Help! My Practice Test Score Seems Wrong!

MBA Interview QuestionsSo you’ve taken your GMAT practice test, looked at your score, and investigated a little further. If you’re like many GMAT candidates, you’ve tried to determine how your score was calculated by:

  • Looking at the number you answered correctly vs. the number you answered incorrectly, and comparing that to other tests you’ve taken.
  • Analyzing your “response pattern” – how many correct answers did you have in a row? Did you have any strings of consecutive wrong answers?

And if you’ve taken at least a few practice tests, you’ve probably encountered at least one exam for which you looked at your score, looked at those dimensions above, and thought “I think my score is flawed” or “I think the test is broken.” If you’re taking a computer-adaptive exam powered by Item Response Theory (such as the official GMAT Prep tests or the Veritas Prep Practice Tests), here’s why your perception of your score may not match up with your actual, valid score:

The number of right/wrong answers is much less predictive than you think.
Your GMAT score is not a function of the number you answered correctly divided by the number you answered overall. Its adaptive nature is more sophisticated than that – essentially, its job is to serve you questions that help it narrow in on your true score. And to do so, it has to test your upper threshold by serving you questions that you’ll probably get wrong. For example, say your true score is an incredibly-high 790. Your test might look something like:

Are you better than average?  (You answer a 550-level question correctly.)

Ok, are you better than a standard deviation above average? (You answer a 650-level question correctly.)

Ok, you’re pretty good. But are you better than 700 good?  (you answer a 700-level question correctly)

Wow you’re really good.  But are you 760+ good? (You answer a 760 level question correctly.)

If you’re 760+ level are you better or worse than 780? (You answer a 780-level question correctly.)

Well, here goes…are you perfect? (You answer an 800-level question incorrectly.)

Ok, so maybe one or more of those earlier questions was a fluke. Are you better than 760? (You answer a 760 question correctly.)

Are you sure you’re not an 800-level student? (You answer 800 incorrectly.)

Ok, but you’re definitely better than 780, right? (You answer a 780 correctly.)

Are you sure you’re not 800-level? (You answer an 800-level question incorrectly.)

And this goes on, because it has to ask you 37 Quant and 41 Verbal questions, so as the test goes on and you answer you own ability level correctly, it then has to ask the next level up to see if it should increase its estimate of your ability.

The point being: because the system is designed to hone in on your ability level, just about everyone misses several questions along the way. The percentage of questions you answer correctly is not a good predictor of your score, because aspects like the difficulty level of each question carry substantial weight. So don’t simply count rights/wrongs on the test, because that practice omits the crucial IRT factor of difficulty level.

Now, savvier test-takers will then often take this next logical step: “I looked at my response pattern of rights/wrongs and based on that it looks like the system should give me a higher score than it did.” Here’s the problem with that:

Of the “ABCs” of Item Response Theory, Difficulty Level is Only One Element (B)…
…and even at that, it’s not exactly “difficulty level” that matters, per se. Each question in an Item Response Theory exam carries three metrics along with it, the A-parameter, B-parameter, and C-parameter. Essentially, those three parameters measure:

A-parameter: How heavily should the system value your performance on this one question?

Like most things with “big data,” computer adaptive testing deals in probabilities. Each question you answer gives the system a better sense of your ability, but each comes with a different degree of certainty.  Answering one item correctly might tell the system that there’s a 70% likelihood that you’re a 700+ scorer while answering another might only tell it that there’s a 55% likelihood. Over the course of the test, the system incorporates those A-parameters to help it properly weight each question.

For example, consider that you were able to ask three people for investment advice: “Should I buy this stock at $20/share?” Your friend who works at Morgan Stanley is probably a bit more trustworthy than your brother who occasionally watches CNBC, but you don’t want to totally throw away his opinion either. Then, if the third person is Warren Buffet, you probably don’t care at all what the other two had to say; if it’s your broke uncle, though, you’ll weight him at zero and rely more on the opinions of the other two. The A-parameter acts as a statistical filter on “which questions should the test listen to most closely?”

B-parameter: This is essentially the “difficulty” metric but technically what it measures is more “at which ability level is this problem most predictive?”

Again, Item Response Theory deals in probabilities, so the B-parameter is essentially measuring the range of ability levels at which the probability of a correct answer jumps most dramatically. So, for example, on a given question, 25% of all examinees at the 500-550 level get it right; 35% of all those at the 550-600 level get it right; but then 85% of users between 600 and 650 get it right. The B-parameter would tell the system to serve that to examinees that it thinks are around 600 but wants to know whether they’re more of a 580 or a 620, because there’s great predictive power right around that 600 line.

Note that you absolutely cannot predict the B-parameter of a question simply by looking at the percentage of people who got it right or wrong! What really matters is who got it right and who got it wrong, which you can’t tell by looking at a single number. If you could go under the hood of our testing system or another CAT, you could pretty easily find a question that has a “percent correct” statistic that doesn’t seem to intuitively match up with that item’s B-parameter. So, save yourself the heartache of trying to guess the B-parameter, and trust that the system knows!

C-parameter: How likely is it that a user will guess the correct answer? Naturally, with 5 choices this metric is generally close to 20%, but since people often don’t guess quite “randomly” this is a metric that varies slightly and helps the system, again, determine how to weight the results.

With that mini-lesson accomplished, what does that mean for you? Essentially, you can’t simply look at the progression of right/wrong answers on your test and predict how that would turn into a score. You simply don’t know the A value and can only start to predict the “difficulty levels” of each problem, so any qualitative prediction of “this list of answers should yield this type of score” doesn’t have a high probability of being accurate.  Furthermore, there’s:

Question delivery values “content balance” more than you think.
If you followed along with the A/B/C parameters, you may be taking the next logical step which is, “But then wouldn’t the system serve the high A-value (high predictive power) problems first?” which would then still allow you to play with the response patterns for at least a reasonable estimate. But that comes with a bit more error than you might think, largely because the test values a fair/even mix of content areas a bit more than people realize.

Suppose, for example, that you’re not really all that bright, but you had the world’s greatest geometry teacher in high school and have enough of a gambling addiction that you’re oddly good with probability. If your first several – high A-value – problems are Geometry, Probability, Geometry, Geometry, Geometry, Probability… you might get all three right and have the test considering you a genius with such predictive power that it never actually figures out that you’re a fraud.

To make sure that all subject areas are covered and that you’re evaluated fairly, the test is programmed to put a lot of emphasis on content balancing, even though it means you’re not always presented with the single question that would give the system the most information about you.

If you have already seem a lot of Geometry questions and no Probability questions, and the best (i.e., highest A-value) question at the moment is another Geometry question, then the system may very well choose a Probability question. The people who program the test don’t give the system a lot of leeway in this regard—all topics need to be covered at about the same rate from one test taker to the next.

So simply put: Some questions count more than others, and they may come later in the test as opposed to earlier, so you can’t quite predict which problems carry the most value.

Compounding that is:

Some questions don’t count at all.
On the official GMAT and on the Veritas Prep Practice Tests, some questions are delivered randomly for the express purpose of gathering information to determine the A, B, and C parameters for use in future tests. These problems don’t count at all toward your score, so your run of “5 straight right answers” may only be a run of 3 or 4 straight.

And then of course there is the fact that:

Every test has a margin of error.
The official GMAT suggests that your score is valid with a margin of error of +/- 30 points, meaning that if you score a 710 the test is extremely confident that your true ability is between 680 and 740, but also that it wouldn’t be surprised if tomorrow you scored 690 or 720. That 710 represents the best estimate of your ability level for that single performance, but not an absolutely precise value.

Similarly, any practice test you take will give you a good prediction of your ability level but could vary by even 30-40 points on either side and still be considered an exceptionally good practice test.

So for the above reasons, a test administered using Item Response Theory is difficult to try to score qualitatively: IRT involves several metrics and nuances that you just can’t see. And, yes, some outlier exams will not seem to pass the “sniff test” – the curriculum & instruction team here at Veritas Prep headquarters has seen its fair share of those, to be sure.

But time and time again the data demonstrates that Item Response Theory tests provide very reliable estimates of scores; a student whose “response pattern” and score seem incompatible typically follows up that performance with a very similar score amidst a more “believable” response pattern a week later.

What does that mean for you?

  • As hard as it is to resist, don’t spend your energy and study time trying to disprove Item Response Theory. The only score that really matters is the score on your MBA application, so use your time/energy to diagnose how you can improve in preparation for that test.
  • Look at your practice tests holistically. If one test doesn’t seem to give you a lot to go on in terms of areas for improvement, hold it up against the other tests you’ve taken and see what patterns stand out across your aggregate performance.
  • View each of your practice test scores more as a range than as an exact number. If you score a 670, that’s a good indication that your ability is in the 650-690 range, but it doesn’t mean that somehow you’ve “gotten worse” than last week when you scored a 680.

A personal note from the Veritas Prep Academics team:
Having worked with Item Response Theory for a few years now, I’ve seen my fair share of tests that don’t look like they should have received the score that they did. And, believe me, the first dozen or more times I saw that my inclination was, “Oh no, the system must be flawed!” But time and time again, when we look under the hood with the psychometricians and programmers who consulted on and built the system, Item Response Theory wins.

If you’ve read this far and are still angry/frustrated that your score doesn’t seem to match what your intuition tells you, I completely understand and have been there, too. But that’s why we love Item Response Theory and our relationship with the psychometric community: we’re not using our own intuition and insight to try to predict your score, but rather using the scoring system that powers the actual GMAT itself and letting that system assess your performance.

With Item Response Theory, there are certainly cases where the score doesn’t seem to precisely match the test, but after dozens of my own frustrated/concerned deep dives into the system I’ve learned to trust the system.  Don’t try to know more than IRT; just try to know more than most of the other examinees and let IRT properly assign you the score you’ve earned.

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

By Brian Galvin and Scott Shrum.

How to Simplify Percent Questions on the GMAT

stressed-studentOne of the most confounding aspects of the GMAT is its tendency to make simple concepts seem far more complex than they are in reality. Percent questions are an excellent example of this.

When I introduce this topic, I’ll typically start by asking my class the following question: If you’ve completed 10% of a project how much is left to do?  I have never, in all my years of teaching, had a class that was unable to tell me that 90% of the project remains. It’s more likely that they’ll react as though I’m insulting their collective intelligence. And yet, when test-takers see this concept under pressure, they’ll often fail to recognize it.

Take the following question, for example:

Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24 min 18 sec, she had completed 10% of her exercise session. The readout indicated which of the following when she had completed 40% of her exercise session.

(A) 10 min. 48 sec.
(B) 14 min. 52 sec.
(C) 14 min. 58 sec.
(D) 16 min. 6 sec.
(E) 16 min. 12 sec.

Hopefully, you’ve noticed that this question is testing the same simple concept that I use when introducing percent problems to my class. And yet, in my experience, a solid majority of students are stumped by this problem. The reason, I suspect, is twofold. First, that figure – 24 min. 18 sec. – is decidedly unfriendly. Painful math often lends itself to careless mistakes and can easily trigger a panic response. Second, anxiety causes us to work faster, and when we work faster, we’re often unable to recognize patterns that would be clearer to us if we were calm.

There’s interesting research on this. Psychologists, knowing that the color red prompts an anxiety response and that the color blue has a calming effect, conducted a study in which test-takers had to answer math questions – the questions were given to some subjects on paper with a red background and to other subjects on paper with a blue background. (The control group had questions on standard white paper.) The red anxiety-producing background noticeably lowered scores and the calming blue background boosted scores.

Now, the GMAT doesn’t give you a red background, but it does give you unfriendly-seeming numbers that likely have the same effect. So, this question is as much about psychology as it is about mathematical proficiency. Our job is to take a deep breath or two and rein in our anxiety before we proceed.

If Dara has completed 10% of her workout, we know she has 90% of her workout remaining. So, that 24 min. 18 sec. presents 90% of her total workout. If we designate her total workout time as “t,” we end up with the following equation:

24 min. 18 sec. = 0.90t

Let’s work with fractions to solve. 18 seconds is 18/60 minutes, which simplifies to 3/10 minutes. 0.9 is 9/10, so we can rewrite our equation as:

24 + 3/10 = (9/10)t
(243/10) = (9/10)t
(243/10)*(10/9) = t
27 = t

Not so bad. Dara’s full workout is 27 minutes long.

We want to know how much time is remaining when Dara has completed 40% of her workout. Well, if she’s completed 40% of her workout, we know she has 60% of her workout remaining. If her full workout is 27 minutes, then 60% of this value is 0.60*27 = (3/5)*27 = 81/5 = 16 + 1/5, or 16 minutes 12 seconds. And we’ve got our answer: E.

Now, let’s say you get this problem with 20 seconds remaining on the clock and you simply don’t have time to solve it properly. Let’s estimate.

Say, instead of 24 min 18 seconds remaining, Dara had 24 minutes remaining (so we know we’re going to underestimate the answer). If that’s 90% of her workout time, 24 = (9/10)t, or 240/9 = t.

We want 60% of this, so we want (240/9)*(3/5).

Because 240/5 = 48 and 9/3 = 3, (240/9)*(3/5) = 48/3 = 16.

We know that the correct answer is over 16 minutes and that we’ve significantly underestimated – makes sense to go with E.

Takeaway: Don’t let the question-writer trip you up with figures concocted to make you nervous. Take a breath, and remember that the concepts being tested are the same ones that, when boiled down to their essence, are a breeze when we’re calm.

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

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

How to Use Pronoun Substitution to Answer GMAT Sentence Correction Questions

SAT/ACTIt was around the time my daughter was born that my wife and I began to have pronoun fights. A certain amount of ambiguity is hard-wired into all language, so when you combine the complexity of English with a healthy dose of sleep deprivation, commands like “put it over there,” become intolerable. What is “it?” Where is “there?” (And why are we fighting over pronoun ambiguity when there’s a screaming child we’re not attending to?)

Lest you fear for the stability of our marriage, rest assured, dear reader, these fights were not hard to resolve – all we had to do was substitute the noun we intended the pronoun to refer to, and suddenly the intolerably vague directive became an unmistakable clear request. There’s a lesson here for the GMAT.

Because pronouns are so common, there’s no avoiding their usage on Sentence Correction questions, and the best way to avoid getting thrown off by them is to substitute in whatever noun or noun phrase these pronouns appear to be referring to. This has two benefits: first, we’ll be better able to assess whether the pronoun is used correctly, should it appear in the underlined portion of the sentence. And secondly, it will help us to understand the meaning of the sentence so that we can properly evaluate whether whatever we choose is, in fact, logical.

Take the following question, for example:

According to public health officials, in 1998 Massachusetts became the first state in which more babies were born to women over the age of thirty than under it.

(A) than
(B) than born
(C) than they were
(D) than there had been
(E) than had been born

Notice that this sentence ends with the pronoun “it.” Because the “it” is not part of the underlined portion of the sentence, test-takers will often pay the word scant attention. This is certainly true of many students who have brought this sentence to my attention. Pretty much all of them selected B as the correct answer and were astonished to learn they were wrong.

So, let’s look at the relevant clause with answer choice B: more babies were born to women over the age of thirty than born under it. This sounded fine to the students’ ears. When I asked them what “it” referred to, however, they quickly recognized that “it” refers to the preceding noun phrase “the age of thirty.” I then asked them to reread the clause, but this time, to substitute the referent in place of the pronoun. The phrase read as follows: more babies were born to women over the age of thirty than born under [the age of thirty.]

The problem was immediately apparent. This clause compares babies born to women over the age of thirty to babies born under the age of thirty! Hopefully, it goes without saying that the writer did not intend to persuade the reader that some population of babies were under the age of 30 when they were born.

Clearly, B is incorrect. Once we substitute the referent for the pronoun, we can quickly see that only answer choice, A, makes any logical sense: more babies were born to women over the age of thirty than under the [age of thirty.]  We’re simply comparing the number of babies born to women in two different age groups. Not only is A the shortest and cleanest answer choice, it’s also the most coherent option. So, we have our answer.

Let’s try another one:

In 1979 lack of rain reduced India’s rice production to about 41 million tons, nearly 25 percent less than those of the 1978 harvest

(A) less than those of the 1978 harvest
(B) less than the 1978 harvest
(C) less than 1978
(D) fewer than 1978
(E) fewer than that of India’s 1978 harvest

Notice the “those” in the underlined portion. What is “those” referring to? It must be referring to some plural antecedent, so our only real option is “tons.” Let’s take a look at the sentence with “tons” in place of “those.”

In 1979 lack of rain reduced India’s rice production to about 41 million tons, nearly 25 percent less than [the tons] of the 1978 harvest. 

Do we want to compare the rice production in 1979 to the “tons” in 1978? Of course not. We want to compare one year’s production to another year’s production, or one harvest to another.

C and D both compare one year’s production to a year, rather than to the production of another year, so those are both wrong.

E gives us another pronoun – this time we have “that,” which must have a singular antecedent. It seems to refer to “rice production,” so let’s make that substitution.

In 1979 lack of rain reduced India’s rice production to about 41 million tons, nearly 25 percent fewer than [the rice production] of India’s 1978 harvest.

Well, this makes no sense – we use “fewer” to compare countable items, so we certainly wouldn’t say that one year’s production is “fewer” than another year’s production. So, E is also out.

This leaves us with answer choice B, which logically compares one year’s harvest to another year’s harvest.

Takeaway: Anytime you see a pronoun in a Sentence Correction sentence, always substitute the referent in place of the pronoun. This practice will clarify the meaning of the sentence and prevent the kind of ambiguity that leads to both incorrect answers and marital discord.

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

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

GMAT Tip of the Week: Don’t Be the April Fool with Trap Answers!

GMAT Tip of the WeekToday, people across the world are viewing news stories and emails with a skeptical eye, on guard to ensure that they don’t get April fooled. Your company just released a press release about a new initiative that would dramatically change your workload? Don’t react just yet…it could be an April Fool’s joke.

But in case your goal is to leave that job for the greener pastures of business school, anyway, keep that April Fool’s Day spirit with you throughout your GMAT preparation. Read skeptically and beware of the way too tempting, way too easy answer.

First let’s talk about how the GMAT “fools” you. At Veritas Prep we’ve spent years teaching people to “Think Like the Testmaker,” and the only pushback we’ve ever gotten while talking with the testmakers themselves has been, “Hey! We’re not deliberately trying to fool people.”

So what are they trying to do? They’re trying to reward critical thinkers, and by doing so, there need to be traps there for those not thinking as critically. And that’s an important way to look at trap answers – the trap isn’t set in a “gotcha” fashion to be cruel, but rather to reward the test-taker who sees the too-good-to-be-true answer as an invitation to dig a little deeper and think a little more critically. One man’s trash is another man’s treasure, and one examinee’s trap answer is another examinee’s opportunity to showcase the reasoning skills that business schools crave.

With that in mind, consider an example, and try not to get April fooled:

What is the greatest prime factor of 12!11! + 11!10! ?

(A) 2
(B) 7
(C) 11
(D) 19
(E) 23

If you’re like many – more than half of respondents in the Veritas Prep Question Bank – you went straight for the April Fool’s answer. And what’s even more worrisome is that most of those test-takers who choose trap answer C don’t spend very long on this problem. They see that 11 appears in both additive terms, see it in the answer choice, and pick it quickly. But that’s exactly how the GMAT fools you – the trap answers are there for those who don’t dig deeper and think critically. If 11 were such an obvious answer, why are 19 and 23 (numbers greater than any value listed in the expanded versions of those factorials 12*11*10*9…) even choices? Who are they fooling with those?

If you get an answer quickly it doesn’t necessarily mean that you’re wrong, but it should at least raise the question, “Am I going for the fool’s answer here?”. And that should encourage you to put some work in. Here, the operative verb even appears in the question stem – you have to factor the addition into multiplication, since factors are all about multiplication/division and not addition/subtraction. When you factor out the common 11!:

11!(12! + 10!)

Then factor out the common 10! (12! is 12*11*10*9*8… so it can be expressed as 12*11*10!):

11!10!(12*11 + 1)

You end up with 11!*10!(133). And that’s where you can check 19 and 23 and see if they’re factors of that giant multiplication problem. And since 133 = 19*7, 19 is the largest prime factor and D is, in fact, the correct answer.

So what’s the lesson? When an answer comes a little too quickly to you or seems a little too obvious, take some time to make sure you’re not going for the trap answer.

Consider this – there are only four real reasons that you’ll see an easy problem in the middle of the GMAT:

1) It’s easy. The test is adaptive and you’re not doing very well so they’re lobbing you softballs. But don’t fear! This is only one of four reasons so it’s probably not this!

2) Statistically it’s fairly difficult, but it’s just easy to you because it’s something you studied well for, or for which you had a great junior high teacher. You’re just that good.

3) It’s not easy – you’re just falling for the trap answer.

4) It’s easy but it’s experimental. The GMAT has several problems in each section called “pretest items” that do not count towards your final score. These appear for research purposes (they’re checking to ensure that it’s a valid, bias-free problem and to gauge its difficulty), and they appear at random, so even a 780 scorer will likely see a handful of below-average difficulty problems.

Look back at that list and consider which are the most important. If it’s #1, you’re in trouble and probably cancelling your score or retaking the test anyway. And for #4 it doesn’t matter – that item doesn’t count. So really, the distinction that ultimately matters for your business school future is whether a problem like the example above fits #2 or #3.

If you find an answer a lot more quickly than you think you should, use some of that extra time to make sure you haven’t fallen for the trap. Engage those critical thinking skills that the GMAT is, after all, testing, and make sure that you’re not being duped while your competition is being rewarded. Avoid being the April Fool, and in a not-too-distant September you’ll be starting classes at a great school.

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

By Brian Galvin.

GMAT Tip of the Week: Your GMAT New Year’s Resolution

GMAT Tip of the WeekHappy New Year! If you’re reading this on January 1, 2016, chances are you’ve made your New Year’s resolution to succeed on the GMAT and apply to business school. (Why else read a GMAT-themed blog on a holiday?) And if so, you’re in luck: anecdotally speaking, students who study for and take the GMAT in the first half of the year, well before any major admissions deadlines, tend to have an easier time grasping material and taking the test. They have the benefit of an open mind, the time to invest in the process, and the lack of pressure that comes from needing a massive score ASAP.

This all relates to how you should approach your New Year’s resolution to study for the GMAT. Take advantage of that luxury of time and lessened-pressure, and study the right way – patiently and thoroughly.

What does that mean? Let’s equate the GMAT to MBA admissions New Year’s resolution to the most common New Year’s resolution of all: weight loss.

Someone with a GMAT score in the 300s or 400s is not unlike someone with a weight in the 300s or 400s (in pounds). There are easy points to gain just like there are easy pounds to drop. For weight loss, that means sweating away water weight and/or crash-dieting and starving one’s self as long as one can. As boxers, wrestlers, and mixed-martial artists know quite well, it’s not that hard to drop even 10 pounds in a day or two…but those aren’t long-lasting pounds to drop.

The GMAT equivalent is sheer memorization score gain. Particularly if your starting point is way below average (which is around 540 these days), you can probably memorize your way to a 40-60 point gain by cramming as many rules and formulas as you can. And unlike weight loss, you won’t “give those points” back. But here’s what’s a lot more like weight loss: if you don’t change your eating/study habits, you’re not going to get near where you want to go with a crash diet or cram session. And ultimately those cram sessions can prove to be counterproductive over the long run.

The GMAT is a test not of surface knowledge, but of deep understanding and of application. And the the problem with a memorization-based approach is that it doesn’t include much understanding or application. So while there are plenty of questions in the below-average bucket that will ask you pretty directly about a rule or relationship, the problems that you’ll see as you attempt to get to above average and beyond will hinge more on your ability to deeply understand a concept or to apply a concept to a situation where you might not see that it even applies.

So be leery of the study plan that nets you 40-50 points in a few weeks (unless of course that 40 takes you from 660 to 700) but then holds you steady at that level because you’re only remembering and not *knowing* or *understanding*. When you’re studying in January for a test that you don’t need to take until the summer or fall, you have the luxury of starting patiently and building to a much higher score.

Your job this next month isn’t to memorize every rule under the sun; it’s to make sure you fundamentally understand the building blocks of arithmetic, algebra, logic, and grammar as it relates to meaning. Your score might not jump as high in January, but it’ll be higher when decision day comes later this fall.

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, Google+ and Twitter!

By Brian Galvin.

How to Make Rate Questions Easy on the GMAT

Integrated Reasoning StrategiesI recently wrote about the reciprocal relationship between rate and time in “rate” questions. Occasionally, students will ask why it’s important to understand this particular rule, given that it’s possible to solve most questions without employing it.

There are two reasons: the first is that knowledge of this relationship can convert incredibly laborious arithmetic into a very straightforward calculation. And the second is that this same logic can be applied to other types of questions. The goal, when preparing for the GMAT, isn’t to internalize hundreds of strategies; it’s to absorb a handful that will prove helpful on a variety of questions.

The other night, I had a tutoring student present me with the following question:

It takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour.  How many minutes will it take Carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?

(A) 26

(B) 33

(C) 36

(D) 44

(E) 48

This question doesn’t seem that hard, conceptually speaking, but here is how my student attempted to do it: first, he saw that the time to complete the trip was given in minutes and the rate of the trip was given in hours so he did a simple unit conversion, and determined that it took Carlos (9/60) hours to complete his trip.

He then computed the distance of the trip using the following equation: (9/60) hours * 22 miles/hour = (198/60) miles. He then set up a second equation: 6miles/hour * T = (198/60) miles. At this point, he gave up, not wanting to wrestle with the hairy arithmetic. I don’t blame him.

Watch how much easier it is if we remember our reciprocal relationship between rate and time. We have two scenarios here. In Scenario 1, the time is 9 minutes and the rate is 22 mph. In Scenario 2, the rate is 6 mph, and we want the time, which we’ll call ‘T.” The ratio of the rates of the two scenarios is 22/6. Well, if the times have a reciprocal relationship, we know the ratio of the times must be 6/22. So we know that 9/T = 6/22.

Cross-multiply to get 6T = 9*22.

Divide both sides by 6 to get T = 9*22/6.

We can rewrite this as T = (9*22)/(3*2) = 3*11 = 33, so the answer is B.

The other point I want to stress here is that there isn’t anything magical about rate questions. In any equation that takes the form a*b = c, a and b will have a reciprocal relationship, provided that we hold c constant. Take “quantity * unit price = total cost”, for example. We can see intuitively that if we double the price, we’ll cut the quantity of items we can afford in half. Again, this relationship can be exploited to save time.

Take the following data sufficiency question:

Pat bought 5 lbs. of apples. How many pounds of pears could Pat have bought for the same amount of money? 

(1) One pound of pears costs $0.50 more than one pound of apples. 

(2) One pound of pears costs 1 1/2 times as much as one pound of apples. 

Statement 1 can be tested by picking numbers. Say apples cost $1/pound. The total cost of 5 pounds of apples would be $5.  If one pound of pears cost $.50 more than one pound of apples, then one pound of pears would cost $1.50. The number of pounds of pears that could be purchased for $5 would be 5/1.5 = 10/3. So that’s one possibility.

Now say apples cost $2/pound. The total cost of 5 pounds of apples would be $10. If one pound of pears cost $.50 more than one pound of apples, then one pound of pears would cost $2.50. The number of pounds of pears that could be purchased for $10 would be 10/2.5 = 4. Because we get different results, this Statement alone is not sufficient to answer the question.

Statement 2 tells us that one pound of pears costs 1 ½ times (or 3/2 times) as much as one pound of apples. Remember that reciprocal relationship! If the ratio of the price per pound for pears and the price per pound for apples is 3/2, then the ratio of their respective quantities must be 2/3. If we could buy five pounds of apples for a given cost, then we must be able to buy (2/3) * 5 = (10/3) pounds of pears for that same cost. Because we can find a single unique value, Statement 2 alone is sufficient to answer the question, and we know our answer must be B.

Takeaway: Remember that in “rate” questions, time and rate will have a reciprocal relationship, and that in “total cost” questions, quantity and unit price will have a reciprocal relationship. Now the time you save on these problem-types can be allocated to other questions, creating a virtuous cycle in which your time management, your accuracy, and your confidence all improve in turn.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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

Success Story Part 3: "The Final Days, and (*eek*)… Results."

(This is the third in a series of blog posts in which Julie DeLoyd, a Veritas Prep GMAT alumna-turned-instructor, will tell the story of her experience through the MBA admissions process. Julie will begin her MBA program at Chicago Booth this fall. You can also read Part 1 and Part 2 to learn Julie’s whole story.)

I had invested 42 hours of summer evenings learning about the ins and outs of the GMAT, and the time finally came for me to do the work on my own. I booked my test date for 5 weeks after my class ended, giving me enough time to go on tour one last time before I really hunkered down.

My band toured the Midwest for about 10 days, driving on vegetable oil fuel and breaking a lot of strings along the way. While another girl was driving, I’d pull out my Veritas Prep books and work on a few problems each day. I wasn’t absorbing too much, honestly, but it was good to keep my GMAT brain active. When I dropped off the girls at the airport, it was time to really get down to business. I set up a study schedule for myself for the last 3 weeks.

21 days to go, with 4 practice tests completed, my schedule looked something like this:
Monday Morning: Sentence Correction
Monday Afternoon: Practice Test

Tuesday Morning:
Go over results of Practice Test
Tuesday Afternoon: Geometry

Wednesday Morning:
Reading Comp
Wednesday Afternoon: Practice test

Thursday Morning:
Go over results of Practice Test
Thursday Afternoon: Critical Reasoning

Friday Morning: Combinatorics and Probability
Friday Afternoon: Problem Solving

Saturday Morning: Practice Test
Saturday Afternoon: Go over results

Sunday: Eat good food, Ride my bike, Spend time with dogs and lovey

Yes, it was a little intense, but it wasn

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