’re told that no team scored more than 6 points, so 6 is the max number of points a team could have earned. If two teams earned the max – 6 points – they’d have earned 12 points between them. If there are 15 points total, and two of the teams earn a total of 12 points, that leaves 3 points for the stragglers. D is the answer.

Takeaway: As soon as you see a min/max term such as “least,” “most,” “minimum,” “or “maximum,” you’ll be well-served to summon some traumatic memories of divvying up your favorite childhood dessert.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

Know the Concept of Cost Price for the GMAT

Quarter Wit, Quarter WisdomMost of us are quite comfortable with the concepts of percentages, cost price and sale price, but when we come across a toughie from these topics, we feel lost. Then we go back to the theory but there seems to be nothing new there – nothing new that could potentially help us tackle such questions with ease in the future. The point is, the basic theory of these topics is quite simple – there isn’t anything else to it – but it’s application to GMAT questions is an altogether different deal. There are small but critical things that you need to keep in mind, one of which we will discuss today: what is the cost price?

Let’s take a look at this with an official question:

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer’s initial cost. What was the dealer’s approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?

(A) 7% loss

(B) 13% loss

(C) 7% profit

(D) 13% profit

(E) 14% profit

Solution:

Here are the various data points:

  • 60 cameras bought at 20% markup.
  • Selling Price = $250
  • 6 not sold and 50% of initial cost refunded
  • Profit/Loss = ?

Now look at the solution:

The cost price per camera = 250/1.2 = 1250/6

The total cost price = (1250/6)*60 = $12,500

50% of the cost of 6 cameras was returned.

The cost price of 6 cameras = (1250/6)*6 = $1250

50% of this = 1250/2 = $625

This means the effective cost price = 12,500 – 625 = $11,875

If the selling price per camera = $250, the total selling price = 54 * 250 = $13500 (only 54 cameras were sold)

Hence, the profit % = [(13500 – 11875) / 11875] x 100 = (1625/11875) x 100 = 13.684%

This gives us approximately 14% as the answer (rounding up). But that is not correct. Before you move ahead, try to figure out the problem with this solution. If you are able to, it means you do understand this topic very well.

Here is the problem with the solution:

The cost price is the total initial cost price. You cannot subtract the refund out of it. The refund is effectively the price at which the 6 cameras were sold. You cannot cancel off your cost price with your sale price and have a smaller cost price. Your initial investment in the transaction is your cost price. When you reduce it by cancelling off some sale price (or refund), you are artificially increasing your profit percentage.

Say, we buy a few thing for $100. While selling them off, we get $50 for half of them. We reduce our cost price by $50 and get $50 as cost price. For the other half, we sell them for $60. We say that $50 is out cost price and $60 is our selling price. The profit we made is $10, which is fine. The issue is that our profit percentage is not (10/50) * 100 = 20%. Rather, our profit percentage will be (10/100) * 100 = 10% only, so $100 would be our actual cost price.

Keeping this in mind, here is the correct algebra solution:

The total cost price = (1250/6)*60 = $12,500

The total selling price = 54 * 250 + $625 = $13,500 + $625 = $14,125 (60 cameras were sold, 54 at $250 each and 6 at 50% of cost price)

The profit = 14,125 – 12,500 = $1625 (same as before)

The profit percentage = (1625/12,500) * 100 = 13%

Therefore, the answer is (D).

Obviously, we can always use our trusted weighted averages formula here for a quick and efficient solution:

Weighted Averages

On 54 cameras, the dealer made a 20% profit and on 6 cameras, he made a 50% loss. The ratio of the cost price of 54 cameras:cost price of 6 cameras = 54:6 = 9:1

Average Profit/Loss percentage = (.2*9 + (-.5)*1)/10 = 1.3/10 = .13 = 13% profit.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube 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!

99th Percentile GMAT Score or Bust! Lesson 8: Reading is FUNdamental

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 lessons 1, 2, 3, 4, 5, 6 and 7!

Lesson Eight:

Reading is FUNdamental:  If you can read this video prompt, there are several GMAT quantitative problems that you should answer correctly…but might not on test day.  As Ravi notes in this video, often students supply incorrect answers to quantitative problems not because they can’t do the math, but because in doing the math they take their attention off of reading the question carefully.  So heed Ravi’s advice: if you’re going to get a math problem wrong, get it wrong because you can’t do the math, not because you can’t read.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube 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

Strategies for the New GMAT Questions that You Need to Know!

MBA Interview QuestionsAbout a month ago, GMAC released the latest version of the GMAT Official Guide, 25% of which consisted of new questions. Though the GMAT tends not to change too drastically over time – how else could a school compare a score received by one candidate in 2015 to a score received by another candidate in 2010? – there can be subtle shifts of emphasis, and paying attention to the composition mix of the questions in the latest version of the Official Guide is a good way to ascertain if any such shift is in the offing.

My concern as an instructor is whether the philosophy I’m advocating and the techniques I’m teaching are as relevant for the newer questions as they have been for the older ones.

This philosophy can be summarized as follows: the GMAT is not, fundamentally, a content-based test, but rather, uses certain elements of our academic background to test how we think under pressure. Because the test is evaluating how we think, and not what we know, the cultivation of simple strategies, such as using the answer choices or picking easy numbers, is just as important as the re-mastery of the content you may have initially learned in eighth grade, but have subsequently forgotten.

Having thoroughly dissected the new questions in the latest version of the Official Guide, I can confidently report that this philosophy is more relevant than ever. Of the over 200 new quantitative questions, I didn’t do extensive calculations for a single problem. If anything, the kind of fluid logic-based approach that we preach at Veritas is more critical than ever.

Take this new question, for example:

Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich? 

A) (m+4)/[m(m-4)]
B) (2m-4)/[m(m-4)]
C) (4m-4)/[m(m-4)]
D) (4m-8)/[m(m-4)]
E) (4m-12)/[m(m-4)]

Of course, we could do this question algebraically. But if the GMAT is testing our ability to make good decisions under pressure, and if the algebra feels hard for you, then a better option is to make your life as easy as possible and select a simple number for m. If m is larger than 4, let’s say that m = 5. “m” represents the number of students, so now we have 5 students and, we’re told in the question stem, a total of 4 sandwiches. (The question of what kind of negligent, hard-hearted school knowingly packs only 4 sandwiches for all of its students to share will have to be addressed in another post. This question feels straight out of Oliver Twist.)

Okay. We’re told that 3 of the sandwiches are divided evenly among the 5 students. (3 sandwiches)/(5 students) means each student gets 3/5 of a sandwich.

Additionally, we’re told that 4 of the students don’t want any part of the remaining sandwich. Because we only have 5 students and 4 of them don’t want the remaining sandwich, the last student will get the entire fourth sandwich.

To summarize what we have so far: Each of the 5 students initially received 3/5 of a sandwich, and then one student received an entire additional sandwich, on top of that initial 3/5. The lucky fifth student received a total of 3/5 + 1 = 8/5 of a sandwich.

Last, we ‘re told that Carol ate a piece of each of the four sandwiches. But we established that only one student ate a piece of every sandwich, so Carol has to be that lucky student! Therefore, Carol ate 8/5 of a sandwich.

We’re asked what fraction of a sandwich Carol ate, so the answer is simply 8/5. Now all we have to do is plug ‘5’ in place of ‘m’ in each answer choice, and the one that gives us 8/5 will be our answer.

Most test-takers will simply start with A and work their way down until they find an option that works. The question-writer knows that this is how most test-takers proceed. Therefore, it’s a more challenging question if the correct answer is towards the bottom of our answer choices. So let’s use this logic to our advantage, start with E, and work our way up.

Answer choice E:  (4m-12)/[m(m-4)]

Substituting ‘5’ in place of ‘m,’ we get (4*5 – 12)/[5(5-4) = 8/5. That’s it! We’re done. The correct answer is E.

Takeaway: Keep reminding yourself that the GMAT (even with its new questions) is not designed to test what you know. While it is important to brush up on all of the fundamentals you acquired years before, the most successful test-takers will fluidly incorporate simple strategies when attacking complex questions, rather than simply grinding through longer calculations. Each new version of the Official Guide validates the wisdom of this approach.

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

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

How to Tackle Evenly Spaced Sets on the GMAT

MBA Applicant Evaluation WorkshopThere’s an amusing anecdote told about the great 18th century mathematician, Carl Friedrich Gauss. Apparently, when Gauss was young, he was something of a troublemaker in school, and as a punishment for one of his disruptive outbursts, his teacher ordered him to calculate the sum of all the numbers from 1 to 100 inclusive, thinking that such a calculation would be taxing and time-consuming. Gauss simply scratched his head, thought for a few seconds, and then astonished his teacher and classmates by spitting out the answer: 5,050. He was about seven years old when this happened.

So then, how is it possible for a child – a genius, perhaps, but still a child – to do such an extensive computation in his head? The answer involves exploiting certain properties of evenly spaced sets. An evenly spaced set, as the name implies, is one in which the gap between each successive element in the set is equal. So a set consisting of consecutive integers would be evenly spaced, as would a set consisting of consecutive multiples of 2 or consecutive multiples of 3, etc.

It is always true of evenly spaced sets that the median – the middle term of the set – is equal to the mean, or arithmetic average, of the set. Moreover, the mean can be calculated by adding the high and the low terms of the set, and then dividing by 2. We can use this property in conjunction with the equation: Average * Number of Terms = Sum to calculate the sum of any large evenly spaced set.

In the case of the set of the integers from 1 to 100 inclusive, it works like this:

Average = (High + Low)/2 = (100 + 1)/2 = 101/2 = 50.5.

The Number of Terms = 100. Technically, the equation for finding the number of terms in an evenly spaced set is [(High-Low)/increment] + 1, but clearly, there are 100 terms between 1 and 100. Just remember, when using this formula, we want to add one to make sure we’re not leaving off the last term.

Average * Number = 50.5 * 100 = 5050.

Not too bad, even for a seven-year-old. (Note to those curious about the history of mathematics, this isn’t exactly how Gauss did the calculation, but it’s close enough.)

Now let’s see this concept in action on the GMAT:

For any positive integer n, the sum of the first n positive integers equals (n(n+1))/2. What is the sum of all the even integers between 99 and 301? 
A) 10,000
B) 20,200
C) 22,650
D) 40,200
E) 45,150 

Notice that we don’t have to bother with the formula they give us. The set of all evens from 99 to 301 inclusive will really be from 100 to 300, as those are the lowest and highest even terms of the set, respectively.

Average = (High + Low)/2 = (300 + 100)/2 = 400/2 = 200.

Number of Terms = [(High-Low)/increment] + 1 = [(300-100)/2] + 1 = 101. (Note: we divide by ‘2’ here because we only want even numbers, or multiples of 2. Thus, there is an increment of 2 between each successive term in the set.)

Average * Number = 200 * 101 = 20,200. The answer is B. Not bad.

Great, you think. Now I can just go on autopilot and apply these formulas anytime I encounter a huge evenly spaced set. But the GMAT doesn’t work like that. Sometimes we use a formula, but just as often, we’ll use logic, or we’ll pick a number, or we’ll work with the answer choices.

This cannot be repeated enough: Quantitative Reasoning is not a math test. It’s a test that requires some mathematical knowledge in order to make good decisions under pressure. Sometimes the best decision is doing little or no math at all.

Consider the following question:

How many positive three-digit integers are divisible by both 3 and 4? 
A) 75
B) 128
C) 150
D) 225
E) 300 

First, note that any number that is divisible by both 3 and 4 will be divisible by 12, as 12 is the least common multiple of 3 and 4. Perhaps you also noted that we’re dealing with an evenly spaced set here, and that, if the set consists of multiples of 12, the increment is clearly 12. But this question is very different from the previous one because we’re not required to calculate a sum. We just need to know how many multiples of 12 exist between 100 and 999.

If my increment is 12, I know I’ll be dividing by 12 at some point. But I can see that my (High – Low) will be at most (999 – 100) = 899. (Technically, our highest multiple of 12 in this set is 996 and our low term is 108, but there’s actually no need to discern this.) Clearly 899/12 will be less than 100, so there have to be fewer than 100 terms in the set. Now look at the answer choices. Only A is less than 100, so I’m done. I don’t have to finish the calculation.

Takeaway: You will be learning many useful formulas for the GMAT, but make sure you don’t use them blindly. Expect to mix formal algebra with the well-worn strategies of picking numbers and working with the answer choices. On the GMAT, flexibility and mental agility will always take precedence over rote memorization.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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.

Advanced Averages Concepts for the GMAT

Quarter Wit, Quarter WisdomLet’s discuss an advanced averages concept today.

Say, you have the following set of consecutive integers: 2, 3, 4, 5, 6, 7, 8

What is the average of this set? There are 7 consecutive integers here and the average is 5, the middle number.

Say the set is changed to: 2, 3, 4, 5, 6, 7, 8, 9 (another consecutive number is added to the extreme right). Now what is the average? It is the average of the two middle numbers (5+6)/2 = 5.5.

Let’s edit the set one more time: 1, 2, 3, 4, 5, 6, 7, 8, 9 (another consecutive number is added to the extreme left). The average now is 5 again.

Whenever you add a number on either side of a set of consecutive integers, the average changes by 0.5. This is obvious because odd number of consecutive integers have the middle number as the average and an even number of consecutive integers have the average of two middle numbers as the average. Since every time you add an integer, the number of integers changes from odd to even or from even to odd, the average changes by 0.5.

By the same logic, what happens when you remove an integer from either extreme?

Given a set 3, 4, 5, 6, 7, 8, 9, how will its average change if you remove 3?

The average of 3, 4, 5, 6, 7, 8, 9 is 6, and the average of 4, 5, 6, 7, 8, 9 is 6.5 — the average increases to 6.5 because you removed a small number.

Now how will the average change if you remove 9 instead of 3?

The average of 3, 4, 5, 6, 7, 8, 9 is 6, and the average of 3, 4, 5, 6, 7, 8 is 5.5 — here, the average decreases to 5.5 because you removed a large number.

So, every time you add or remove a number from one of the extremes, the average will move by 0.5.

What happens if you remove a number from somewhere in the middle?

The average changes but by how much? When you remove the greatest or the least number, the average changes by 0.5. So when you remove some other number, the average will change by something less than 0.5. For example, from the set 3, 4, 5, 6, 7, 8, 9, if you remove 8, the average changes from 6 to 5.667. If instead, you remove 7, the average changes to 5.833.

A few takeaways:

  1. When you remove an integer very close to the average, the average changes by very little. If you remove the average, the average doesn’t change (changes by 0). When you remove a number close to the extreme, the average changes by a larger number (up to a maximum of 0.5).
  2. When you remove a number less than the average, the average increases. When you remove a number more than the average, the average decreases.
  3. When you remove the smallest number, the average increases by 0.5. When you remove the greatest number, the average decreases by 0.5.

Now, a question based on this concept:

In a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard. A student erased one number. The average of the remaining numbers was 29(14/19). What was the number that the student erased?

(A) 13

(B) 16

(C) 28

(D) 36

(E) 50

Solution:

The numbers on the board: 1, 2, 3, 4, …

The new average is 29(14/19). Since the average changes by not more than 0.5 when you remove an integer from a set of consecutive integers, the original average was either 29.5 or 30. So originally there were either 58 numbers (average 29.5) or 59 numbers (average 30).

When you remove a number, you are left with either 57 numbers or with 58 numbers. Now, the new average will tell you whether you are left with 57 numbers or 58 numbers. The denominator is 19 in the fraction, so when you divide the sum of all remaining integers by the number of integers, the number of integers (denominator) is 19 or a multiple of 19 — 57 is a multiple of 19, 58 is not. So you must have been left with 57 integers and the original number of integers must be 58. This means the original average must have been 29.5.

The original average of 29(1/2) increases to 29(14/19), i.e. an increase of 14/19 – 1/2 = 9/38.

When an integer was removed, the average increased by 9/38 so the integer must be less than the original average. Now use the concept of average that we have learned. One integer was bringing the rest of the numbers down by 9/38 each so the integer must have been (9/38)*57 = 13.5, which is less than the original average of 29.5.

This means the integer that was removed must have been (29.5 – 13.5) = 16, so the answer is B.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube 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: There’s a Hole in the Bucket… But Not in Your GMAT Score!

GMAT Tip of the WeekIf you’ve ever attended a summer camp or roasted marshmallows over a campfire, there’s a good chance you know the popular children’s singalong song “There’s a Hole in the Bucket.”  Sparing you the repeat lyrics, let’s take a look at the ridiculous (and GMAT-relevant) musical conversation between Dear Henry and Dear Liza:

Henry: There’s a hole in the bucket (dear Liza, dear Liza, dear Liza…)

Liza: Then fix it (dear Henry, dear Henry, dear Henry…)

Henry: With what shall I fix it?

Liza: With straw.

Henry: The straw is too long.

Liza: Well, cut it.

Henry: With what shall I cut it?

Liza: With an axe.

Henry: The axe is too dull.

Liza: Then sharpen it.

Henry: With what shall I sharpen it?

Liza: With a stone.

Henry: The stone is too dry.

Liza: Then wet it.

Henry: With what shall I wet it? (Editor’s note: really, Henry?)

Liza: With water.

Henry: With what shall I fetch it?

Liza: With a bucket.

Henry (and his redemption): There’s a hole in the bucket.

<Repeat over and over again>

Now, what makes that song such a children’s and family favorite?  In some part it’s popular because it repeats upon itself, but mostly it’s popular because even small children have to laugh at Henry’s heroic lack of critical thought.  Henry simply can’t function unless Liza directly hands him the specific next step.

…and Liza and Henry’s conversation is not all that much unlike many GMAT tutoring sessions.

Among the pool of GMAT test-takers, there are plenty of Henrys.  And as much as you may laugh at him, you’re playing the part of Henry just a little too much when you:

  • Stop working on a problem in less than 2 minutes and flip to the back of the book for the solution. (“With what shall I solve it, dear textbook, dear textbook…”)
  • Give up on the calculations without first checking the answer choices to see if they afford you a shortcut. (“The calculation is too long, dear GMAT, dear GMAT”)
  • Frustratedly ask “but how am I supposed to see that I should do that?”. (“But how should I know that, dear teacher, dear teacher…”)
  • Write off the question as flawed because you disagree with the correct answer. (“The solution is just wrong, dear answer key, dear answer key…”)

Eavesdrop on a GMAT tutoring session at your local library or coffee shop and there’s a good chance you’ll hear more Liza-and-Henry than you’d expect.  Students frequently ask for the rule but not the lesson, and tutors often simply oblige.  But to avoid Henrydom on test day (this conversation should last 3-5 seconds, not be a song that kids will sing for an entire field trip bus ride.  Figure it out, Henry!) you need to train yourself to ask and answer those questions for yourself.

We at Veritas Prep suggest the “toolkit” approach as opposed to a “if it’s this kind of problem I will steadfastly use this method without critical thought” mindset.  When the bucket has a hole or the straw is too long, ask yourself what other tools are in your toolkit.

For example, if you blank on a rule, try proving it with small numbers.  Unsure whether Even + Odd is Even or Odd?  Just try 2 + 1 (an even plus and odd) and recognize that the answer is 3 (Odd!).  Or if the algebra looks too messy, see if you can plug in an answer choice to get a better feel for the solutions’ relationship to the problem.

What makes “There’s a Hole in the Bucket” funny is what could ultimately make your own GMAT test experience miserable: you (and Henry) have to employ a combination of critical thinking, trial-and-error, and patience to solve problems. The exam simply isn’t testing your ability to memorize a “Liza List” of steps to solve each problem; many hard problems are designed specifically to reward those who overcome the adversity of the “obvious” method leading you down a rabbit hole of awful algebra or those who find a familiar theme in a completely unfamiliar setup.  So to train yourself to be an anti-Henry:

  • Force yourself to fight and struggle through hard practice problems. The written solution isn’t likely to be nearly as helpful as your having had to struggle to gain understanding.
  • Think in terms of your “toolkit” – if your first inclination doesn’t lead to success, rummage around your toolkit to see what other types of concepts might apply to that problem.
  • When you don’t know or can’t remember a rule, test the concept with small numbers to see if you can retrain your brain or prove the relationship to yourself.
  • Hold your tutor accountable – they should be asking you probing questions like Socrates, not handing you one-time solutions and steps like Liza (she’s not totally innocent in this either…she enables Henry way too much!)

The way the song goes, there will be a hole in Henry’s bucket forever, but if there’s a hole in your GMAT score you can fix it with a new study mindset (even if the straw is too long…).

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

By Brian Galvin.

Why is There “Math” in the GMAT Critical Reasoning Section?

No MathThe Critical Reasoning portion of the GMAT will sometimes test basic mathematical concepts. My more verbally-minded students sometimes complain that this tendency is unfair, as the test seems to have imported a question-type from the section of the test that they find less agreeable into the section they consider their strength. But the truth is that the “math” in Critical Reasoning is really about logic and intuition rather than higher-level abstraction.

Take percentages, for instance. We can understand percentage reasoning without doing much calculation. When I introduce this topic, I’ll offer a simple real-world example:

In the 2014 playoffs, Lebron James made roughly 56% of his field goal attempts. In the 2015 playoffs, he made roughly 42% of his attempts. Therefore, he made fewer field goals in 2015 than in 2014.

You don’t need to be an avid basketball fan to recognize the glaring logical flaw in this statement. To determine whether that percentage dip is meaningful, we have to know how many shot attempts he was taking. Because he took so many more shots in 2015 than in 2014, he ended up making more field goals in that year, when his field goal percentage was lower. The notion that a percentage isn’t terribly meaningful without knowing the percent of what is obvious to everyone.

What the GMAT will typically do, however, is to test the exact same concept using a scenario that we may not grasp quite as intuitively. Consider the following official argument:

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

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

  1. People who moved from one state to another when they retired moved a greater distance, on average, last year than such people did ten years ago.
  2. People were more likely to retire to North Carolina from another state last year than people were ten years ago.
  3. The number of people who moved from one state to another when they retired has increased significantly over the past ten years.
  4. The number of people who left Florida when they retired to live in another state was greater last year than it was 10 years ago.
  5. Florida attracts more people who move form one state to another when they retired than does any other state.

The logic here may not be as obvious as the Lebron example, but it is, in fact, identical. The argument’s conclusion is that Florida’s economy will suffer negative consequences. The central premise is that of the people moving from one state to another, a smaller percentage are going to Florida now than were going to Florida ten years ago. The assumption is that a smaller percentage moving to Florida means fewer people moving to Florida.

This line of reasoning is no more valid than asserting that Lebron shooting a lower percentage in 2015 than in 2014 means he made fewer shots in 2015. Just as we needed to know if there was a change in the total number of shots Lebron was taking in order to evaluate whether the change in percentage was meaningful, we need to know if there was a change in the total number of people moving from one state to another in order to properly assess whether it’s meaningful that a smaller percentage are moving to Florida.

Let’s evaluate the answer choices one by one:

  1. The distance people moved doesn’t matter. Out of Scope. A is out.
  2. North Carolina isn’t relevant to what’s happening in Florida. Out of Scope. B is out.
  3. This is the logical equivalent of pointing out that Lebron took many more shots in 2015 than in 2014. If far more people are moving from one state to another now than were moving from one state to another ten years ago, it’s possible that more total people are moving to Florida, even if a smaller percentage of movers are going to Florida. This looks good.
  4. First, the number of people leaving Florida has no bearing on whether a smaller percentage of people moving to Florida will have an impact on Florida’s economy. Moreover, we’re trying to weaken the idea that Florida’s economy will suffer. If more people are leaving Florida, it would strengthen the notion that Florida’s economy will endure negative consequences. That’s the opposite of what we want. D is out.
  5. Tempting perhaps, but ultimately, irrelevant. Just because Lebron led the league in field goals made in both 2015 and 2014 (he didn’t, but play along), doesn’t mean he didn’t make fewer field goals in 2015. E is out.

The answer is C.  If more people are moving from state to state, a lower percentage moving to Florida may not mean that fewer people are coming to Florida, just as Lebron’s dip in field goal percentage does not mean he was making fewer field goals if he was taking more shots.

Takeaway: The “math” concepts tested in Critical Reasoning are, in fact, logic concepts. By connecting the prompt to a more concrete real-world example, we make this logic far more intuitive and easily graspable when we encounter it on the test.

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

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

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

99th Percentile GMAT Score or Bust! Lesson 7: Read Like You Drive

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 lessons 1, 2, 3, 4, 5, and 6!

Lesson Seven:

Read Like You Drive: very few GMAT examinees will make mistakes driving to the GMAT test center, but most test-takers will make several Reading Comprehension mistakes once they’re there. As Ravi will discuss in this video, however, the two activities are much more similar than you realize: your job is to follow the signs. Certain keywords in Reading Comprehension passages will tell you when to yield, stop, turn, and pass with care, and if you’re following those signs properly you can proceed much faster than your self-imposed “speed limit” (most people read the passages far too slowly – stay out of the left lane!) and save valuable time for the questions themselves.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube 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

Is Positive Thinking Enough to Actually Succeed on the GMAT?

QuestioningAt some point during each course I teach, I’ll ask my students if they’re familiar with this famous quote from Henry Ford “Whether you think you can, or you think you can’t – you’re right.”  Of course, they always know it. It’s a quote so popular it’s become a pedagogical cliché. Next, I’ll ask them if they believe the quote is true. They usually do. I’ll follow up with a series of GMAT-related questions. “Who struggles with probability questions?” “Who sees Reading Comprehension as a weakness?” Different hands go up for different questions.

They realize immediately that there’s a disconnect here. Why would anyone maintain the belief that he or she struggles in a given area if he or she subscribes to the notion that the pessimistic belief is a self-fulfilling prophesy? My sense is that this disconnect is rooted in our tendency to nod politely when greeted with popular aphorisms we’d like to be true, while at some level, not really believing them.

We can pay lip service to Henry Ford all we want. Our actual belief is something more along the lines of: sure, it would be nice if you could improve your performance via thought alone, but that doesn’t actually work. It’s a fantasy, one that is so appealing that we’ll collectively agree to pretend that it’s true.

 Part of my job as an instructor is to get my students to move past the cliché and somehow internalize the truth of the sentiment that our beliefs do matter. This isn’t a New Age chimera that we’d like to be true. It’s an area of extensive scientific research. In 2007, researchers at Stanford University conducted a study in which they tracked the development of 7th grade students who believed that intelligence was innate vs. students who believed that intelligence is a fluid phenomenon, something that can be cultivated and improved through dedicated effort.

The students who believed that intelligence is innate were deemed the “fixed mindset” group, and the group who believed that intelligence could be improved were deemed the “growth mindset” group. Most importantly, at the start of the study, these groups had similar academic background. Sure enough, over the next couple of years, there was a marked divergence in performance – the growth mindset group outperformed their fixed mindset peers by a significant margin (take a look at this study here).

One component of the growth mindset is the belief that adversity isn’t evidence of an inherent shortcoming, but rather, an opportunity to learn and improve. This is absolutely essential on the GMAT. Students will, on average, take about a half-dozen practice tests. It is extremely rare that every one of those practice tests goes well.

At some point, during every class I teach, I’ll get a panicked email, the general gist of which is that things had been going well, but now, after a disappointing practice test, the student has significant doubts about whether the previous successes were real. I’m often asked if it will be necessary to push the test date back. The growth mindset compels us to see this setback as a positive. Isn’t it better to uncover the need for a strategic tweak on a low stakes practice test than on the official exam?

 Sure enough, once my students are able to re-frame their beliefs from, “I’m just not good at X,” to, “Maybe I’ve struggled with X in the past, but with a little practice I can actual convert this former liability into an asset,” they improve. The student who struggled with probability wasn’t inherently bad at probability, but had a less than stellar teacher in high school or college and never learned the underlying concepts properly. The student who struggled with Reading Comprehension simply wasn’t taking notes properly.

Most importantly, the students who believed that they just weren’t good at standardized tests realized that the ability to do well on standardized tests is a skill that they simply hadn’t acquired yet. In the past, when they were convinced that they couldn’t do well on, say, the SAT, they hadn’t bothered to study, because what was the point of expending any effort if the result was going to be disappointment? Once they see that they their past struggles weren’t functions of innate deficits, but rather, of self-limiting beliefs, a world of possibility opens up.

Takeaway: how we frame our thoughts with respect to academic performance is extraordinarily important. Unfortunately, our culture generally pays lip service to the growth mindset while perpetuating the notion of a fixed one. We’ll thoughtlessly spout that Henry Ford quote, all the while thinking of people as high IQ or low IQ, not realizing that IQ is itself malleable (take a look at this idea here).

Think of someone you knew in high school who did unusually well on the SAT’s. You probably thought, “That person is great at standardized tests,” rather than “That person has been successful at cultivating a particular skill set that translated well in the domain of this one particular exam.” But the latter is true. So don’t set arbitrary limits of yourself, because, contrary to some our deepest intuitions, belief and performance are inextricably linked.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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

2 Simple Calculation Tricks to Help You Overcome the GMAT Quant Section

tutoringMuch of the Quant section of the GMAT involves calculations, and as calculators are not allowed, we need to be able to add, subtract, multiply and divide numbers quickly and accurately. A surprising number of errors are made on easier problems simply because of computational error and, interestingly, many trap answers on the exam come from common errors made in computations!

American legend Wyatt Earp once said of gunfights, “Fast is fine, but accuracy is everything.” For the GMAT, if we can combine speed with accuracy, not only will you minimize silly mistakes but you can also pick up time that can be spent reasoning through more difficult problems or double-checking your work. Here are two simple math tricks that can help:

1) The Distributive Property is Your Friend

Many of us recall the basic properties of operations (associative property, commutative property, distributive property and identity property), but rarely do we consciously use them except in some algebraic manipulations. However the Distributive Property is also very useful in quickly and easily multiplying larger numbers.

For example, take the following: 163 x 30. Multiplying this out long-hand is not overly difficult, however, since we do not do this in our everyday lives, we are prone to errors. Using the Distributive Property here can help.  Intuitively, many of us would see that 163 x 30 can be broken up into 163 x 10 three times – THAT is the Distributive Property. We can then re-write the expression as 163 x (10 x 3), and then “distribute” the operands into (163 x 10) x 3

Now, couple the Distributive Property with some other tricks that many of you already use, and this tip becomes even more valuable.  Take, for instance, a more difficult calculation to “distribute” – say, 163 x 48.  You could “distribute” this into 163 x (40 + 8) and get 163 x 40 (an easy calculation) + 163 x 8.

A common trick that is used when multiplying by 8 or 9 is multiply the number by 10 and then subtract out “extra.” In this case, we would multiply 163 by 10 and then subtract out the 2 additional 163’s. If we combine these steps on the front end, we could say 163 x 48 can be re-written as 163 x (50 – 2) and get (163 x 50) – (163 x 2). 1633 x 50 can be further broken down as 163 x 10 x 5, 1630 x 5. Putting it all together, we get 163 x 50 = 163 x 10 x 5 = 1,630 x 5 = ½ of 16300 = 8,150.

8,150 – (163 x 2) = 8, 150 – 326 = 7, 824

This is a good trick to help make long-hand multiplication simpler. Be careful in breaking numbers down into too many pieces as this can overly complicate the process and lead to errors.

2) Estimation and Proportionality

The GMAT expects us to be able to move between fractions, decimals, percents and even ratios easily. Many times this is straightforward, but other times it can be quite vexing. For instance, a problem may tell you that the ratio of boys to girls in a particular class is 4:9 and ask what percentage of the class is boys. Obviously, we can see that the TRAP answer would be 44% (4/9 = 44%). But, how can we easily and accurately calculate, or estimate, the correct answer?

Here is a trick to help with that: because we have ratios down pat, we know that a ratio of 4:9 tells us that there are 4 boys out of a class of 13, so the proper fraction would be 4/13. Now the tough part is turning this into a percent. Since percents simply are fractions with a denominator of 100, we can set up an algebraic equation. In this case, we have 4/13 = x/100 and using cross-multiplication we see the answer is 400 ÷ 13, 30 and 10/13, or a little less than 31%.

An easier way, might be to use proportionality to estimate the answer. Here is how that would work:  proportionally, our fraction of 4/13 needs to be converted to a fraction over 100. To increase our denominator of 13 to 100, we need to multiply it by a bit over 7 ½. To keep the fraction in its original proportion, we will also need to multiply the numerator by the same (a bit over 7 ½), giving us a value of a little over 30%.

The takeaway from this is that by sharpening your computational skills, you can save time, improve accuracy and even minimize your effort on the exam. This can translate to higher scores by eliminating silly mistakes and saving brain power for the more difficult questions.

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

By Dennis Cashion, a Veritas Prep instructor based in Denver.

Why You Shouldn’t Rely on Your Ear for GMAT Sentence Correction Questions

Phone InterviewThe other night, when we were reviewing Sentence Correction strategies in class, a student asked if it was acceptable to rely on his ear to find the correct answer. This was what he’d done when he’d taken his diagnostic test, and he’d performed quite well on this section, so he figured it just made more sense to devote his study time to other areas. It’s a common question. After all, if you’re naturally good at something, does it really make sense to make an investment of time and energy just to tamper with an approach that’s been effective?

Whenever I get this question, I always take pains to give a nuanced response. My goal, when I’m teaching, isn’t to indoctrinate anyone or impose a given philosophical approach to a problem. The last thing any of us should be doing when we take the GMAT is wringing our hands over whether our instinct for how to tackle the problem is the “right” one. However, some approaches have potential shortcomings that we need to be mindful of, and using your ear alone to solve Sentence Correction questions is no exception.

The first problem with using your ear alone is that while a good instinct for syntax and grammar is immensely helpful for writers, on the GMAT, this instinct will often cause us to reject sentences that are technically correct but are specifically engineered to sound a little off. If you were a question-writer for the GMAT, and your goal was to make a given question as challenging as possible, wouldn’t you make some correct answers sound a little strange to amplify the difficulty of the question?

In these cases, we simply have to use a blend of logic and grammar rules to rule out the four definitively wrong answer choices. The remaining answer, which sounds strange, but has no glaring errors, will have to be correct. Take this official question, for example:

For many revisionist historians, Christopher Columbus has come to personify devastation and enslavement in the name of progress that has decimated native people of the Western Hemisphere.

A) devastation and enslavement in the name of progress that has decimated native peoples of the Western Hemisphere.
B) devastation and enslavement in the name of progress by which native peoples of the Western Hemisphere have been decimated.
C) devastating and enslaving in the name of progress those native peoples of the Western Hemisphere that have been decimated.
D) devastating and enslaving those native peoples of the Western hemisphere which in the name of progress are decimated.
E) the devastation and enslavement in the name of progress that have decimated the native peoples of the Western Hemisphere.

I like to pride myself on having a good ear when it comes to Sentence Correction, but none of these options strike me as terribly appealing. Let’s evaluate them one by one:

A, in its entirety, reads as follows: Christopher Columbus has come to personify devastation and enslavement in the name of progress that has decimated native peoples of the Western Hemisphere.

Notice, the relative clause beginning with “that.” “That” has a singular verb “has,” meaning that the antecedent for “that” should be the closest singular noun. Here, the closest singular noun is “progress.” Read literally, the sentence is saying that progress has decimated native peoples! That makes no sense. Eliminate A.

B: Christopher Columbus has come to personify devastation and enslavement in the name of progress by which native peoples of the Western Hemisphere have been decimated.

Again, it sounds like “progress” is responsible for the decimation of native peoples. No good.

C: Christopher Columbus has come to personify devastating and enslaving in the name of progress those native peoples of the Western Hemisphere that have been decimated. 

Here “that” seems to refer to “native peoples.” The GMAT prefers “who” when referring to people. Moreover, the phrase “those native peoples that have been decimated” makes it sound as though there were some native peoples who were devastated and others who weren’t. This is not the intended meaning of the sentence. Eliminate C.

D: Christopher Columbus has come to personify devastating and enslaving those native peoples of the Western hemisphere which in the name of progress are decimated. 

This one is riddled with problems. Again the phrase “those native peoples” is problematic. “Which” appears to refer to people, when the GMAT would prefer “who.” And last the verb “are” implies that the action is happening in the present tense. Clearly incorrect.

That leaves us with E: Christopher Columbus has come to personify the devastation and enslavement in the name of progress that have decimated the native peoples of the Western Hemisphere. 

It still sounds off to my ear, but if we read the sentence without the prepositional phrase “in the name of progress,” we get: Christopher Columbus has come to personify the devastation and enslavement that have decimated the native peoples of the Western Hemisphere. This makes perfect sense. Notice that because “that” has the plural verb “have,” it must have a plural antecedent, so “that” refers to “devastation and enslavement.” Not the world’s prettiest sentence, but far superior to the other four options, each of which have glaring mistakes.

Takeaway: No single strategy will allow you to answer every question within a given category correctly. Because some correct Sentence Correction answers are engineered to sound strange, it’s important to keep logic and grammar in mind as we’re justifying our decisions to eliminate the incorrect answers.

*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, YouTube 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

A Closer Look at Set and Ratio GMAT Quant Questions

Quarter Wit, Quarter WisdomWriting this post on Teacher’s Day made me dedicate this post to questions on teachers! Considering that all GMAT questions are written by teachers, oddly enough, I found very few questions actually involving them. Looks like we are a humble bunch! Today, we will discuss two GMAT Quant questions on two different topics of discussion – sets and ratios. Both questions are official and of higher difficulty.

Question 1: Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teacher surveyed were women?

Statement I: In the survey 36% of men and 50% of women said that they consider engaging in research activity an essential goal.

Statement II: In the survey 288 men said that they consider engaging in research activity an essential goal.

Solution:

On reading the question stem we realise that this question involves two variables:

Research Essential – Not Essential

Men – Women

This should immediately make us think about a matrix. Not that we cannot solve the question without one, but you know that I am a huge proponent of visual approaches.

We are given that 42% of total teachers (1400) considered research essential. So this means that 58% did not consider it essential. No need to actually calculate the number right now, let’s wait and see what else we know (anyway, we love to procrastinate calculations in Data Sufficiency questions).

Statement I: In the survey 36% of men and 50% of women said that they consider engaging in research activity an essential goal.

Say the number of women is W. We need the value of W. The number of men must be ‘Total – W’ = 1400 – W. 36% of men and 50% of women consider research essential. Knowing this, we see that we get:

TeachersDay

36% * (1400 – W) + 50% * W = 42% * 1400

This is a linear equation in W so we can solve it to get the value of W. Therefore, this statement alone is sufficient.

Statement II: In the survey 288 men said that they consider engaging in research activity an essential goal.

This statement doesn’t tell us the number of women who consider research essential, so it is not sufficient alone, therefore the answer is A, Statement I alone is sufficient but Statement II is not.

Question 2: If the ratio of the number of teachers to the number of students is the same in School District A and School District B, what is the ratio of the number of students in School District A to the number of students in School District B?

Statement I: There are 10,000 more students in School District A than there are in School District B.

Statement II: The ratio of the number of teachers to the number of students in School District A is 1 to 20.

Solution:

In both schools, the ratio of the number of teachers : the number of students is the same.

Statement I: There are 10,000 more students in School District A than there are in School District B.

We don’t know the number of students in either school district, so it is not informative enough to know that School District A has 10,000 more students. Therefore, this statement alone is not sufficient.

Statement II: The ratio of the number of teachers to the number of students in School District A is 1 to 20.

With this statement, we know that the ratio of the number of teachers : the number of students in School District A = 1:20.

Say the number of teachers in A = a; the number of students in A = 20a. We also know the ratio of the number of teachers : the number of students in School District B = 1:20.

Say the number of teachers in B = b; the number of students in B = 20b. Mind you, we don’t know the value of a and b. All we know is that the teacher student ratio is 1:20 in both.

The ratio of the number of students in A: the number of students in B = 20a : 20b = a:b. With this ratio, we don’t know a:b (even using both statements, we just know that a – b = 10,000). Therefore, the answer is E, Statements 1 and 2 together are not sufficient.

Were you able to solve both questions effortlessly? No? Don’t worry, that’s what we are here for! (Ignore the preposition at the end. It sounds most natural this way.)

Not so humble anymore, eh? :)

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube 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!

Master the GMAT by Applying Jedi-like Skills

Yoda ForceOnce you begin studying for the GMAT, you’ll realize quickly that there are different levels of mastery. There’s that initial level of competence in which you learn, or relearn, many of the foundational concepts that you learned in middle school and have since forgotten. There’s a more intermediate level of mastery in which you’re able to blend strategic thinking with foundational concepts.

Then there’s the highest level in which you achieve a kind of trance-like, fugue state that allows you to incorporate multiple strategies to break down a single complex problem and then seamlessly shift to a fresh set of strategies on the next problem, which, of course, will be testing slightly different concepts from the previous one.

It’s the GMAT equivalent of becoming a Jedi who can anticipate his opponent’s next light saber strike several moves in advance or becoming Neo in the Matrix, finally deciphering the structure of the streaming code that animates his synthetic world. Pick whatever sci-fi analogy you like – it’s this kind of expertise that we’re shooting for when we prepare for the test. The pertinent questions are then the following: how do we accomplish this level of expertise, and what does it look like once we’re finally there?

Fortunately for you, dear student, our books are organized with this philosophy in mind. Once you’ve worked through the skill-builders and the lessons, you’ll likely be at the intermediate level of competence. Then it will be through drilling with homework problems and taking practice tests that you’ll achieve the level of mastery we seek. But let’s take a look at a Sentence Correction question to get a sense of how our thought processes might unfold, once we’re functioning in full Jedi-mode.

Unlike most severance packages, which require workers to stay until the last day scheduled to collect, workers at the automobile company are eligible for its severance package even if they find a new job before they are terminated. 

(A) the last day scheduled to collect, workers at the automobile company are eligible for its severance package

(B) the last day they are scheduled to collect, workers are eligible for the automobile company’s severance package

(C) their last scheduled day to collect, the automobile company offers its severance package to workers

(D) their last scheduled day in order to collect, the automobile company’s severance package is available to workers

(E) the last day that they are scheduled to collect, the automobile company’s severance package is available to workers

Having done hundreds of questions, you’ll notice one structural clue leap immediately: “unlike.” When you see words such as “like” or “unlike” you know that you’re dealing with a comparison, so your first task is to make sure you’re comparing appropriate items. You’ll also note that the clause beginning with “which require” modifies “severance packages,” so whatever is compared to these severance packages will come after the modifier.

In A, you’re comparing “severance packages” to “workers.” We’d rather compare severance packages to severance packages or workers to workers. No good.

In B, again, you’re comparing “severance packages” to “workers.”

In C, you’re comparing “severance packages” to “the automobile company.” Nope.

That leaves us with D and E, both of which compare “severance packages” to “automobile’s company severance package.” Here, you’re comparing one group of severance packages to another, so this is logical. But now you have to switch gears – the comparison issue allowed you to eliminate some incorrect answer choices, but you’ll have to use another issue to differentiate between your remaining options.

Once we’re down to two options, you can simply read the two sentences and look for differences. One difference is that E contains the word “that” in the phrase “the last day that they are scheduled to collect.” Perhaps it sounds okay to your ear, but you’ll recall that when “that” is used as a relative pronoun, it should touch the noun it modifies. In this case, it touches, “last day.” Read literally, the phrase, “the last day that they are scheduled to collect,” makes it sound as though “they” are collecting the “last day.” Surely this isn’t what the sentence intends to convey, so we’re then left with ‘D,’ which is the correct answer.

Takeaway:

Notice how many disparate concepts you had to juggle here: You had to recognize the structural clue indicating that “unlike” signifies a comparison; recognize that temporarily skipping over a longer modifying phrase is an effective way to get a sense of the core clause you’re evaluating; recall that once you’re down to two answer choices, you can simply zero in on differences between your options; remember the rule stipulating that relative pronouns must touch what they modify; and last, you had to recognize that Sentence Correction is not only about grammar but also about logic and meaning, and all in under a minute and a half. I’d say that’s pretty Jedi-like.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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

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

GMAT Tip of the Week: Test Day Should Not Be Labor Day

GMAT Tip of the WeekAs we head into the Labor Day weekend here in the U.S., it seems a fitting time to talk about labor.  Precious few people consider the GMAT to be a labor of love; to most aspiring (and perspiring?) MBAs, the GMAT is a lot of hard work.  And while, to earn the score that you’re hoping for, it’s likely that you’ll have to put in a good amount of sweat and a few tears (but hopefully no blood…), it’s important to recognize that test day itself should not be a Labor Day!

Your hard work should take place well before you get to the test center, so that on test day you’re not overworking yourself.  Working too hard on test day takes time (which is a precious resource on the exam), saps your mental energy (which also tends to be in short supply as you get later into the test with only two 8-minute breaks to recharge), and leads to errors.  Accordingly, here are a few tips to help you take the heavy labor out of your test day:

1. Only do the math you absolutely have to do.

The GMAT rewards efficiency and ingenuity, and has been known to set up problems that can be awful if done “by the book” but relatively smooth if you recognize common patterns.  For example:

  • Answers are assets! If the math looks like it’s going to get messy, look at the answer choices.  If they’re really far apart, you may be able to estimate after just a step or two.  Or if the answer choices are really “clean” numbers (0, 1, 10…these are really easy numbers with which to perform calculations) you may be able to plug them into the problem and backsolve without any algebra.
  • Don’t multiply until you’ve divided. Working step by step through a problem, you may see that you have to multiply, say, 51 by 18.  Which is an ugly thing to have to do for two reasons: that calculation will take time by hand, and it will leave you with a new number that will be hard to work with for the following step.  But the next step might be to divide by 34.  If you save the multiplication (just call it (51)(18) and don’t actually perform the step), then you can divide by 2 and 17.  Which works out pretty cleanly: 51/17 is 3 and 18/2 is 9, so now you’re just multiplying 3 by 9 and the answer has to be 27.   The GMAT goes heavy on divisibility, so keep in mind that you’ll do a lot of division on this test…meaning that it usually makes sense to wait to multiply until after you’ve seen what you’ll have to divide by.
  • Think in terms of number properties. Often you can determine quickly whether the answer has to be even or odd, or whether it has to be positive or negative, or what the first or last digit will be.  If you’ve made those determinations, quickly scan the answer choices and see how many fit those criteria.  If only one does, you’re done.  And if 2-3 do but they’re easier to plug in to the problem or to estimate between, then you can avoid doing the actual math.

2. Don’t take too many notes.

Particularly with Reading Comprehension passages, GMAT test-takers on average take far too many notes.  This hurts you for two reasons: first, it’s time consuming, and on a question type that’s already time consuming by nature.  And second, very few of the notes that people take are useful. People tend to take notes on details – you generally write down what you don’t think you’ll remember – but the test will typically only ask you about one detail per passage.  And the passage stays on the screen the whole time, so if you need to find a detail it’s just as easy to find it on the screen as it is in your notes (plus you’ll want to read the exact way that it was written, which your notes won’t necessarily have).  So use your time wisely: use your initial read of the passage to get a feel for the general direction of the passage, and then you’ll know which area/paragraph to go back to if and when you do need to find the details.

3. Stay flexible.

The GMAT is a test that rewards “mental agility,” meaning that it often designs problems that look like they should be solved one way (say, algebra) but quickly become labor-intensive that way and then reward those who are able to quickly change approaches (maybe to backsolving or picking numbers).  When it looks like you’ve just set yourself up for a massive amount of work, take a quick step back and re-analyze.  At this point are the answer choices more helpful?  Should you abandon your number-picking and go back to doing the algebra?  Does re-reading the question allow you to set it up differently?  Generally speaking, if the math starts to get labor-intensive you’re missing a better method.  So let that be your catalyst for re-assessing.

As you sit down to take the GMAT (to get into a great business school to become a more valuable member of the labor force), those 4 hours you spend at the test center probably won’t be a labor of love.  But they shouldn’t be full of labor, anyway.  Heed this advice to lighten your labor and the GMAT just might feel like more of a day off than anything (like, you know, Labor Day).

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

99th Percentile GMAT Score or Bust! Lesson 6: Practice Tests Aren’t Real Tests

Veritas 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 Lessons 1, 2, 3, 4 and 5!

Lesson Six:

Practice Tests Aren’t Real Tests: read the popular GMAT forums and you’ll see lots of handwringing and bellyaching about practice tests scores…but not very much analysis beyond the scores themselves.  In this video, Ravi (along with his alter ego Allen Iverson) talks about practice, stressing the importance of using the tests to increase your score more than to merely try to predict it.  Pacing is paramount and diagnosis is divine; as Ravi will explain, practice tests are critical for learning how you would perform if that were the real thing, with the added bonus of having the opportunity to fix those things that you don’t like about that practice performance.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook, YouTube 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

Think Like Einstein to Answer GMAT Data Sufficiency Questions

I recently read Manjit Kumar’s, Quantum, which is about the philosophical disagreement between Niels Bohr and Albert Einstein with respect to the nature of reality.  In high school physics, we learned about Heisenberg’s Uncertainty Principle, which posits that we can never know both the position and the momentum of an electron with absolute certainty. The more precisely we measure an electron’s position, the less we know about its momentum, and vice versa.

There are two ways to interpret this phenomenon. Einstein thought that an electron had a defined position and momentum. We simply weren’t capable of documenting both at the same time due to the clumsiness of our measuring instruments. Bohr, on the other hand, believed that an electron didn’t have a position or momentum until we measured it. In other words, the electron doesn’t exist before it’s observed (which, of course, raises knotty metaphysical questions about how the observer exists, if the observer is herself made of sub-atomic particles, none of which exist before they’re observed. But this one is a little harder to connect to the GMAT, so the reader is invited to contemplate such a conundrum in his or her own time, once the test is in the rear view mirror).

Though physicists, by and large, are more likely to accept Bohr’s interpretation than Einstein’s, on the GMAT we’ll want to reason more like Einstein, particularly when it comes to Data Sufficiency. In almost every class I teach, a student will ask a question along the lines of, “Is it possible that, in a value question, Statement 1 will tell you definitively that x equals 8, and that Statement 2 will tell you definitively that x equals some other number?” The answer is a resounding “No” – x has a unique value, the question is whether we can definitively divine what that value is. If Statement 1 tells us decisively that x = 8, Statement 2 cannot tell us that x equals, say, 10.

Let’s see how this principle can be helpful in action:

If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?

1)     If the integer is divided by 45, the remainder is 30.

2)     The integer is divisible by 2

Statement 1 tells me that when I divide an integer by 45, I get a remainder of 30. So I could test 75, because that will give a remainder of 30 when divided by 45 (And, just as importantly, it gives a remainder of 3 when divided by 9 – I have to satisfy the conditions embedded in the question stem too!). The question asks me for the remainder when the integer is divided by 5. Well, 75/5 will give no remainder, so the remainder, in this case, is 0.

Let’s see if that will always be the case. Next, we’ll test 105, which gives a remainder of 30 when divided by 45, and gives a remainder of 3 when divided by 9 [note: I can generate fresh numbers to test by simply adding the divisor, 30, to the previous number I test (75 + 30 = 105)]. Clearly 105/5 will give a remainder of 0, as any number that ends in 5 will be divisible by 5. The same will be true of 145, or 175, or 205. The remainder, when the integer in question is divided by 5 will always be 0, so Statement 1 is sufficient.

Now let’s reason like Einstein. We know that the answer to the question has a definitive value of 0. That can’t change. The only way Statement 2 can be sufficient is if it gives us that same value. So let’s pick a number that is divisible by 2 but gives a remainder of 3 when divided by 9. 12 will work. The remainder, when 12 is divided by 5, is 2. All we need to see is that we did not get 0.

We don’t have to test another number. Statement 2 cannot, alone, be sufficient, because we already know – the Einsteins that we are – that the value in question is 0. Statement 2 cannot tell us that the value is definitively 2 (if we continued to test, we’d eventually find values that gave us a remainder of 0 when we divided by 5, but because there are other possibilities, Statement 2 doesn’t give us enough information to determine, without a doubt, that the value is 0). We’re done. Statement 2 is insufficient. The answer is A: Statement 1 alone is sufficient.

Note that this same logic will work on “YES/NO” questions as well. If Statement 1 tells us that the answer to the question is definitively “YES”, Statement 2 cannot tell us that the answer is definitively “NO”, and vice versa. Recognizing this can save us valuable time.

Takeaway: Although Niels Bohr might say that there is no answer to a Data Sufficiency question until we evaluate a statement, for these questions we want to think more like Einstein and recognize that, in the mind of the question-writer, there is an objective answer – the question is whether we have enough information to definitely deduce what that answer is. There may be no objective reality in the quantum world, but on the GMAT, there most certainly is.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook, YouTube 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