GMAT Rate Questions: Tackling Problems with Multiple Components

stopwatch-620A few posts ago, I tackled rate/work questions, which are invariably a source of consternation for GMAT test-takers. On the latest official practice tests that GMAC has released, these questions showed up with surprising frequency, so I thought it might be worthwhile to tackle a challenging incarnation of this question type: one in which a single machine begins a project and then multiple machines complete the partially-finished work.

To review, the key for dealing with this type of question is to apply the following rules:

  1. Rate * Time = Work
  2. Rates are additive in work questions.
  3. Rate and time have a reciprocal relationship.

For the questions involving partially completed jobs, we’ll throw in the addendum that a completed job can be designated as “1”’

And that’s it!

Here’s a question I saw on my recent practice test:

Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump Z, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?

A) 6
B) 12
C) 15
D) 18
E) 24

Okay, deep breath. Recall our three aforementioned rules. Next, let’s designate the rates for the pumps as x, y, and z, respectively.

If pump x can pump out ¼ of the water in 2 hours, then it would take 4*2 = 8 hours to pump out all the water alone. If pump x can complete 1 tank in 8 hours, then x = 1/8.

If x removes ¼ of the water on its own, then all three pumps working together have to remove the ¾ of the water left in the tank. We’re told that together they can do this in 3 hours. If x, y, and z together can do ¾ of the work in 3 hours, then x + y + z = (¾)/3 = 3/12 = ¼.

We’re told that y, alone, could have pumped out the rest of the water in 18 hours – again, there was ¾ of a tank left, so y = (¾)/18 = 1/24.

To summarize, we know that x = 1/8, y = 1/24, and x + y + z = ¼;  Not so hard to solve for z, right?

1/8 + 1/24 + z = ¼

Multiply everything by 24, and we get:

3 + 1 + 24z = 6

24z = 2

z = 1/12.

That’s z’s rate. If rate and time have a reciprocal relationship, we know that it would take z 12 hours to pump out all the water of one tank alone. The answer is, therefore, B.

Takeaway: The joy of seeing new material from GMAC (Is joy the right word?) is the realization that no matter how many additional layers of complexity the question-writers throw at us, the old verities hold true. So when you see tough questions, slow down. Remind yourself that the strategies you’ve cultivated will unlock even the toughest problems. Then, dive in and discover, yet again, that these questions are never quite as hard as they appear at first glance.

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.

Avoid Obtaining the Wrong Values in Percent Increase Questions

stressed-studentMany test takers make mistakes in percent increase quantitative GMAT questions, not because they do not understand the principle of percent increase, but rather, because they don’t evaluate the correct values.

A quick recap: percent increase questions can be identified (often literally) by the words “percent increase,” and tend to be word problems that don’t read in the most straightforward manner. The first step to take when working towards answering these questions is to be cautious and evaluate them carefully.

The second step is to, of course, use the percent increase formula – (new value – initial value) / (initial value) x 100%.

Let’s start by going through a sample GMAT practice problem:

In 2005, 25 percent of the math department’s 40 students were female, and in 2007, 40 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?

A) 15%
B) 50%
C) 62.5%
D) 115%
E) 160%

At first can be difficult to determine what the answer is for this question, but keep in mind that the best place to start looking is in the last sentence and/or the actual question that is posed. In this case, the new value is the number of female students in 2007, “the number of female students in the department?”

By working backwards through this problem, we would take  40% of 65 (our final value), which we can easily calculate as 0.4*65 (or 2/5*65), giving us a total of 26 students in 2007.

Our initial value must then be the number of female students in 2005, which we can get by calculating 25% of 40. 0.25*40 (or 1/4*40) leaves us with a total of 10 female students in 2005.

Breaking up the question up into smaller, more manageable chunks gives us the ability to plug 26 and 10 into the percent increase formula – (26‐10)/10 = 16/10 = 1.6 = 160%. Therefore, the correct answer is E.

This strategy of not trying to figure out the conclusion without evaluating all the separate parts of the question is important to tackle percent change GMAT problems, but can be applied across a variety of quantitative questions. Understanding that these questions can be much more manageable, and are more about strategy versus understanding complex math concepts, is the key to success on the Quantitative Section.

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 Ashley Triscuit, a Veritas Prep GMAT instructor based in Boston.

So, You’re Terrible at Integrated Reasoning…

08fba0fSince its release on the June 2012 exam, the Integrated Reasoning portion of the GMAT has had some test takers stumped. This 30-minute, 12 question section is oddly scored on a 1 to 8 scale, and no partial credit is given, even for multi-part, multi-answer questions.

For the past several years, it was a matter of debate as to whether business schools evaluated applicants on the basis of the Integrated Reasoning Section. Admissions offices can be slow to adapt to changes in standardized tests, waiting for enough points of comparison to consider whether the change corresponds with other ways that applicants are assessed. But in the past 1-2 MBA admissions cycles, it has become apparent that admissions teams are ready to actively add the Integrated Reasoning Section as a factor in their assessments.

But this tough nut of a section is not inundated with years of Official Guide and test-prep-company-generated questions like the Quantitative and Verbal Sections. After taking a practice test or two, you may find yourself scoring a 2/8 or 3/8 and completely at a loss on how to improve your Integrated Reasoning score.

The first step you can take to improve your IR score is understanding what types of questions to expect on the Integrated Reasoning Section, and then adjust your approach to each question with a corresponding appropriate strategy. The Integrated Reasoning questions can be bucketed into four categories:

  1. Table Analysis: sorting given tables and making the most of information presented
  2. Graphics Interpretation: reading and interpreting a graph
  3. Multi-Source Reasoning: using all the given information to assess statements
  4. Two-Part Analysis: determine the correctness of two parts of a question (all parts need to be selected correctly, with no partial credit given!)

What many test takers fail to recognize that that the IR Section is not necessarily its own unique section, but rather, it is a “summary” section – you can apply all the strategies you have learned for the Quantitative and Verbal Sections to these types of questions. Anticipation, process of elimination, etc. Integrated Reasoning is multi-faceted, as should be your corresponding strategies.

The next step is practice, practice, practice with the resources you do have available. Timing is hands-down the biggest challenge for test takers on this section, so make sure you’ve completed all the gimmes that the MBA.com website provides (with 48 questions recently released for additional practice).

And if you feel you need more help preparing for the IR Section, consider checking out Veritas Prep’s GMAT course offerings – we were the leader in test preparation companies anticipating strategies and providing dedicated Integrated Reasoning practice. Assess areas that you have made careless mistakes, ways you could better sort tables and charts, and other areas where you could have gotten to the conclusion more readily over being mired down into nitty gritty, and unnecessary, details.

With a bit of understanding and preparation, and figuring out how you are able to best read, assess, review, and interpret tables and information, you should be able to edge closer to the coveted 8/8 IR score.

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 Ashley Triscuit, a Veritas Prep GMAT instructor based in Boston.

Quarter Wit, Quarter Wisdom: Why Critical Reasoning Needs Your Complete Attention on the GMAT!

Quarter Wit, Quarter WisdomLet’s look at a tricky and time consuming official Critical Reasoning question today. We will learn how to focus on the important aspects of the question and quickly evaluate our answer choices:

Tiger beetles are such fast runners that they can capture virtually any nonflying insect. However, when running toward an insect, a tiger beetle will intermittently stop and then, a moment later, resume its attack. Perhaps the beetles cannot maintain their pace and must pause for a moment’s rest; but an alternative hypothesis is that while running, tiger beetles are unable to adequately process the resulting rapidly changing visual information and so quickly go blind and stop. 

Which of the following, if discovered in experiments using artificially moved prey insects, would support one of the two hypotheses and undermine the other? 

(A) When a prey insect is moved directly toward a beetle that has been chasing it, the beetle immediately stops and runs away without its usual intermittent stopping. 
(B) In pursuing a swerving insect, a beetle alters its course while running and its pauses become more frequent as the chase progresses.
(C) In pursuing a moving insect, a beetle usually responds immediately to changes in the insect’s direction, and it pauses equally frequently whether the chase is up or down an incline. 
(D) If, when a beetle pauses, it has not gained on the insect it is pursuing, the beetle generally ends its pursuit. 
(E) The faster a beetle pursues an insect fleeing directly away from it, the more frequently the beetle stops.

First, take a look at the argument:

  • Tiger beetles are very fast runners.
  • When running toward an insect, a tiger beetle will intermittently stop and then, a moment later, resume its attack.

There are two hypotheses presented for this behavior:

  1. The beetles cannot maintain their pace and must pause for a moment’s rest.
  2. While running, tiger beetles are unable to adequately process the resulting rapidly changing visual information and so quickly go blind and stop.

We need to support one of the two hypotheses and undermine the other. We don’t know which one will be supported and which will be undermined. How will we support/undermine a hypothesis?

The beetles cannot maintain their pace and must pause for a moment’s rest.

Support: Something that tells us that they do get tired. e.g. going uphill they pause more.

Undermine: Something that says that fatigue plays no role e.g. the frequency of pauses do not increase as the chase continues.

While running, tiger beetles are unable to adequately process the resulting rapidly changing visual information and so quickly go blind and stop.

Support: Something that says that they are not able to process changing visual information e.g. as speed increases, frequency of pauses increases.

Undermine: Something that says that they are able to process changing visual information e.g. it doesn’t pause on turns.

Now, we need to look at each answer choice to see which one supports one hypothesis and undermines the other. Focus on the impact each option has on our two hypotheses:

(A) When a prey insect is moved directly toward a beetle that has been chasing it, the beetle immediately stops and runs away without its usual intermittent stopping.

This undermines both hypotheses. If the beetle is able to run without stopping in some situations, it means that it is not a physical ailment that makes him take pauses. He is not trying to catch his breath – so to say – nor is he adjusting his field of vision.

(B) In pursuing a swerving insect, a beetle alters its course while running and its pauses become more frequent as the chase progresses.

If the beetle alters its course while running, it is obviously processing changing visual information and changing its course accordingly while running. This undermines the hypothesis “it cannot process rapidly changing visual information”. However, if the beetle pauses more frequently as the chase progresses, it is tiring out more and more due to the long chase and, hence, is taking more frequent breaks. This supports the hypothesis, “it cannot maintain its speed and pauses for rest”.

Answer choice B strengthens one hypothesis and undermines the other. This must be the answer, but let’s check our other options, just to be sure:

(C) In pursuing a moving insect, a beetle usually responds immediately to changes in the insect’s direction, and it pauses equally frequently whether the chase is up or down an incline.

This answer choice undermines both hypotheses. If the beetle responds immediately to changes in direction, it is able to process changing visual information. In addition, if the beetle takes similar pauses going up or down, it is not the effort of running that is making it take the pauses (otherwise, going up, it would have taken more pauses since it takes more effort going up).

(D) If, when a beetle pauses, it has not gained on the insect it is pursuing, the beetle generally ends its pursuit.

This answer choice might strengthen the hypothesis that the beetle is not able to respond to changing visual information since it decides whether it is giving up or not after pausing (in case there is a certain stance that tells us that it has paused), but it doesn’t actually undermine the hypothesis that the beetle pauses to rest. It is very possible that it pauses to rest, and at that time assesses the situation and decides whether it wants to continue the chase. Hence, this option doesn’t undermine either hypothesis and cannot be our answer.

(E) The faster a beetle pursues an insect fleeing directly away from it, the more frequently the beetle stops.

This answer choice strengthens both of the hypotheses. The faster the beetle runs, the more rest it would need, and the more rapidly visual information would change causing the beetle to pause. Because this option does not undermine either hypothesis, it also cannot be our answer.

Only answer choice B strengthens one hypothesis and undermines the other, therefore, our answer must be B.

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

How to Simplify Sequences on the GMAT

SAT/ACTThe GMAT loves sequence questions. Test-takers, not surprisingly, do not feel the same level of affection for this topic. In some ways, it’s a peculiar reaction. A sequence is really just a set of numbers. It may be infinite, it may be finite, but it’s this very open-endedness, this dizzying level of fuzzy abstraction, that can make sequences so difficult to mentally corral.

If you are one of the many people who fear and dislike sequences, your main consolation should come from the fact that the main weapon in the question writer’s arsenal is the very fear these questions might elicit. And if you have been a reader of this blog for any length of time, you know that the best way to combat this anxiety is to dive in and convert abstractions into something concrete, either by listing out some portion of the sequence, or by using the answer choices and working backwards.

Take this question for example:

For a certain set of numbers, if x is in the set, then x – 3 is also in the set. If the number 1 is in the set, which of the following must also be in the set? 

I. 4
II. -1
III. -5

A) I only
B) II only
C) III only
D) I and II
E) II and III

Okay, so let’s list out the elements in this set. We know that 1 is in the set. If x= 1, then x – 3 = -2. So -2 is in the set. If x = -2 is in the set, then x – 3 = -5. So -5 is in the set.

By this point, the pattern should be clear: each term is three less than the previous term, giving us a sequence that looks like this: 1, -2, -5, -8, -11….

So we look at our options, and see we that only III is true. And we’re done. That’s it. The answer is C.

Sure, Dave, you may say. That is much easier than any question I’m going to see on the GMAT. First, this is an official question, so I’m not sure where you’re getting the idea that you’d never see a question like this. Second, you’d be surprised by how many test-takers get this wrong.

There is the temptation to assume that if 1 is in the set, then 4 must also be in the set. And note that this is, in fact, a possibility. If x = 4, then x – 3 = 1. But the question asks us what “must be” in the set. So it’s possible that 4 is in our set. But it’s also possible our set begins with 1, in which case 4 would not be included. This little wrinkle is enough to generate a substantial number of incorrect responses.

Still, surely the questions get harder than this. Well, yes. They do. So what are you waiting for? I’m not sure where this testy impatience is coming from, but if you insist:

The sequence a1, a2, a3, . . , an of n integers is such that ak = k if k is odd and ak = -ak-1 if k is even. Is the sum of the terms in the sequence positive?

1) n is odd

2) an is positive

Yikes! Hey, you asked for a harder one. This question looks far more complicated than the previous one, but we can attack it the same way. Let’s establish our sequence:

a1 is the first term in the sequence. We’re told that ak = k if k is odd. Well, 1 is odd, so now we know that a1 = 1. So far so good.

a2 is the second term in the sequence. We’re told that ak = -ak-1 if k is even. 2 is even, so a2 = -a2-1 , meaning that a2 = -a1. Well, we know that a1 = 1, so if a2 = -a1 then a2 = -1.

So, here’s our sequence so far: 1, -1…

Let’s keep going.

a3 is the third term in the sequence. Remember that ak = k if k is odd. 3 is odd, so now we know that a3 = 3.

a4 is the fourth term in the sequence. Remember that ak = -ak-1 if k is even. 4 is even, so a4 = -a4-1 , meaning that a4 = -a3We know that a3 = 3, so if a4 = -a3 then a4 = -3.

Now our sequence looks like this: 1, -1, 3, -3…

By this point we should see the pattern. Every odd term is a positive number that is dictated by its place in the sequence (the first term = 1, the third term = 3, etc.) and every even term is simply the previous term multiplied by -1.

We’re asked about the sum:

After one term, we have 1.

After two terms, we have 1 + (-1) = 0.

After three terms, we have 1 + (-1) + 3 = 3.

After four terms, we have 1 + (-1) + 3 + (-3) = 0.

Notice the trend: after every odd term, the sum is positive. After every even term, the sum is 0.

So the initial question, “Is the sum of the terms in the sequence positive?” can be rephrased as, “Are there an ODD number of terms in the sequence?”

Now to the statements. Statement 1 tells us that there are an odd number of terms in the sequence. That clearly answers our rephrased question, because if there are an odd number of terms, the sum will be positive. This is sufficient.

Statement 2 tells us that an is positive. an is the last term in the sequence. If that term is positive, then, according to the pattern we’ve established, that term must be odd, meaning that the sum of the sequence is positive. This is also sufficient. And the answer is D, either statement alone is sufficient to answer the question.

Takeaway: sequence questions are nothing to fear. Like everything else on the GMAT, the main obstacle we need to overcome is the self-fulfilling prophesy that we don’t know how to proceed, when, in fact, all we need to do is simplify things a bit.

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.

You’re Fooling Yourself: The GMAT is NOT the SAT!

StudentWhile a fair number of GMAT test takers study for and complete the exam a number of years into their professional career (the average age of a B-school applicant is 28, a good 6-7 years removed from their undergraduate graduation), you may be one of the ambitious few who is studying for the GMAT during, or immediately following, your undergraduate studies.

There are pros and cons to applying to business school entry straight out of undergraduate – your application lacks the core work experience that many of the higher-tier programs prefer, but unlike the competition, you have not only taken a standardized test in the past 6 years, but you are also (likely) still in the studying mindset and know (versus trying to remember) exactly what it takes to prepare for a difficult exam.

However, you may also fall into a common trap that many younger test takers find themselves in – you decide to tackle the GMAT like your old and recent friend, the SAT.

Now, are there similarities between the GMAT and SAT? Of course.

For starters, the SAT and GMAT are both multiple-choice standardized exams. The math section of the SAT covers arithmetic, geometry, and algebra, just like the quantitative section of the GMAT, with some overlap in statistics and probability. Both exams test a core, basic understanding of English grammar, and ask you to answer questions based on your comprehension of dry, somewhat complex reading passages. The SAT and GMAT also both require you write essays (although the essay on the SAT is now optional), and timing and pacing are issues on both exams, though perhaps more so on the GMAT.

But this is largely where the overlap ends. So, does that mean everything you know and prepped for the SAT should be thrown out the window?

Not necessarily, but it does require a fundamental shift in thinking. While applying your understanding of the Pythagorean Theorem, factorization, permutations, and arithmetic sequences from the SAT will certainly help you begin to tackle GMAT quantitative questions, there are key differences in what the GMAT is looking to assess versus the College Board, and with that, the strategy in tackling these questions should also be quite different.

Simply put, the GMAT is testing how you think, not what you know. This makes sense, when you think about what types of skills are required in business school and, eventually, in the management of business and people. GMAC doesn’t hide what the GMAT is looking to assess – in fact, goals of the GMAT’s assessment are clearly stated on its website:

The GMAT exam is designed to test skills that are highly important to business and management programs. It assesses analytical writing and problem-solving abilities, along with the data sufficiency, logic, and critical reasoning skills that are vital to real-world business and management success. In June 2012, the GMAT exam introduced Integrated Reasoning, a new section designed to measure a test taker’s ability to evaluate information presented in new formats and from multiple sources─skills necessary for management students to succeed in a technologically advanced and data-rich world.

To successfully show that you are a candidate worth considering, in your preparation for the exam, make sure you consider what the right strategy and approach will be. Strategy, strategy, strategy. You need to understand which rabbit holes the GMAT can take you down, what tricks not to fall for (especially via misdirection), and how identification of question types can best inform the next steps you take.

An additional, and really, really important point is to keep in mind is that the GMAT is a computer-adaptive exam, not a pen-and-paper test.

Computer-adaptive means that your answer selection dictates the difficulty level of the next question – stacking itself up to a very accurate assessment of how easily you are able to answer easy, medium, and hard questions. Computer-adaptive also means you are not able to skip around, or go back to questions… including the reading comprehension ones. Just like on any game show, you must select your final answer before moving on.

As a computer-adaptive test, the GMAT not only punishes pacing issues, but can be even more detrimental to those who rush and make careless mistakes in the beginning. To wage war against the CAT format, test takers must be careful and methodical in assessing and answering test questions correctly.

Bottom line: don’t treat the GMAT like the SAT, or assume that because you did well on the SAT, you will also do so on the GMAT (or, vice versa). Make sure you are aware of the components of the GMAT that are different and where the similarities between the two tests end.

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 Ashley Triscuit, a Veritas Prep GMAT instructor based in Boston.

Solving GMAT Standard Deviation Problems By Using as Little Math as Possible

GMATThe other night I taught our Statistics lesson, and when we got to the section of class that deals with standard deviation, there was a familiar collective groan – not unlike the groan one encounters when doing compound interest, or any mathematical concept that, when we learned it in school, involved an intimidating-looking formula.

So, I think it’s time for me to coin an axiom: the more painful the traditional formula associated with a given topic, the simpler the actual calculations will be on the GMAT. (Please note, though the axiom is awaiting official mathematical verification by Veritas’ hard-working team of data scientists, the anecdotal evidence in support of the axiom is overwhelming.)

So, let’s talk standard deviation. If you’re like my students, your first thought is to start assembling a list of increasingly frantic questions: Do we need to know that horrible formula I learned in Stats class? (No.) Do we need to know the relationship between variance and Standard deviation? (You just need to know that there is a relationship, and that if you can solve for one, you can solve for the other.) Etc.

So, rather than droning on about what we don’t need to know, let’s boil down what we do need to know about standard deviation. The good news – it isn’t much. Just make sure you’ve internalized the following:

  • The standard deviation is a measure of the dispersion the elements of the set around mean. The farther away the terms are from the mean, the larger the standard deviation.
  • If we were to increase or decrease each element of the set by “x,” the standard deviation would remain unchanged.
  • If we were to multiply each element of the set by “x,” the standard deviation would also be multiplied by “x.”
  • If the mean of a set is “m” and the standard deviation is “d,” then to say that something is within 3 standard deviations of a set is to say that it falls within the interval of (m – 3d) to (m + 3d.) And to say that something is within 2 standard deviations of the mean is to say that it falls within the interval of (m – 2d) to (m + 2d.)

That’s basically it. Not anything to get too worked up about. So, let’s see some of these principles in action to substantiate the claim that we won’t have to do too much arithmetical grinding on these types of questions:

If d is the standard deviation of x, y, z, what is the standard deviation of x+5, y+5, z+5 ? 

A) d
B) 3d
C) 15d
D) d+5
E) d+15

If our initial set is x, y, z, and our new set is x+5, y+5, and z+5, then we’re adding the same value to each element of the set. We already know that adding the same value to each element of the set does not change the standard deviation. Therefore, if the initial standard deviation was d, the new standard deviation is also d. We’re done – the answer is A. (You can see this with a simple example. If your initial set is {1, 2, 3} and your new set is {6, 7, 8} the dispersion of the set clearly hasn’t changed.)

Surely the questions get harder than this, you say. They do, but if you know the aforementioned core concepts, they’re all quite manageable. Here’s another one:

Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end? 

1) For each tank, 30% of water at the beginning was removed
2) The average volume of water in the tanks at the end was 63 gallons 

We know the initial standard deviation. We want to know if it’s possible to determine the new standard deviation after water is removed. To the statements we go!

Statement 1: If 30% of the water is removed from each tank, we know that each term in the set is multiplied by the same value: 0.7. Well, if each term in a set is multiplied by 0.7, then the standard deviation of the set is also multiplied by 0.7. If the initial standard deviation was 10 gallons, then the new standard deviation would be 10*(0.7) = 7 gallons. And we don’t even need to do the math – it’s enough to see that it’s possible to calculate this number. Therefore, Statement 1 alone is sufficient.

Statement 2: Knowing the average of a set is not going to tell us very much about the dispersion of the set. To see why, imagine a simple case in which we have two tanks, and the average volume of water in the tanks is 63 gallons. It’s possible that each tank has exactly 63 gallons and, if so, the standard deviation would be 0, as everything would equal the mean. It’s also possible to have one tank that had 126 gallons and another tank that was empty, creating a standard deviation that would, of course, be significantly greater than 0. So, simply knowing the average cannot possibly give us our standard deviation. Statement 2 alone is not sufficient to answer the question.

And the answer is A.

Maybe at this point you’re itching for more of a challenge. Let’s look at a slightly tougher one:

7.51; 8.22; 7.86; 8.36 
8.09; 7.83; 8.30; 8.01
7.73; 8.25; 7.96; 8.53 

A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviations of the mean? 

A)Four
B) Six
C) Nine
D) Ten
E) Eleven

Okay, so the standard deviation is 0.3 ounces. We want the values that are within 1.5 standard deviations of the mean. 1.5 standard deviations would be (1.5)(0.3) = 0.45 ounces, so we want all of the values that are within 0.45 ounces of the mean. If the mean is 8.1 ounces, this means that we want everything that falls between a lower bound of (8.1 – 0.45) and an upper bound of (8.1 + 4.5). Put another way, we want the number of values that fall between 8.1 – 0.45 = 7.65 and 8.1 + 0.45 = 8.55.

Looking at our 12 values, we can see that only one value, 7.51, falls outside of this range. If we have 12 total values and only 1 falls outside the range, then the other 11 are clearly within the range, so the answer is E.

As you can see, there’s very little math involved, even on the more difficult questions.

Takeaway: remember the axiom that the more complex-looking the formula is for a concept, the simpler the calculations are likely to be on the GMAT. An intuitive understanding of a topic will always go a lot further on this test than any amount of arithmetical virtuosity.

*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 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.

Quarter Wit, Quarter Wisdom: Using Visual Symmetry to Solve GMAT Probability Problems

Quarter Wit, Quarter WisdomToday, let’s take a look at an official GMAT question involving visual skills. It takes a moment to understand the given diagram, but at close inspection, we’ll find that this question is just a simple probability question – the trick is in understanding the symmetry of the figure:

The figure shown represents a board with 4 rows of pegs, and at the bottom of the board are 4 cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has the probability 1/2 of passing through the opening immediately to the left of that peg and probability 1/2 of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end in cell 2?

qwqw pegs pic

 

 

 

 

(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2

First, understand the diagram. There are small pegs arranged in rows and columns. The ball falls between two adjacent pegs and hits the peg directly below. When it does, there are two ways it can go – either to the opening on the left or to the opening on the right. The probability of each move is equal, i.e. 1/2.

The arrow show the first path the ball takes. It is dropped between the top two pegs, hits the peg directly below it, and then either drops to the left side or to the right. The same process will be repeated until the ball falls into one of the four cells – 1, 2, 3 or 4.

Method 1: Using Symmetry
Now that we understand this process, let’s examine the symmetry in this diagram.

Say we flip the image along the vertical axis – what do we get? The figure is still exactly the same, but now the order of cells is reversed to be 4, 3, 2, 1. The pathways in which you could reach Cell 1 are now the pathways in which you can use to reach Cell 4.

OR think about it like this:

To reach Cell 1, the ball needs to turn left-left-left.

To reach Cell 4, the ball needs to turn right-right-right.

Since the probability of turning left or right is the same, the situations are symmetrical. This will be the same case for Cells 2 and 3. Therefore, by symmetry, we see that:

The probability of reaching Cell 1 = the probability of reaching Cell 4.

Similarly:

The probability of reaching Cell 2 = the probability of reaching Cell 3. (There will be multiple ways to reach Cell 2, but the ways of reaching Cell 3 will be similar, too.)

The total probability = the probability of reaching Cell 1 + the probability of reaching Cell 2 + the probability of reaching Cell 3 + the probability of reaching Cell 4 = 1

Because we know the probability of reaching Cells 1 and 4 are the same, and the probabilities of reaching Cells 2 and 3 are the same, this equation can be written as:

2*(the probability of reaching Cell 1) + 2*(the probability of reaching Cell 2) = 1

Let’s find the probability of reaching Cell 1:

After the first opening (not the peg, but the opening between pegs 1 and 2 in the first row), the ball moves left (between pegs 1 and 2 in second row) or right (between pegs 2 and 3 in second row). It must move left to reach Cell 1, and the probability of this = 1/2.

After that, the ball must move left again – the probability of this occurring is also 1/2, since probability of moving left or right is equal. Finally, the ball must turn left again to reach Cell 1 – the probability of this occurring is, again, 1/2. This means that the total probability of the ball reaching Cell 1 = (1/2)*(1/2)*(1/2) = 1/8

Plugging this value into the equation above:

2*(1/8) + 2 * probability of reaching Cell 2 = 1

Therefore, the probability of reaching Cell 2 = 3/8

Method 2: Enumerating the Cases
You can also answer this question by simply enumerating the cases.

At every step after the first drop between pegs 1 and 2 in the first row, there are two different paths available to the ball – either it can go left or it can go right. This happens three times and, hence, the total number of ways in which the ball can travel is 2*2*2 = 8

The ways in which the ball can reach Cell 2 are:

Left-Left-Right

Left-Right-Left

Right-Left-Left

So, the probability of the ball reaching Cell 2 is 3/8.

Note that here there is a chance that we might miss some case(s), especially in problems that involve many different probability options. Hence, enumerating should be the last option you use when tackling these types of questions on the GMAT.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: Mother Knows Best

GMAT Tip of the WeekThis weekend is Mother’s Day here in the United States, and also, as the first full weekend in May, a weekend that will kick off a sense of study urgency for those intent on the September Round 1 MBA admissions deadlines. (If your mother were here she’d tell you why: if you want two full months to study for the GMAT and two full months to work on your applications, you have to start studying now!)

In honor of mothers everywhere and in preparation for your GMAT, let’s consider one of the things that makes mothers so great. Even today as an adult, you’ll likely find that if you live a flight or lengthy drive/train from home, when you leave your hometown, your mother loads you up with snacks for the plane, bottled water for the drive, hand sanitizer for the airport, etc. Why is that? When it comes to their children – no matter how old or independent – mothers are prepared for every possible situation.

What if you get hungry on the plane, or you’re delayed at your connecting airport and your credit card registers fraud because of the strange location and you’re unable to purchase a meal?! She doesn’t want you getting sick after touching the railing on an escalator, so she found a Purell bottle that’s well less than the liquid limit at security (and also packed a clear plastic bag for you and your toiletries). Moms do not want their children caught in a unique and harmful (or inconvenient) situation, so they plan for all possible occurrences.

And that’s how you should approach Data Sufficiency questions on the GMAT.

When a novice test-taker sees the problem:

What is the value of x?

(1) x^2 = 25

(2) 8 < 2x < 12

He may quickly say “oh it’s 5” to both of them. 5 is the square root of 25, and the second equation simplifies to 4 < x < 6, and what number is between 4 and 6? It’s 5.

But your mother would give you caution, particularly because her mission is to avoid *negative* outcomes for you. She’d be prepared for a negative value of x (-5 satisfies Statement 1) and for nonintegers (x could be 4.00001 or 5.9999 given Statement 2). Knowing those contingencies, she’d wisely recognize that you need both statements to guarantee one exact answer (5) for x.

Just like she’d tie notes to your mittens or pin them on your shirt when you were a kid so that you wouldn’t forget (and like now she’ll text you reminders for your grandmother’s birthday or to RSVP to your cousin’s wedding), your mom would suggest that you keep these unique occurrences written down at the top of your noteboard on test day: Negative, Zero, Noninteger, Infinity, Biggest/Smallest Value. That way, you’ll always check for those unique situations before you submit your answer, and you’ll have a much better shot at a challenge-level problem like this:

The product of consecutive integers a, b, c, and d is 5,040. What is the value of d?

(1) d is prime

(2) d < c < b < a

So where does mom come in?

Searching for consecutive integers, you’ll likely factor 5,040 to 7, 8, 9, and 10 (the 10 is obvious because 5,040 ends in a 0, and then when you see that the rest is 504 and know that’s divisible by 9, and you’re just about done). And so with Statement 1, you’ll see that the only prime number in the bunch is 7, meaning that d = 7 and Statement 1 is sufficient. And Statement 2 seems to support that exact same conclusion – as the smallest of the 4 integers, d is, again, 7.

Right?

Enter mom’s notes: did you consider zero? (irrelevant) Did you consider nonintegers? (they specified integers, so irrelevant) Did you consider negative numbers?

That’s the key. The four consecutive integers could be -10, -9, -8, and -7 meaning that d could also be -10. That wasn’t an option for Statement 1 (only positives are prime) and so since you did the “hard work” of factoring 5,040 and then finally got to where Statement 2 was helpful, there’s a high likelihood that you were ready to be finished and saw 7 as the only option for Statement 2.

This is why mom’s reminders are so helpful: on harder problems, the “special circumstances” numbers that mom wants to make sure you’re always prepared for tend to be afterthoughts, having taken a backseat to the larger challenges of math. But mother knows best – you may not be stranded in a foreign airport without a snack and your car might not stall in the desert when you don’t have water, but in the rare event that such a situation occurs she wants you to be prepared. Keep mom’s list handy at the top of your noteboard (alas, the Pearson/Vue center won’t allow you to pin it to your shirt) and you, like mom, will be prepared for all situations.

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.

How to Avoid Trap Answers On GMAT Data Sufficiency Questions

GMAT TrapsWhen I’m not teaching GMAT classes or writing posts for our fine blog, I am, unfortunately, writing fiction. Anyone who has taken a stab at writing fiction knows that it’s hard, and because it’s hard, it is awfully tempting to steer away from pain and follow the path of least resistance.

This tendency can manifest itself in any number of ways. Sometimes it means producing a cliché rather than straining for a more precise and original way to render a scene. More often, it means procrastinating – cleaning my desk or refreshing espn.com for the 700th time – rather than doing any writing at all. The point is that my brain is often groping for an easy way out. This is how we’re all wired; it’s a dangerous instinct, both in writing and on the GMAT.

This problem is most acute on Data Sufficiency questions. Most test-takers like to go on auto-pilot when they can, relying on simple rules and heuristics rather than proving things to themselves – if I have the slope of a line and one point on that line, I know every point on that line; if I have two linear equations and two variables I can solve for both variables, etc.

This is not in and of itself a problem, but if you find your brain shifting into path-of-least-resistance mode and thinking that you’ve identified an answer to a question within a few seconds, be very suspicious about your mode of reasoning. This is not to say that you should simply assume that you’re wrong, but rather to encourage you to try to prove that you’re right.

Here’s a classic example of a GMAT Data Sufficiency question that appears to be easier than it is:

Joanna bought only $.15 stamps and $.29 stamps. How many $.15 stamps did she buy?

1) She bought $4.40 worth of stamps
2) She bought an equal number of $.15 stamps and $.29 stamps

Here’s how the path-of-least-resistance part of my brain wants to evaluate this question. Okay, for Statement 1, there could obviously be lots of scenarios. If I call “F” the number of 15 cent stamps and “T” the number of 29 cent stamps, all I know is that .15F + .29T = 4.40. So that statement is not sufficient. Statement 2 is just telling me that F = T. Clearly no good – any number could work. And together, I have two unique linear equations and two unknowns, so I have sufficiency and the answer is C.

This line of thinking only takes a few seconds, and just as I need to fight the urge to take a break from writing to watch YouTube clips of Last Week Tonight with John Oliver because it’s part of my novel “research,” I need to fight the urge to assume that such a simple line of reasoning will definitely lead me to the correct answer to this question.

So let’s rethink this. I know for sure that the answer cannot be E – if I can solve for the unknowns when I’m testing the statements together, I clearly have sufficiency there. And I know for sure that the answer cannot be that Statement 2 alone is sufficient. If F = T, there are an infinite number of values that will work.

So, let’s go back to Statement 1. I know that I cannot purchase a fraction of a stamp, so both F and T must be integer values. That’s interesting. I also know that the total amount spent on stamps is $4.40, or 440 cents, which has a units digit of 0. When I’m buying 15-cent stamps, I can spend 15 cents if I buy 1 stamp, 30 cents if I buy two, etc.

Notice that however many I buy, the units digit must either be 5 or 0. This means that the units digit for the amount I spend on 29 cent stamps must also be 5 or 0, otherwise, there’d be no way to get the 0 units digit I get in 440. The only way to get a units digit of 5 or 0 when I’m multiplying by 29 is if the other number ends in 5 or 0 . In other words, the number of 29-cent stamps I buy will have to be a multiple of 5 so that the amount I spend on 29-cent stamps will end in 5 or 0.

Here’s the sample space of how much I could have spent on 29-cent stamps:

Five stamps: 5*29 = 145 cents
Ten stamps: 10*29 = 290 cents
Fifteen stamps: 15* 29 = 435 cents

Any more than fifteen 29-cent stamps and I ‘m over 440, so these are the only possible options when testing the first statement.

Let’s evaluate: say I buy five 29-cent stamps and spend 145 cents. That will leave me with 440 – 145 = 295 cents left for the 15-cent stamps to cover. But I can’t spend exactly 295 cents by purchasing 15-cent stamps, because 295 is not a multiple of 15.

Say I buy ten 29-cent stamps, spending 290 cents. That leaves 440 – 290 = 150. Ten 15-cent stamps will get me there, so this is a possibility.

Say I buy fifteen 29-cent stamps, spending 435 cents. That leaves 440 – 435 = 5. Clearly that’s not possible to cover with 15-cent stamps.

Only one option works: ten 29-cent stamps and ten 15-cent stamps. Because there’s only one possibility, Statement 1 alone is sufficient, and the answer here is actually A.

Takeaway: Don’t take the GMAT the way I write fiction. Following the path of least-resistance will often lead you right into the trap the question writer has set for unsuspecting test-takers. If something feels too easy on a Data Sufficiency, it probably is.

*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 follow us on Facebook, YouTube, Google+ and Twitter!

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

Quarter Wit, Quarter Wisdom: Using the Standard Deviation Formula on the GMAT

Quarter Wit, Quarter WisdomWe have discussed standard deviation (SD) in detail before. We know what the formula is for finding the standard deviation of a set of numbers, but we also know that GMAT will not ask us to actually calculate the standard deviation because the calculations involved would be way too cumbersome. It is still a good idea to know this formula, though, as it will help us compare standard deviations across various sets – a concept we should know well.

Today, we will look at some GMAT questions that involve sets with similar standard deviations such that it is hard to tell which will have a higher SD without properly understanding the way it is calculated. Take a look at the following question:

Which of the following distribution of numbers has the greatest standard deviation? 

(A) {-3, 1, 2} 
(B) {-2, -1, 1, 2} 
(C) {3, 5, 7} 
(D) {-1, 2, 3, 4} 
(E) {0, 2, 4}

At first glance, these sets all look very similar. If we try to plot them on a number line, we will see that they also have similar distributions, so it is hard to say which will have a higher SD than the others. Let’s quickly review their deviations from the arithmetic means:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2
For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2
For answer choice C, the mean = 5 and the deviations are 2, 0, 2
For answer choice D, the mean = 2 and the deviations are 3, 0, 1, 2
For answer choice E, the mean = 2 and the deviations are 2, 0, 2

We don’t need to worry about the arithmetic means (they just help us calculate the deviation of each element from the mean); our focus should be on the deviations. The SD formula squares the individual deviations and then adds them, then the sum is divided by the number of elements and finally, we find the square root of the whole term. So if a deviation is greater, its square will be even greater and that will increase the SD.

If the deviation increases and the number of elements increases, too, then we cannot be sure what the final effect will be – an increased deviation increases the SD but an increase in the number of elements increases the denominator and hence, actually decreases the SD. The overall effect as to whether the SD increases or decreases will vary from case to case.

First, we should note that answers C and E have identical deviations and numbers of elements, hence, their SDs will be identical. This means the answer is certainly not C or E, since Problem Solving questions have a single correct answer.

Let’s move on to the other three options:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2
For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2
For answer choice D, the mean = 2 and the deviations are 3, 0, 1, 2

Comparing answer choices A and D, we see that they both have the same deviations, but D has more elements. This means its denominator will be greater, and therefore, the SD of answer D is smaller than the SD of answer A. This leaves us with options A and B:

For answer choice A, the mean = 0 and the deviations are 3, 1, 2
For answer choice B, the mean = 0 and the deviations are 2, 1, 1, 2

Now notice that although two deviations of answers A and B are the same, answer choice A has a higher deviation of 3 but fewer elements than answer choice B. This means the SD of A will be higher than the SD of B, so the SD of A will be the highest. Hence, our answer must be A.

Let’s try another one:

Which of the following data sets has the third largest standard deviation?

(A) {1, 2, 3, 4, 5} 
(B) {2, 3, 3, 3, 4} 
(C) {2, 2, 2, 4, 5} 
(D) {0, 2, 3, 4, 6} 
(E) {-1, 1, 3, 5, 7}

How would you answer this question without calculating the SDs? We need to arrange the sets in increasing SD order. Upon careful examination, you will see that the number of elements in each set is the same, and the mean of each set is 3.

Deviations of answer choice A: 2, 1, 0, 1, 2
Deviations of answer choice B: 1, 0, 0, 0, 1 (lowest SD)
Deviations of answer choice C: 1, 1, 1, 1, 2
Deviations of answer choice D: 3, 1, 0, 1, 3
Deviations of answer choice E: 4, 2, 0, 2, 4 (highest SD)

Obviously, option B has the lowest SD (the deviations are the smallest) and option E has the highest SD (the deviations are the greatest). This means we can automatically rule these answers out, as they cannot have the third largest SD.

Deviations of answer choice A: 2, 1, 0, 1, 2
Deviations of answer choice C: 1, 1, 1, 1, 2
Deviations of answer choice D: 3, 1, 0, 1, 3

Out of these options, answer choice D has a higher SD than answer choice A, since it has higher deviations of two 3s (whereas A has deviations of two 2s). Also, C is more tightly packed than A, with four deviations of 1. If you are not sure why, consider this:

The square of deviations for C will be 1 + 1+ 1 + 1  + 4 = 8
The square of deviations for A will be 4 + 1 + 0 + 1 + 4 = 10

So, A will have a higher SD than C but a lower SD than D. Arranging from lowest to highest SD’s, we get: B, C, A, D, E. Answer choice A has the third highest SD, and therefore, A is our answer

Although we didn’t need to calculate the actual SD, we used the concepts of the standard deviation formula to answer these questions.

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

Breaking Down Changes in the New Official GMAT Practice Tests: Unit Conversions in Shapes

QuadrilateralRecently, GMAC released two more official practice tests. Though the GMAT is not going to test completely new concepts – if the test changed from year to year, it wouldn’t really be standardized – we can get a sense of what types of questions are more likely to be emphasized by noting how official materials change over time. I thought it might be interesting to take these practice tests and break down down any conspicuous trends I detected.

In the Quant section of the first new test, there was one type of question that I’d rarely encountered in the past, but saw multiple times within a span of 20 problems. It involves unit conversions in two or three-dimensional shapes.

Like many GMAT topics, this concept isn’t difficult so much as it is tricky, lending itself to careless mistakes if we work too fast. If I were to draw a line that was one foot long, and I asked you how many inches it was, you wouldn’t have to think very hard to recognize that it would be 12 inches.

But what if I drew a box that had an area of 1 square foot, and I asked you how many square inches it was? If you’re on autopilot, you might think that’s easy. It’s 12 square inches. And you better believe that on the GMAT, that would be a trap answer. To see why it’s wrong, consider a picture of our square:

 

 

 

 

 

We see that each side is 1 foot in length. If each side is 1 foot in length, we can convert each side to 12 inches in length. Now we have the following:

DG blog pic 2

 

 

 

 

 

Clearly, the area of this shape isn’t 12 square inches, it’s 144 square inches: 12 inches * 12 inches = 144 inches^2.

Another way to think about it is to put the unit conversion into equation form. We know that 1 foot = 12 inches, so if we wanted the unit conversion from feet^2 to inches^2, we’d have to square both sides of the equation in order to have the appropriate units. Now (1 foot)^2 = (12 inches)^2, or 1 foot^2 = 144 inches^2.  So converting from square feet to square inches requires multiplying by a factor of 144, not 12.

Let’s see this concept in action. (I’m using an older official question to illustrate – I don’t want to rob anyone of the joy of encountering the recently released questions with a fresh pair of eyes.)

If a rectangular room measures 10 meters by 6 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter = 100 centimeters)

A) 24,000
B) 240,000
C) 2,400,000
D) 24,000,000
E) 240,000,000

First, we can find the volume of the room by multiplying the dimensions together: 10*6*4 = 240 cubic meters. Now we want to avoid the trap of thinking, “Okay, 100 centimeters is 1 meter, so 240 cubic meters is 240*100 = 24,000 cubic centimeters.”  Remember, the conversion ratio we’re given is for converting meters to centimeters – if we’re dealing with 240 cubic meters, or 240 meters^3, and we want to find the volume in cubic centimeters, we’ll need to adjust our conversion ratio accordingly.

If 1 meter = 100 centimeters, then (1 meter)^3 = (100 centimeters)^3, and 1 meter^3 = 1,000,000 centimeters^3. [100 = 10^2 and (10^2)^3 = 10^6, or 1,000,000.] So if 1 cubic meter = 1,000,000 cubic centimeters, then 240 cubic meters = 240*1,000,000 cubic centimeters, or 240,000,000 cubic centimeters, and our answer is E.

Alternatively, we can do all of our conversions when we’re given the initial dimensions. 10 meters = 1000 centimeters. 6 meters = 600 centimeters. 4 meters  = 400 centimeters. 1000 cm * 600 cm * 400 cm = 240,000,000 cm^3. (Notice that when we multiply 1000*600*400, we can simply count the zeroes. There are 7 total, so we know there will be 7 zeroes in the correct answer, E.)

Takeaway: Make sure you’re able to do unit conversions fluently, and that if you’re dealing with two or three-dimensional space, that you adjust your conversion ratios accordingly. If you’re dealing with a two-dimensional shape, you’ll need to square your initial ratio. If you’re dealing with a three-dimensional shape, you’ll need to cube your initial ratio. The GMAT is just as much about learning what traps to avoid as it is about relearning the elementary math that we’ve long forgotten.

*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 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.

Quarter Wit, Quarter Wisdom: An Innovative Use of the Slope of a Line on the GMAT

Quarter Wit, Quarter WisdomLet’s continue our discussion on coordinate geometry today.

The concept of slope is extremely important on the GMAT – it is not sufficient to just know how to calculate it using (y2 – y1)/(x2 – x1).

In simple terms, the slope of a line specifies the units by which the y-coordinate changes and the direction in which it changes with each 1 unit increase in the x-coordinate. If the slope (m) is positive, the y-coordinate changes in the same direction as the x-coordinate. If m is negative, however, the y-coordinate changes in the opposite direction.

For example, if the slope of a line is 2, it means that every time the x-coordinate increases by 1 unit, the y-coordinate increases by 2 units. So if the point (3, 5) lies on a line with a slope of 2, the point (4, 7) will also lie on it. Here, when the x-coordinate increases from 3 to 4, the y-coordinate increases from 5 to 7 (by an increase of 2 units). Similarly,  the point (2, 3) will also lie on this same line – if the x-coordinate decreases by 1 unit (from 3 to 2), the y-coordinate will decrease by 2 units (from 5 to 3). Since the slope is positive, the direction of change of the x-coordinate will be the same as the direction of change of the y-coordinate.

Now, if we have a line where the slope is -2 and the point (3, 5) lies on it, when the x-coordinate increases by 1 unit, the y-coordinate DECREASES by 2 units – the point (4, 3) will also lie on this line. Similarly, if the x-coordinate decreases by 1 unit, the y-coordinate will increase by 2 units. So, for example, the point (2, 7) will also lie on this line.

This understanding of the concept of slope can be very helpful, as we will see in this GMAT question:

Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K? 

(A) 5
(B) 10
(C) 5√(5)
(D) 15
(E) 10√(5)

Method 1: The Traditional Approach
Traditionally, one would solve this question like this:

The equation of a line with slope m and constant c is given as y = mx + c. Therefore, the equations of lines L and K would be:

Line L: y = (-2)x + a
and
Line K: y = (1/2)x + b

As both these lines pass through (6,8), we would substitute x=6 and y=8 to get the values of a and b.

Line L: 8 = (-2)*6 + a
a = 20

Line K: 8 = (1/2)*6 + b
b = 5

Thus, the equations of the 2 lines become:

Line L: y = (-2)x + 20
and
Line K: y = (1/2)x + 5

The x-intercept of a line is given by the point where y = 0. So, the x-intercept of line L is given by:

0 = (-2)x + 20
x = 10

This means line L intersects the x-axis at the point (10, 0).

Similarly, the y-intercept of a line is given by the point where x = 0. So, y-intercept of line K is given by:

y = (1/2)*0 + 5
y = 5

This means that line K intersects the y-axis at the point (0, 5).

Looking back at our original question, the distance between these two points is given by √((10 – 0)^2 + (0 – 5)^2) = 5√(5). Therefore, our answer is C.

Method 2: Using the Slope Concept
Although the using the traditional method is effective, we can answer this question much quicker using the concept we discussed above.

Line L has a slope of -2, which means that for every 1 unit the x-coordinate increases, the y-coordinate decreases by 2. Line L also passes through the point (6, 8). We know the line must intersect the x-axis at y = 0, which is a decrease of 8 y-coordinates from the given point (6,8). If y increases by 8, according to our slope concept, x will increase by 4 to give 6 + 4 = 10. So the x-intercept of line L is at (10, 0).

Line K has slope of 1/2 and also passes through (6, 8). We know the this line must intersect the y-axis at x = 0, which is a decrease of 6 x-coordinates from the given point (6,8). This means y will decrease by 1/2 of that (6*1/2 = 3) and will become 8 – 3 = 5. So the y-intercept of line K is at (0, 5).

The distance between the two points can now be found using the Pythagorean Theorem – √(10^2 + 5^2) = 5√(5), therefore our answer is, again, C.

Using the slope concept makes solving this question much less tedious and saves us a lot of precious time. That is the advantage of using holistic approaches over the more traditional approaches in tackling GMAT questions.

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

Coordinate Geometry: Solving GMAT Problems With Lines Crossing Either the X-Axis or the Y-Axis

Quarter Wit, Quarter WisdomToday let’s learn about the cases in which lines on the XY plane cross, or do not cross, the x- or y-axis. Students often struggle with questions such as this:

Does the line with equation ax+by = c, where a,b and c are real constants, cross the x-axis?

What concepts will you use here? How will you find whether or not a line crosses the x-axis? What conditions should it meet? Think about this a little before you move ahead.

We know that most lines on the XY plane cross the x-axis as well as the y-axis. Even if it looks like a given line doesn’t cross either of these axes, eventually, it will if it has a slope other than 0 or infinity.

QWQW pic 1

 

 

 

 

 

Note that by definition, a line extends infinitely in both directions – it has no end points (otherwise it would be a line “segment”). We cannot depict a line extending infinitely, which is why we will only show a small section of it. Ideally, a line on the XY plane should be shown with arrowheads to depict that it extends infinitely on both sides, but we often omit them for our convenience. For instance, if we try to extend the example line above, we see that it does, in fact, cross the x-axis:

QWQW pic 2

 

 

 

 

 

So what kind of lines do not cross either the x-axis or the y-xis? We know that the equation of a line on the XY plane is given by ax + by  + c = 0. We also know that if we want to find the slope of a line, we can use the equation y = (-a/b)x – c/b, where the slope of the line is -a/b.

A line with a slope of 0 is parallel to the x-axis. For the slope (i.e. -a/b) to be 0, a must equal 0. So if a = 0, the line will not cross the x-axis – it is parallel to the x-axis. The equation of the line, in this case, will become y = k. In all other cases, a line will cross the x-axis at some point.

Similarly, it might appear that a line doesn’t cross the y-axis but it does at some point if its slope is anything other than infinity. A line with a slope of infinity is parallel to the y-axis. For -a/b to be infinity, b must equal 0. So if b = 0, the line will not cross the y-axis. The equation of the line in this case will become x = k. In all other cases, a line will cross the y-axis at some point.

Now, we can easily solve this official question:

Does the line with equation ax+by = c, where a, b and c are real constants, cross the x-axis?

Statement 1: b not equal to 0

Statement 2: ab > 0

As we discussed earlier, all lines cross the x-axis except lines which have a slope of 0, i.e. a = 0.

Statement 1: b not equal to 0

This tells statement us that b is not 0 – which means the line is not parallel to y-axis – but it doesn’t tell us whether or not a is 0, so we don’t know whether the line is parallel to the x-axis or crosses it. Therefore, this statement alone is not sufficient.

Statement 2: ab>0

If ab > 0, it means that neither a nor b is 0 (since any number times 0 will equal 0). This means the line is parallel to neither x-axis nor the y-xis, and therefore must cross the x-axis. This statement alone is sufficient and our answer is B.

Hopefully this has helped clear up some coordinate geometry concepts today.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: Death, Taxes, and the GMAT Items You Know For Certain

GMAT Tip of the WeekHere on April 15, it’s a good occasion to remember the Benjamin Franklin quote: “In this world nothing can be said to be certain, except death and taxes.” Franklin, of course, never took the GMAT (which didn’t become a thing until a little ways after his own death, which he accurately predicted above). But if he did, he’d have plenty to add to that quote.

On the GMAT, several things are certain. Here’s a list of items you will certainly see on the GMAT, as you attempt to raise your score and therefore your potential income, thereby raising your future tax bills in Franklin’s honor:

Integrated Reasoning
You will struggle with pacing on the Integrated Reasoning section. 12 prompts in 30 minutes (with multiple problems per prompt) is an extremely aggressive pace and very few people finish comfortably. Be willing to guess on a problem that you know could sap your time: not only will that help you finish the section and protect your score, it will also help save your stamina and energy for the all-important Quant Section to follow.

Word Problems
On the Quantitative Section, you will certainly see at least one Work/Rate problem, one Weighted Average problem, and one Min/Max problem. This is good news! Word problems reward repetition and preparation – if you’ve put in the work, there should be no surprises.

Level of Difficulty
If you’re scoring above average on either the Quant or Verbal sections, you will see at least one problem markedly below your ability level. Because each section contains several unscored, experimental problems, and those problems are delivered randomly, probability dictates that every 700+ scorer will see at least one problem designed for the 200-500 crowd (and probably more than that). Do not try to read in to your performance based on the difficulty level of any one problem! It’s easy to fear that such a problem was delivered to you because you’re struggling, but the much more logical explanation is that it was either random or difficult-but-sneakily-so, so stay confident and move on.

Data Sufficiency
You will see at least one Data Sufficiency problem that seems way too easy to be true. And it’s probably not true: make sure that you think critically any time the testmaker is directly baiting you into a particular answer.

Sentence Correction
You will have to pick an answer that you don’t like, that doesn’t catch the ear the way you’d write or say it. Make sure that you prioritize the major errors that you know you can routinely catch and correct, and not let the GMAT bait you into a decision you’re just not qualified to make.

Reading Comprehension

You will see a passage that takes you a few re-reads to even get your mind to process it. Remember to be question-driven and not passage-driven – get enough out of the passage to know where to look when they ask you a specific question, but don’t worry about becoming a subject-matter expert on the topic. GMAT passages are designed to be difficult to read (particularly toward the end of a long test), so know that your competitive advantage is that you’ll be more efficient than your competition.

Critical Reasoning
You will have the opportunity to make quick work of several Critical Reasoning problems if you notice the tiny gaps in logic that each argument provides, and if you’re able to notice the subtle-but-significant words that make conclusions extra specific (and therefore harder to prove).

Few things are certain in life, but as you approach the GMAT there are plenty of certainties that you can prepare for so that you eliminate surprises and proceed throughout your test day confidently. On this Tax Day, take inventory of the things you know to be certain about the GMAT so that your test day isn’t so taxing.

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.

Quarter Wit, Quarter Wisdom: Be Tolerant Towards Pronoun Ambiguity on the GMAT

Quarter Wit, Quarter WisdomWe encounter many different types of pronoun errors on the GMAT Verbal Section. Some of the most common errors include:

Using a pronoun without an antecedent. For example, the sentence, “Although Jack is very rich, he makes poor use of it,” is incorrect because “it” has no antecedent. The antecedent should instead be “money” or “wealth.”

Error in matching the pronoun to its antecedent in number and gender. For example, the sentence, “Pack away the unused packets, and save it for the next game,” is incorrect because the antecedent of “it” is referring to “unused packets,” which is plural.

Using a nominative/objective case pronoun when the antecedent is possessive. For example, the sentence, “The client called the lawyer’s office, but he did not answer,” is incorrect because the antecedent of “he” should be referring to “lawyer,” but it appears only in the possessive case. Official GMAT questions will not give you this rule as the only decision point between two options.

But note that the rules governing pronoun ambiguity are not as strict as other rules! Pronoun ambiguity should be the last decision point for eliminating an option after we have taken care of SV agreements, tenses, modifiers, parallelism etc.

Every sentence that has two nouns before a pronoun does not fall under the “pronoun ambiguity error” category. If the pronoun agrees with two nouns in number and gender, and both nouns could be the antecedent of the pronoun, then there is a possibility of pronoun ambiguity. But in other cases, logic can dictate that only one of the nouns can really perform (or receive) an action, and so it is logically clear to which noun the pronoun refers.

For example, “Take the bag out of the car and get it fixed.”

What needs to get fixed? The bag or the car? Either is possible. Here we have a pronoun ambiguity, but it is highly unlikely you will see something like this on the GMAT.

A special mention should be made here about the role nouns play in the sentence. Often, a pronoun which acts as the subject of a clause refers to the noun which acts as a subject of the previous clause. In such sentences, you will often find that the antecedent is unambiguous. Similarly, if the pronoun acts as the direct object of a clause, it could refer to the direct object of the  previous clause. If the pronoun and its antecedent play parallel roles, a lot of clarity is added to the sentence. But it is not necessary that the pronoun and its antecedent will play parallel roles.

Let’s look at a different example, “The car needs to be taken out of the driveway and its brakes need to get fixed.”

Here, obviously the antecedent of “its” must be the car since only it has brakes, not the driveway. Besides, the car is the subject of the previous clause and “its” refers to the subject. Hence, this sentence would be acceptable.

A good rule of thumb would be to look at the options. If no options sort out the pronoun issue by replacing it with the relevant noun, just forget about pronoun ambiguity. If there are options that clarify the pronoun issue by replacing it with the relevant noun, consider all other grammatical issues first and then finally zero in on pronoun ambiguity.

Let’s take a quick look at some official GMAT questions involving pronouns now:

Congress is debating a bill requiring certain employers provide workers with unpaid leave so as to care for sick or newborn children. 

(A) provide workers with unpaid leave so as to 
(B) to provide workers with unpaid leave so as to 
(C) provide workers with unpaid leave in order that they 
(D) to provide workers with unpaid leave so that they can 
(E) provide workers with unpaid leave and 

The answer is (D). Why? The correct sentence would use “to provide” (not “provide”) and “so that” (not “so as to”), and should read, “Congress is debating a bill requiring certain employers to provide workers with unpaid leave so that they can care for sick or newborn children.” In this sentence, “they” logically refers to “workers.” Even though “they” could refer to employers, too, after you sort out the rest of the errors, you are left with (D) only, hence answer must be (D).

Let’s look at another question:

While depressed property values can hurt some large investors, they are potentially devastating for homeowners, whose equity – in many cases representing a life’s savings – can plunge or even disappear.

(A) they are potentially devastating for homeowners, whose
(B) they can potentially devastate homeowners in that their
(C) for homeowners they are potentially devastating, because their
(D) for homeowners, it is potentially devastating in that their
(E) it can potentially devastate homeowners, whose

The correct answer is (A). The correct sentence should read, “While depressed property values can hurt some large investors, they are potentially devastating for homeowners, whose equity – in many cases representing a life’s savings – can plunge or even disappear.” The pronoun “they” logically refers to “depressed property values.” Both the pronoun and its antecedent serve as subjects in their respective clauses, so the pronoun antecedent is quite clear.

One more question:

Although Napoleon’s army entered Russia with far more supplies than they had in their previous campaigns, it had provisions for only twenty-four days. 

(A) they had in their previous campaigns 
(B) their previous campaigns had had 
(C) they had for any previous campaign 
(D) in their previous campaigns 
(E) for any previous campaign

The correct answer is (E). The correct sentence should read, “Although Napoleon’s army entered Russia with far more supplies than for any previous campaign, it had provisions for only twenty-four days.”

The pronoun “it” logically refers to “Napolean’s army” and not Russia. Both the pronoun and its antecedent serve as subjects in their respective clauses, so the pronoun antecedent is quite clear. Note that the pronoun and its antecedent are a part of the non-underlined portion of the sentence so we don’t need to worry about the usage here but it strengthens our understanding of pronoun ambiguity.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: Ernie Els, The Masters, and the First Ten GMAT Questions

GMAT Tip of the WeekAt this weekend’s The Masters golf tournament, the most notable piece of news isn’t the leaderboard, but rather the guy least likely to get near it. Ernie Els set a record with a nine-stroke, quintuple bogey on his first hole of the tournament, effectively ending his tournament minutes after he began it. And in doing so, he also provided you with some insight into the “First Ten Questions” myth that concerns so many GMAT test-takers.

With 18 holes each day for 4 days (Quick mental math! 18×4 is the same as 9×8 – halve the first number and double the second to make it a calculation you know well – so that’s 72 holes), any one hole shouldn’t matter. So why was Els’ first hole such a catastrophe?

It forces him to be nearly perfect the rest of the tournament, because he’s playing at such a disadvantage.

Meanwhile, Day 1 leader Jordan Spieth shot par (“average”) his first few holes and Rory McElroy, in second place at the end of the day, bogeyed (one stroke worse than average) a total of four holes on day one. The leaders were far from perfect themselves – another important lesson for the GMAT – but by avoiding a disastrous start, they allowed themselves plenty of opportunities to make up for mistakes.

And that brings us to the GMAT. Everyone makes mistakes on the GMAT, and that often happens regardless of difficulty level. So if you’re shooting for a top score and you miss half of the first ten questions, you have a few problems to contend with.

For starters, you have to “get hot” here soon and go on a run of correct answers. Secondly, you now have a lot fewer problems available to go on that hot streak (there are only 27 more Quant or 31 more Verbal questions after the first ten). And finally, the scoring/delivery algorithm doesn’t see you as “elite” yet so the questions are going to be a little easier and less “valuable,” meaning that you’ll need to “get hot” both to prove to the computer that you belong at the top level and then to demonstrate that you can stay there.

That’s the Ernie Els problem – regardless of how good you are, you’re probably going to make mistakes, so when you force yourself to be nearly perfect on the “easier” problems you end up with a tricky standard to live up to. Even if you really should be scoring at the 700-level, you don’t have a 100% probability of answering every 500-level problem correctly. That may well be in the 90%+ range, and maybe your likelihood at the 600 level is 75 or 80%. Getting 7, 8, 9 problems right in a row is a tall order as you dig your way out of that hole.

So the first 10 problems ARE important, but not because they have that much more power over the rest of the test – it’s because the more of them you miss, the more unrealistically perfect you have to be. The key is to “not blow it” on the first 10, rather than to “do everything you can to get them all right,” which is the mindset that holds back plenty of test-takers.

Again take the Masters: the leaderboard on Thursday night is never that close to the leaderboard on Sunday evening. Very often it’s someone who starts well, but is a few strokes off the lead the first few days, who wins. The GMAT is similar: a lot can happen from questions 11 through 37 (or 41), so by no means can you celebrate victory a quarter of the way through. Your goal shouldn’t be to be perfect, but rather to get off to a good start. Getting  7 questions right and having sufficient time to complete the rest of the section is much, much better than getting 9 right but forcing yourself to rush later on.

Essentially, as Ernie Els and thousands of GMAT test-takers have learned the hard way, you won’t win it in the first quarter, but you can certainly lose it there.  As you budget your time for the first 10 questions of each section, take a few extra seconds to double-check your work and make sure you’re not making egregious mistakes, but don’t over-invest at the expense of the critical problems to come.

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.

Use This Tip to Avoid Critical Reasoning Traps on the GMAT

GMAT TrapsWhen you’ve been teaching test prep for a while you begin to be able to anticipate the types of questions that will give your students fits. The reason isn’t necessarily because these questions are unusually hard in a conventional sense, but because embedded within these problems is a form of misdirection that is nearly impossible to resist. It’s often worthwhile to dissect these problems in greater detail to reveal some deeper truths about how the test works.

Here is a problem I knew I’d be asked about often the moment I saw it:

W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. What is the value of W?

  1. X is a prime number
  2. Z is not a prime number

The first instinct for most students I work with is, “I’m told nothing about W in either statement. There have to be many possibilities, so each statement alone is not sufficient.” When this thought occurs to you during the test, it’s important to resist it. By this, I don’t mean that you should simply assume that you’re wrong – there likely will be times when your first instincts are correct. Instead, what I mean is that you should take a bit more time to prove your assumptions to yourself. If there really are many workable scenarios, it won’t take much time to find them.

First, whenever there is an unusually large number and we’re dealing with multiplication, we want to take the prime factorization of that large number so that we can work with that figure’s basic building blocks and make it more manageable. In this case, the prime factorization of 1995 is 3 * 5 * 7 * 19. (First we see that five is a factor of 1995 because 1995 = 5*399. Next, we see that 3 is a factor of 399, because the digits of 399 sum to a multiple of 3. Now we have 5 * 3 * 133. Last, we know that 133 = 7 * 19, because if there are twenty 7’s in 140, there must be nineteen 7’s in 133.)

Now we can use these building blocks to form two-digit numbers that multiply to 1995. Here is a list of two-digit numbers we can assemble from those prime factors:

3 * 5 = 15

3 * 7 = 21

3 * 19 = 57

5 * 7 = 35

5 * 19 = 95

These are our candidates for WX and YZ. There aren’t many possibilities for multiplying two of these two-digit numbers and still getting a product of 1995. In fact, there are only two: 95*21 = 1995 and 35*57 = 1995. But we’re told that each digit must be unique, so 35*57 can’t work, as two of our variables would equal 5. This means that we know, before we even look at the statements, that our two two-digit numbers are 95 and 21 – we just need to know which is which.

It’s possible that WX = 95 and YZ = 21, or WX = 21 and YZ = 95. That’s it. What at first appeared to be a very open-ended question actually has very few workable solutions. Now that we’ve established our sample space of possibilities, let’s examine the statements:

Statement 1: If we know X is prime, we know that WX cannot be 21, as X would be 1 in this scenario and 1 is not a prime number. This means that WX has to be 95, and thus we know for a fact that W = 9. This statement alone is sufficient to answer the question.

Statement 2: If we know that Z is not prime, we know that YZ cannot be 95, as Z would be 5 in this scenario and 5 is, of course, prime. Thus, YZ is 21 and WX is 95, and again, we know for a fact that W is 9, so this statement alone is also sufficient.

The answer is D, either statement alone is sufficient to answer the question, a result very much at odds with most test-taker’s initial instincts.

Takeaway: the GMAT is engineered to wrong-foot test-takers, using our instincts against us.  Rather than simply assuming our instincts are wrong – they won’t always be – we want to be methodical about proving our intuitions one way or another by confirming them in some instances, refuting them in others. By being thorough and methodical, we reduce the odds that we’ll step into one of the traps the question-writer has set for us and increase the odds that we’ll answer the question correctly.

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 by him, here.

Are There Set Rules for Answering GMAT Sentence Correction Questions?

SAT WorryThe other day I was working with a tutoring student on Sentence Correction when she expressed some understandable frustration: when we did Quantitative questions together, she said, she felt like she could rely on ironclad rules that never varied (the rules for exponents don’t change depending on the context of the problem, for example), but when we did Sentence Correction, the relevant rules at play in a given question seemed less obvious.

Was there a way, she wondered, to view Sentence Correction with the same unwavering consistency with which we view Quantitative questions? While I understand her frustration, the answer is, alas, an unqualified “no.” English is far too complex for us to boil down Sentence Correction to a series of stimulus-response reflexes. Context and logic always matter.

To see why we can’t go on autopilot during Sentence Correction questions, consider the following problem:

Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also caused erosion and very quickly deforested whole regions. 

A) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also

B) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast), which gave consumers relatively inexpensive houses and furniture, but also

C) The systematic clearing of forests in the United States, creating farmland (especially in the Northeast) and giving consumers relatively inexpensive houses and furniture, but also

D) The systematic clearing of forests in the United States created farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also

E) The systematic clearing of forests in the United States not only created farmland (especially in the Northeast), giving consumers relatively inexpensive houses and furniture, but it

If you fully absorbed the class discussion about the importance of parallel construction, you probably noticed an indelible parallel marker here: “not only.” Okay, you think. Any time I see not only x, I know but also y should show up later in the sentence.

This isn’t wrong, per se, but the construction “not only/but also” is only applicable in certain circumstances. So before we jump to the erroneous conclusion that this is the construction that is called for in this sentence, let’s examine its underlying logic in more detail.

Take the simple example, “On the way to work, I not only got stuck in traffic, but also….” Think about your expectations for what should come next in this sentence – getting stuck in traffic was the first unfortunate thing to happen to this hapless subject, and we’re expecting a second unfortunate event in the latter part of the sentence. Not only/but also is appropriate when we’re talking about similar things.

Now consider the construction. “On the way to work, I got stuck in traffic, but…” Now our expectations are markedly different – the second half of the sentence is going to contrast with the first. We’re expecting something different.

Let’s go back to our GMAT sentence. We’re comparing the consequences of the clearing of forests. First, the clearing “created farmland and gave consumers inexpensive houses” (good things). However, it also “caused erosion and deforested the region” (bad things). Because we’re comparing two very different consequences, the construction “not only/but also” – which is used to compare similar things – is inappropriate. Now we can safely eliminate answers A, B and E.

That leaves us with C and D. First, let’s examine C. Notice there’s a participial modifier in the middle of the sentence set off by commas, and a sentence should still be logical if we remove these modifiers. We would then be left with, “The systematic clearing of forests in the United States, but also caused erosion and very quickly deforested whole regions.” This clearly doesn’t work – the initial subject (the systematic clearing) has no verb, so C is wrong. This leaves us with answer choice D, which is the correct answer.

Takeaway: though noticing common constructions on Sentence Correction problems can be helpful, we can never go on autopilot. Ultimately, context, logic, and meaning will always come into play. Before you select any answer, always ask yourself if the sentence is logically coherent before you select it. If you want to ace the GMAT, turning off your brain is not an option.

*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 follow us on FacebookYouTubeGoogle+ and Twitter!

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

Quarter Wit, Quarter Wisdom: Using a Venn Diagram vs. a Double Set Matrix on the GMAT

Quarter Wit, Quarter WisdomCritics may have given a rotten rating to the recently released “Batman v. Superman” movie, but we sure can use it to learn a valuable GMAT lesson. A difficult decision point for GMAT test takers is picking the probable winner between Venn diagrams and Double Set Matrices for complicated sets questions. If that is true for you too, then the onscreen rivalry between Batman and Superman will help you remember this trick:

Venn diagrams are like Superman – all powerful. They can help you solve almost all questions involving either 2 or 3 overlapping sets. But then, there are some situations in which double set matrix method (aka Batman with his amazing weaponry) might be easier to use. It is possible to solve these questions using Venn diagrams, too, but it is more convenient to solve them using a Double Set Matrix.

We have discussed solving three overlapping sets using Venn diagrams here.

Today, we will look at the case in which using a Double Set Matrix is easier than using a Venn diagram – in instances where we have two sets of variables, such as English/Math and Middle School/High School, or Cake/Ice cream and Boys/Girls, etc.

Eventually, we will solve our question again using a Venn diagram, for those who like to use a single method for all similar questions. First, take a look at our question:

A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

(A) 18
(B) 27
(C) 36
(D) 72
(E) 180

To solve this problem using a Double Set Matrix, first jot down one set of variables as the row headings and the other as the column headings, as well as a row and column for “totals.” Now all you need to do is add in the information line by line as you read through the question.

“…male graduate students outnumber male undergraduates by a ratio of 7 to 2…
QWQW graph 1

 

 

“…females constitute 70% of the group.

Female students make up 70% of the group, which implies that male students (total of 9x) make up 30% of the group.

9x = (30/100)*Total Students

Total Students = 30x

Since 9x is the total number of male students while 30x is the total number of all students, the total number of female students must be 30x – 9x = 21x.

QWQW graph 2

 

 

If undergraduate students make up 1/6 of the group…

Undergrad students make 1/6 of the group, i.e. (1/6)*30x = 5x

If the total number of undergrad students is 5x and the number of male undergrad students is 2x, the number of female undergrad students must be 5x – 2x = 3x.

This implies that the number of graduate females must be 18x, since the total number of females is 21x.

QWQW graph 3

 

 

Therefore, the number of graduate females must be a multiple of 18. 27 is the only answer choice that is not a multiple of 18, so it cannot be the number of graduate females – therefore, our answer must be B.

Now, here is how Superman can rescue us in this question. An analysis similar to the one above will give us a Venn diagram which looks like this:

qwqw pic

 

 

 

 

 

 

Of course, we will get the same answer: the number of graduate females must be a multiple of 18. We know 27 is not a multiple of 18, so it cannot be the number of graduate females and therefore, our answer is still B.

Hopefully, next time you come across an overlapping sets question, you will know exactly who your superhero is!

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: 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.

Updated GMAT Score Cancellation and Reinstatement Policies: What This Means For You

GMAT Cancel ScoresGMAC has updated its score cancelation and reinstatement policies for GMAT test-takers. A full description of these changes is included in GMAC’s recently published blog article, but here are some highlights and guidance on what this means for future GMAT test-takers:

What is Changing?
If you took the GMAT and felt like you needed more time to decide whether or not to cancel your score, then you’ll be happy with GMAC’s new policy. Test-takers now have 5 years to reinstate their scores and 3 days to cancel them. Before this, test-takers had to be much more rushed in making their decisions, with only 60 days to reinstate their scores, and a mere 2 minutes to cancel them.

The cost of these actions is also much more forgiving: it is now only $50 to reinstate your score (compared to the previous $100 fee), however you will have to pay a fee of $25 to cancel your score if you choose to do so after leaving the test center.

What is NOT Changing?
GMAC has kept several of its cancelation and reinstatement policies intact. For example, it is still true that if you choose to cancel your score, no one but you will know about it. There is also still no fee to cancel your score at the test center, and the period you must wait to retake the GMAT is still 16 days.

Why Does This Matter?
Why do we even care about this change in the GMAC’s policies? Well for one, it allows for much more flexibility in the test-taking process, as test-takers

who choose to cancel their scores now have much more time to prepare for their next test administration. (No more scrambling to prepare for a retest in 16 days!) However, it is still important to remember that the GMAT retest policy still applies, in that you cannot take the GMAT more than 5 times in 12 months, so it is important to build a “buffer” into your prep schedule. If you test too close to an MBA application deadline, you won’t have time to retest.

These changes in policy also just go to show us that nothing in life is free (except canceling at the test center). If you want the convenience and luxury of having extra time to make your decisions, you’d better be ready to pay up for it. To minimize this cost, test-takers should have a target GMAT score in mind as well as a plan going into the test, and then actually stick to that plan upon receiving a final score. Think of this like buying an airline ticket – many airlines will let you hold a ticket for free, but it can cost an additional fee to hold it for up to a week. The same idea applies here. Additional time isn’t going to change your score and it shouldn’t impact what score you’re willing to accept, so have a game plan going into test day and stick to it to avoid unnecessary fees.

It is also worth noting that most business schools will still accept a candidate’s highest GMAT score (after all, it is in the school’s best interests to report having students with high average GMAT scores), so if you take the GMAT and score moderately higher than you did the last time you took the test, it may not be necessary to actually cancel your lower score. Talk to the schools to which you’re applying to understand the programs’ policies, but don’t overthink it. Unless there’s a significant gap between your old and new score (+100 points), or you achieved an extremely low score one of the times you took the test (below 500 points), save your money and keep all of your scores.

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

By Joanna Graham

What Makes GMAT Quant Questions So Hard?

Quarter Wit, Quarter WisdomWe know that the essentials of the GMAT Quant section are pretty simple: advanced topics such as derivatives, complex numbers, matrices and trigonometry are not included, while fundamentals we all learned from our high school math books are included. So it would be natural to think that the GMAT Quant section should not pose much of a problem for most test-takers (especially for engineering students, who have actually covered far more advanced math during their past studies).

Hence, it often comes as a shock when many test-takers, including engineering students, receive a dismal Quant score on the first practice test they take. Of course, with practice, they usually wise up to the treachery of the GMAT, but until then, the Quant section is responsible for many a nightmare!

Today, let’s see what kind of treachery we are talking about – problems like this make some people laugh out loud and others pull at their hair!

Is the product pqr divisible by 12?
Statement 1: p is a multiple of 3
Statement 2: q is a multiple of 4

This seems like an easy C (Statements 1 and 2 together are sufficient, but alone are not sufficient), doesn’t it? P is a multiple of 3 and q is a multiple of 4, so together, p*q would be a multiple of 3*4 = 12. If p * q is already a multiple of 12, then obviously it would seem that p*q*r would be a multiple of 12, too.

But here is the catch – where is it mentioned that r must be an integer? Just because p and q are integers (multiples of 3 and 4 respectively), it does not imply that r must also be an integer.

If r is an integer, then sure, p*q*r will be divisible by 12. Imagine, however, that p = 3, q = 4 and r = 1/12. Now the product p*q*r = 3*4*(1/12) = 1. 1 is not divisible by 12, so in this case, pqr is not divisible by 12. Hence, both statements together are not sufficient to answer the question, and our answer is in fact E!

This question is very basic, but it still tricks us because we want to assume that p, q and r are clean integer values.

Along these same lines, let’s try the another one:

If 10^a * 3^b * 5^c = 450^n, what is the value of c?
Statement 1: a is 1.
Statement 2:  b is 2.

The first thing most of us will do here is split 450 into its prime factors:

450 = 2 * 3^2 * 5^2

450^n = 2^n * 3^2n * 5^2n

And do the same thing with the left side of the equation:

10^a * 3^b * 5^c = 2^a * 3^b * 5^(a+c)

Bringing the given equation back, we get:

2^a * 3^b * 5^(a+c) = 2^n * 3^2n * 5^2n

Statement 1: a is 1.

Equating the power of 2 on both sides, we see that a = n = 1.

a + c = 2n (equating the power of 5 on both sides)

1 + c = 2

c = 1

Statement 2:  b is 2.

Equating the power of 3 on both sides, we see that b = 2n = 2, so n = 1.

If n = 1, a = 1 by equating the powers of 2 on both sides.

a + c = 2n (equating the power of 5 on both sides)

1 + c = 2

c = 1

So it seems that both statements are separately sufficient. But hold on – again, the variables here don’t need to be cleanly fitting integers. The variables could pan out the way discussed in our first problem, or very differently.

Say, n = 1. When Statement 1 gives you that a = 1, you get 10^1 * 3^b * 5^c = 450^1.

3^b * 5^c = 45

Now note that value of c depends on the value of b, which needn’t be 2.

If b  = 3, then 3^3 * 5^c = 45.

5^c = 45/27

C will take a non-integer value here.

c = .3174

The question does not mention that all variables are integers, therefore there are infinite values that c can take depending on the values of b. Similarly, we can see that Statement 2 alone is also not sufficient. Using both statements together, you will get:

2^a * 3^b * 5^(a+c) = 450^n

2^1 * 3^2 * 5^(1 + c) = 450^n

5^(1 + c) = 450^n/18

By now, you’ve probably realized that depending on the value of n, c can take infinite different values. If n = 1, c = 1. If n = 2, c = 4.8. And so on… We don’t need to actually find these values – it is enough to know that different values of n will give different values of c.

With this in mind, we can see that both statements together are not sufficient, and therefore our answer must be E.

Hopefully, in future, this sneaky trick will not get you!

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: Verbal Is About The Beat, Not The Lyrics

GMAT Tip of the WeekOn our final Friday of Hip Hop Month here in the “GMAT Tip of the Week” space, let’s take a moment to appreciate the unsung (or at least non-singing) heroes of hip hop. Did you like Snoop and Tupac in the early 90s, or Eminem in the late 90s? They spit the rhymes, but what you likely enjoy most through your Beats By Dre are Dr. Dre’s classic beats.

A fan of Jay-Z and Cam’ron in the early 2000s? There’s no H to the Izzo or Heart of the City without Kanye West’s beats behind them. More recently, Kane Beatz and DJ Khaled have been the masterminds behind those bangers that you know as Drake, Lil’ Wayne, or Nicki Minaj hits.

So, ok The Game wouldn’t get far without Kanye behind him, and 50 Cent would be in da club cleaning the bathrooms without that classic beat by Dre. But what does this have to do with your GMAT score?

One of the biggest mistakes you can make as a GMAT examinee is to see the question for its subject matter (“it’s about crime rates” or “it’s about antihistamines”) and not for its structure (“it’s a wordplay difference” or “that’s classic generalization”). The subject matter is the lyrics that tend to get the glory, but the standardized-format structure is the beat. Even though you may find the lyrics “Go Shorty, it’s your birthday…” in your head, that’s not at all what you like about that song. It’s the epic beat. The same is true for GMAT verbal questions: what makes them tick, and what you should keep your focus on, is the structure behind that content.

Consider two examples, which may look entirely different but are actually the exact same question:

Example #1: The city of Goshorn has a substantial problem with its budgeting process for public works projects. Last year’s Sullivan Park expansion ran nearly 50% over budget, for example, and the city has gone from running an annual budget surplus for nearly two decades straight to now facing prohibitive budget deficits.

Which of the following, if true, most strengthens the argument that Goshorn has a substantial problem with its budgeting process?

(A) The Sullivan Park expansion project featured the smallest cost-above-budget percentage of all Goshorn’s public works projects.
(B) Goshorn’s budgeting process for public works has not been updated in nearly 20 years.
(C) A new hiking and jogging trail in Goshorn cost more than twice as much to construct as did a similar project completed just ten years earlier.
(D) Goshorn’s revenue from property taxes has decreased markedly since the height of the real estate boom five years earlier.
(E) The city of Goshorn does not receive any federal or state funding for its public works projects, although several nearby cities do.

————————————————————
Example #2: The introduction of a new drug into the marketplace should be contingent upon our having a good understanding of its social impact. However, the social impact of the newly marketed antihistamine is far from clear. It is obvious, then, that there should be a general reduction in the pace of bringing to the marketplace new drugs that are now being created.

Which one of the following, if true, most strengthens the argument?

(A) The social impact of the new antihistamine is much better understood than that of most new drugs being tested.
(B) The social impact of some of the new drugs being tested is poorly understood.
(C) The economic success of some drugs is inversely proportional to how well we understand their social impact.
(D) The new antihistamine is chemically similar to some of the new drugs being tested.
(E) The new antihistamine should be next on the market only if most new drugs being tested should be on the market also.

In each case, exactly one example is provided as evidence that there is an overall, general problem going on. In the first, that example is Sullivan Park, a project that ran over budget, leading to the conclusion that “the city has a substantial problem with its budgeting process.” In the second, exactly one new antihistamine is known to be poorly understood, leading to the conclusion that there should be a “general reduction” in the pace of bringing drugs to market (since, as the argument states, drugs should be well understood before they’re brought to the marketplace).

This is classic generalization, a common theme in Critical Reasoning problems. One example is given and a much broader conclusion is drawn, which is a flawed argument because you just don’t know whether that example is an outlier or the norm. In each of these two problems, your job is to strengthen the argument, so you want to employ the “Strengthen a Generalization Error” strategy – you want to find evidence in the answer choice that the single piece of evidence is indicative of the majority of data points.

With the first example, Answer Choice A does that by showing that Sullivan Park was actually the best-budgeted project (the smallest cost-above-budget percentage). If that poorly-budgeted project is the best, then all the other projects must be worse, and THEN you have a substantial problem overall. In the second example, again Choice A serves the exact same purpose: if the one antihistamine we know about is better understood than most, then most drugs are less-understood, meaning that the majority of drugs are poorly understood. And if that’s the case, then yes, we can draw that general conclusion.

The overall lesson?

GMAT verbal problems can be about anything under the sun: elections in fake countries, the heights of trees in the Galapagos, warranty claims on heavy duty trucks, the visibility of particles breaking off from comets…but that’s not what the test is about. Focus on the beats, and not the lyrics. And the common Critical Reasoning beats are:

1) Generalization
Like you saw here, if a general/universal conclusion is drawn from one data point, you want to either show that that data point is indicative of most/all (Strengthen) or that it’s an outlier (Weaken).

2) Correlation/Causation
Just because two things occur together (For example, “It’s dark so it must be nighttime.”) does not mean that one causes the other (What about an eclipse, or the fact that your hotel room has blackout shades?).

3) Clever Wordplay
This is the most common type of logical error in Critical Reasoning, in which one premise uses a closely-related term (for example “arrests”) to the term that another premise and/or the conclusion uses (“crimes committed”). When you identify that those two things are close but not quite the same, then your job is clear: find an answer choice that links them together (in a Strengthen question) or one that shows that they’re clearly not the same thing (Weaken).

4) Statistics and Data Flaws
When statistics are used in Critical Reasoning problems, look to make sure that the proper type of statistic is used (does an absolute number make sense, or should it be a percentage?) and that the statistic directly relates to the conclusion (much like the “Clever Wordplay” strategy).

Most importantly, recognize that the content of these problems is more or less a necessary evil: the problems have to be about something, but that’s not what they’re really testing. They’re testing your understanding of the underlying logic and structure. So in honor of all the great DJs that have gotten your shoulders shaking and toes tapping over the years, remember that to beat the GMAT, you’ll have to do it with the beats.

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.

New GMAT Undergraduate Pricing Initiative

featured_money@wdd2xIn an effort to attract more undergraduate test takers, GMAC is rolling out a tiered pricing structure for students who register for the GMAT before June 1, 2016 and complete the test by December 31, 2016.

While targeted undergrad outreach efforts and undergrad discounts on the GMAT aren’t new to GMAC, the scale and diversity in pricing is. (GMAC piloted discounting test registration fees a few years ago on select U.S. undergrad campuses as part of a partnership program with select test prep companies and universities.) But like any good sale, is the deal too good to be true?  Let’s take a closer look at the offers (and fine print):

Both options feature discounted registration fees, but limited score report options and more expensive additional score reports (ASRs). ASRs are currently $28 per report.

Option 1: $150 registration fee, No initial score reports (ASR: $50 each)

Option 2: $200 registration fee, 2 initial score reports (ASR: $50 each)

Option 3: $250 registration fee, 5 initial score reports (ASR: $28 each)**

**Current GMAT pricing

Keep in mind that the average GMAT test taker submits 2.7 score reports with their business school applications so GMAC is hoping to recover some of those initial cost savings down the road, but yes, that $50 ASR fee can create a little sticker shock.

So is there an upside to any of these options?

For students who aren’t thinking about grad school anytime soon and, more importantly, have time to prepare for the GMAT (think second-semester Seniors or students with a lighter course load), Option 1 does have a few merits. Because these students don’t have grad school or specific programs on their radar, the lack of score reports isn’t an issue. And since scores are good for five years, it gives students a chance to bank a good score early while not shelling out the full $250.

This is the population that GMAC is targeting with this promotion because the reality is most students will end up sending score reports to multiple programs. However, if the cost of an ASR increases down the road, at least this locks in a lower test fee and possibly a competitive ASR fee.

Students who are applying to a graduate program now (think Juniors or Seniors looking at a pre-work-experience programs) should definitely consider Option 2. Since these students already know which program they’re aiming for, the two free score reports at the test center are a bargain (and ultimately save the student $50).

What isn’t mentioned on the website but should be considered is the current GMAT registration fee of $250. This fee hasn’t changed in over a decade, and while GMAC hasn’t made any announcements about a price hike, it’s unreasonable to think that it’ll remain $250 forever. The odds of the fees increasing in the next  5- 10 years? Hard to say, but there’s likely some merit in locking in a lower priced test.

When you examine Option 3, or the current GMAT standard, you should also look at the GMAT’s primary competitor, the GRE, which is a more widely recognized brand at the undergrad level. ETS just increased GRE fees in the U.S. from $160 to $205 in January of 2016 (ETS does offer a reduced fee certificate to undergrads who meet certain criteria which reduces the cost by 50%). So by offering a variety of pricing options, GMAC is making the GMAT more financially competitive with the GRE.

Regardless of whether you take the GMAT or GRE, Veritas Prep is committed to helping you prepare to do your best on test day. You can find additional information about the GMAC tiered pricing here and information on Veritas Prep’s GMAT prep offerings here.  We also encourage students to sign up for one of our free online GMAT seminars, and to follow us on FacebookYouTubeGoogle+, and Twitter!

By Joanna Graham

Quarter Wit, Quarter Wisdom: Dealing with Tangents on the GMAT

Quarter Wit, Quarter WisdomConsidering a two dimensional figure, a tangent is a line that touches a curve at a single point.  Here are some examples of tangents:
QWQW 1

 


 

In each of these cases, the line touches the curve at a single point. In the case of a circle, when you draw the radius of the circle from the center to the point of contact with the tangent, the radius is perpendicular to the tangent (as demonstrated in the figure on the right, above). A question discussing this concept is given in our post here.

Today, we will look at a question involving a tangent to a parabola:

If f(x) = 3x^2 – tx + 5 is tangent to the x-axis, what is the value of the positive number t?

(A) 2√15
(B) 4√15
(C) 3√13
(D) 4√13
(E) 6√15

Let’s first try to understand what the question is saying.

f(x) is a tangent to the x-axis. We know that the x-axis is a straight line, so f(x) must be a curve. A quadratic equation, such as our given equation of f(x) = 3x^2 -tx +5, gives a parabola. Since the x^2 term in the equation is positive, the parabola would be facing upwards and touching the x-axis at a single point, such as:

QWQW 2

 

 

 

 

 

Since the parabola touches the x-axis in only one point, it means the quadratic has only one root, or in other words, the quadratic must be a perfect square.

Therefore, f(x) = 3x^2 – tx + 5 = √3(x)^2 – tx + (√5)^2

To get f(x) in the form a^2 – 2ab + b^2 = (a – b)^2,

tx = 2ab = (2√3)x * √5

t = 2√15

Note that if t takes this value, the quadratic will have only one root.

Plugging this value of t back into our equation, we will get: f(x) = √3(x)^2 – 2(√15)(x) + (√5)^2

f(x) = (√3)x – (√5)^2

We know that the root of f(x) is the point where the value of the y coordinate is 0. Therefore:

(√3)x – (√5)^2  = 0

x = (√5)/(√3)

At this x co-ordinate, the parabola will touch the x axis.

[This calculation was shown only to help you completely understand the question. We could have easily stopped at t = 2(√15).]

Therefore, our answer is A.

The question can be solved in various other ways – think of how, and write your thoughts in the comments below!

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

The GMAC Executive Assessment: Part 2

GMAT Select Section Order PilotIn our first post, we broke down the new GMAC® Executive Assessment which provides EMBA candidates with an alternative testing option to the GMAT. While on paper, the exam might resemble a “mini-GMAT,” a deeper dive reveals an assessment with GMAT roots, but a distinct personality of its own.

 
More Business Focus
A look at sample questions from the website suggests that the EA pulls from item pools that are similar, if not identical, to the GMAT. In fact, some questions seem to have more of a “business” feel compared to your traditional GMAT question. (The GMAT has long been touted as an exam that doesn’t reward or punish lack of a traditional business background, as it aims to test critical reasoning and higher order thinking skills that are industry-agnostic.)

This may be a coincidence, but one can’t ignore the fact that most EMBA candidates have significant work experience (10+ years typically) and most likely a stronger sense of business in general compared to their 24-year-old counterparts looking at full-time programs. Regardless, any leaning towards business (whether intentional or not) would likely be attractive to more EMBA candidates.

Integrated Reasoning Grows in Prominence
One other interesting aspect of the EA is the increased proportion of Integrated Reasoning (IR) questions. IR makes up exactly one-third of this assessment and is incorporated into the candidate’s total score. Conversely, IR is a small portion (30 minutes) of the GMAT exam. The GMAT quantitative and verbal sections are each 75 minutes in length, and the GMAT total score represents a combination of the quantitative and verbal sub-scores. GMAT IR scores are reported separately from the total score.

While GMAC has published survey research on the “relevance” of skills tested on IR, the deeper integration of IR into the EA assessment and total score seems to further support the notion that the skills tested are truly relevant and strong indicators of success in a graduate business program. And perhaps these skills are even more important at the EMBA level.

Pilot Program for Now
The Executive Assessment (EA) is currently in a Beta phase that will last at least 18 months (or a full admissions cycle and academic year) to allow for validity studies to be conducted. GMAC has long been committed to developing assessment products that are not only relevant, but valid predictors of success in a graduate management program. The six pilot programs were selected because they were willing to commit the necessary time, energy and resources to see this phase through.

The EA targets a different demographic than the GMAT (older, significant work experience, further removed from the undergrad experience) and the test doesn’t leverage computer-adaptive testing in the way that the current GMAT does. Thus, norms for this assessment will differ, further underscoring the importance of measuring exam outcomes against academic performance in an EMBA program.  At this time, there are no plans to add additional programs until after the Beta phase is complete.

Only “Modest Preparation” Required
One of the biggest differences between the EA and GMAT is the amount of preparation that GMAC is advocating for it. It’s no secret that candidates need to prepare for the GMAT, and GMAC survey research indicates that the average candidate spends between 60 and 90 days preparing for the GMAT.  However, the EA recognizes that candidates are less likely to have the bandwidth for preparation that traditional GMAT candidates might have.  The EA will help schools to differentiate competencies that are a little “rusty” versus those that are “ready” and enable them to prescribe pre-work to ensure all candidates begin their EMBA programs on an even playing field.

That being said, candidates looking to distinguish themselves from other applicants can certainly benefit from preparation. Given the overlap with GMAT content, leveraging current GMAT materials to gain a better understanding of question types is a good starting point.  Pacing, as always, will be paramount, and additional time and focus on IR will be crucial given its more significant role in the exam (and total score).

If you’re interested in learning more about GMAT preparation and customized options for EA preparation, please visit our GMAT Website or attend one of our upcoming free online GMAT seminars. And, be sure to follow us on FacebookYouTubeGoogle+, and Twitter!

By Joanna Graham

GMAT Tip of the Week: Your Mind Is Playing Tricks On You

GMAT Tip of the WeekOf all the song lyrics of all the hip hop albums of all time, perhaps the one that captures the difficulty of the GMAT the most comes from the Geto Boys:

It’s f-ed up when your mind is playing tricks on you.

The link above demonstrates a handful of ways that your mind can play tricks on you when you’re in the “fog of war” during the GMAT, but here, four Hip Hop Months later in the middle of yet another election season that has many Millennial MBA aspirants feeling the Bern, it’s time to detail one more. Consider this Critical Reasoning problem:

Among the one hundred most profitable companies in the United States, nearly half qualify as “socially responsible companies,” including seven of the top ten most profitable on that list. This designation means that these companies donate a significant portion of their revenues to charity; that they adhere to all relevant environmental and product safety standards; and that their hiring and employment policies encourage commitments to diversity, gender pay equality, and work-life balance.

Which of the following conclusions can be drawn based on the statements above?

(A) Socially responsible companies are, on average, more profitable than other companies.
(B) Consumers prefer to purchase products from socially responsible companies whenever possible.
(C) It is possible for any company to be both socially responsible and profitable.
(D) Companies do not have to be socially responsible in order to be profitable.
(E) Not all socially responsible companies are profitable.

How does your mind play tricks on you here? Check out these statistics from the Veritas Prep Practice Tests:

Socially responsible

When you look at the two most popular answer choices, there’s a stark difference in what they mean outside the context of the problem. The most popular – but incorrect – answer says what you want it to say. You want social responsibility to pay off, for companies to be rewarded for doing the right thing. But it’s the words that don’t appeal to your heart and/or conscience that are the most important on these problems, and the justification for “any company” to be both socially responsible and profitable isn’t there in the argument.

Sure, several companies in the top 10 and top 100 are both socially responsible and profitable, but ANY company means that if you pick any given company, that particular company has to be capable of both. And it may very well be that in certain industries, the profit margins are too slim for that to be possible.

Say, for example, that in one of the commodities markets there simply isn’t any brand equity for social responsibility, and the top competitors are so focused on pushing out competition that any cost outside of productivity would put a company into the red. It’s not a thought you necessarily want to have, but it’s a possible outcome given the prompt, and it invalidates answer (C). Since Inference answers MUST BE TRUE, C just doesn’t meet that standard.

Which brings you to D, the correct but unpopular answer. That’s not what your heart and conscience want to conclude at all – you’d love for there to be a world in which consumers will reject any products from companies that aren’t made by companies taking the moral high ground, but if you look specifically at the facts of the argument, 3 of the top 10 most profitable companies and more than half of the top 100 are not socially responsible. So answer choice D is airtight – it’s not what you want to hear, but it’s definitely true based on the argument.

The lesson? Once you get that MBA you have the opportunity to change the world, but while you’re in the GMAT test center doing Critical Reasoning problems, you can only draw conclusions based on the facts that they give you. Don’t let your outside opinions frame the way that you read the problem. If you know that you have some personal interest in the topic, that’s a sign that you’ll need to be even more literal about what’s written. Your mind can play tricks on you – as it did for nearly half of test-takers here – so know that on test day you have to get it under control.

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.

2 Tips to Make GMAT Remainder Questions Easy

stressed-studentSeveral months ago, I wrote an article about remaindersBecause this concept shows up so often on the GMAT, I thought it would be useful to revisit the topic. At times, it will be helpful to know the kind of terminology we’re taught in grade school, while at other times, we’ll simply want to select simple numbers that satisfy the parameters of a Data Sufficiency statement.

So let’s explore each of these scenarios in a little more detail. A simple example can illustrate the terminology: if we divide 7 by 4, we’ll have 7/4 = 1 + ¾.

7, the term we’re dividing by something else, is called the dividend. 4, which is doing the dividing, is called the divisor. 1, the whole number component of the mixed fraction, is the quotient. And 3 is the remainder. This probably feels familiar.

In the abstract, the equation is: Dividend/Divisor = Quotient + Remainder/Divisor. If we multiply through by the Divisor, we get: Dividend = Quotient*Divisor + Remainder.

Simply knowing this terminology will be sufficient to answer the following official question:

When N is divided by T, the quotient is S and the remainder is V. Which of the following expressions is equal to N? 

A) ST
B) S + V
C) ST + V
D) T(S+V)
E) T(S – V) 

In this problem, N – which is getting divided by something else – is our dividend, T is the divisor, S is the quotient, and V is the remainder. Plugging the variables into our equation of Dividend = Quotient*Divisor + Remainder, we get N = ST + V… and we’re done! The answer is C.

(Note that if you forgot the equation, you could also pick simple numbers to solve this problem. Say N = 7 and T = 3. 7/3 = 2 + 1/3.  The Quotient is 2, and the remainder is 1, so V = 1. Now, if we plug in 3 for T, 2 for S, and 1 for V, we’ll want an N of 7. Answer choice C will give us an N of 7, 2*3 + 1 = 7, so this is correct.)

When we need to generate a list of potential values to test in a data sufficiency question, often a statement will give us information about the dividend in terms of the divisor and the remainder.

Take the following example: when x is divided by 5, the remainder is 4. Here, the dividend is x, the divisor is 5, and the remainder is 4. We don’t know the quotient, so we’ll just call it q. In equation form, it will look like this: x = 5q + 4. Now we can generate values for x by picking values for q, bearing in mind that the quotient must be a non-negative integer.

If q = 0, x = 4. If q = 1, x = 9. If q=2, x = 14. Notice the pattern in our x values: x = 4 or 9 or 14… In essence, the first allowable value of x is the remainder. Afterwards, we’re simply adding the divisor, 5, over and over. This is a handy shortcut to use in complicated data sufficiency problems, such as the following:

If x and y are integers, what is the remainder when x^2 + y^2 is divided by 5?

1) When x – y is divided by 5, the remainder is 1
2) When x + y is divided by 5, the remainder is 2

In this problem, Statement 1 gives us potential values for x – y. If we begin with the remainder (1) and continually add the divisor (5), we know that x – y = 1 or 6 or 11, etc. If x – y = 1, we can say that x = 1 and y = 0. In this case, x^2 + y^2 = 1 + 0 = 1, and the remainder when 1 is divided by 5 is 1. If x – y = 6, then we can say that x = 7 and y = 1. Now x^2 + y^2 = 49 + 1 = 50, and the remainder when 50 is divided by 5 is 0. Because the remainder changes from one scenario to another, Statement 1 is not sufficient alone.

Statement 2 gives us potential values for x + y. If we begin with the remainder (2) and continually add the divisor (5), we know that x + y = 2 or 7 or 12, etc. If x + y = 2, we can say that x = 1 and y = 1. In this case, x^2 + y^2 = 1 + 1 = 2, and the remainder when 2 is divided by 5 is 2. If x + y = 7, then we can say that x = 7 and y = 0. Now x^2 + y^2 = 49 + 0 = 49, and the remainder when 49 is divided by 5 is 4. Because the remainder changes from one scenario to another, Statement 2 is also not sufficient alone.

Now test them together – simply select one scenario from Statement 1 and one scenario from Statement 2 and see what happens. Say x – y = 1 and x + y = 7. Adding these equations, we get 2x = 8, or x = 4. If x = 4, y = 3. Now x^2 + y^2 = 16 + 9 = 25, and the remainder when 25 is divided by 5 is 0.

We need to see if this will ever change, so try another scenario. Say x – y = 6 and x + y = 12. Adding the equations, we get 2x = 18, or x = 9. If x =  9, y = 3, and x^2 + y^2 = 81 + 9 = 90. The remainder when 90 is divided by 5 is, again, 0. No matter what we select, this will be the case – we know definitively that the remainder is 0. Together the statements are sufficient, so the answer is C.

Takeaway: You’re virtually guaranteed to see remainder questions on the GMAT, so you want to make sure you have this concept mastered. First, make sure you feel comfortable with the following equation: Dividend = Divisor*Quotient + Remainder. Second, if you need to select values, you can simply start with the remainder and then add the divisor over and over again. If you internalize these two ideas, remainder questions will become considerably less daunting.

*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 follow us on FacebookYouTubeGoogle+ and Twitter!

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

The GMAC Executive Assessment: A New Way to Evaluate EMBA Applicants

GMAT Select Section Order PilotImagine a world where you could take the GMAT, but it was over in 90 minutes, and no advanced preparation was required. It sounds too good to be true, but the Graduate Management Admission Council (GMAC®) launched a new product, the GMAC® Executive Assessment, on March 1 that is designed to give Executive MBA programs a new way to evaluate candidates.

EMBA programs have struggled with making standardized testing compulsory in recent years. Candidates typically have much more work experience than full-time or part-time applicants, and thus are further removed from an academic classroom experience (and often have even less time to prepare for and take a standardized test). The GMAC® Executive Assessment gives applicants another testing option that looks a lot like the GMAT, but may have an easier path to success.

Let’s take a closer look at how this is similar to and different from the GMAT:

Shorter Sections
The GMAC® Executive Assessment contains three (3) sections: Integrated Reasoning, Verbal and Quantitative. Each section is just 30 minutes long, and the exam is delivered on-demand at existing test centers around the globe. Scores are valid for 5 years, unofficial scores are provided at the test center upon completion, and the same basic registration guidelines hold true (compared to the GMAT exam). Candidates are required to register at least 24 hours in advance, ID requirements at the test center are the same as the GMAT, and while there is an on-screen calculator for IR, there isn’t one for the Quantitative section.

In terms of test structure, there are 40 questions: 12 Integrated Reasoning, 14 Verbal, and 14 Quantitative. Regarding pacing, there are no differences across Integrated Reasoning, but you do gain a little bit of time on the verbal and quantitative sections (compared to the GMAT). Also, the order of sections is slightly different than the GMAT, with Integrated Reasoning leading off, followed by Verbal and then Quantitative.

From a content perspective, the test seems to be consistent with current GMAT questions, but with a slightly more skewed focus towards business. If some of the practice questions posted by GMAC® look familiar, they are – they appeared in previous versions of the Official Guide which seems to suggest content that that is consistent with current GMAT questions.

Finally, once you start the test, it will be a race to the finish with no breaks between sections.

Bigger Price, Different Retake Policy
While the test is similar to the GMAT from a content perspective, there are definitely some significant differences. First, prepare yourself for a little sticker shock: you might think since you’re getting fewer questions and you’re in and out of the test center faster, there might be a discount, however, this shorter assessment will actually cost you more ($350, compared to $250 for the GMAT). However, there is no fee for rescheduling – unless you’re less than 24 hours from your appointment – or for additional score reports.

If you’re not happy with your score, you can re-test, but you can only do so once, so make sure you’re ready! Rather than waiting 16 days to re-test like the GMAT, the waiting period is only 24 hours.

Computer Adaptive? Yes, But…
This test is not computer adaptive in the way that the GMAT is, so your answer to a question does not dictate which question you’ll see next. Rather, questions are released in groups (based on your performance on the previous group). This type of testing is called multi-stage adaptive design. The score scale is different as well – total scores will be reported on a scale of 100-200, and individual sections on scales of 0-20.

How Do You Prepare for the Executive Assessment?
One of the benefits of the Executive Assessment being touted by GMAC® is the reduction in significant preparation for this test. GMAC® advocates minimal preparation and has not rolled out any preparation materials specifically designed for this assessment. While a shorter test might suggest less preparation required, it also give candidates an opportunity to truly shine and demonstrate mastery of certain subjects and critical reasoning skills.

Which EMBA Programs Accept It Today?
Just like currency, a test is only as good as the institutions that accept it. Currently, the exam is being touted as an EMBA admissions tool. Six schools have signed on to use it as part of their admissions processes:  INSEAD (France), CEIBS (China), London Business School (United Kingdom), the University of Hong Kong, Columbia University (New York, USA), and the University of Chicago (Illinois, USA). How the schools are using it varies by program.

In terms of preference, LBS’ website suggests that they’ll accept either the Executive Assessment or the GMAT while CEIBS indicates a preference for the Executive Assessment. Columbia, the University of Chicago, and the University of Hong Kong will accept the GMAT, GRE or Executive Assessment, and INSEAD only lists the GMAT currently (as of 3/11/2016), but we can assume they’ll accept either  the GMAT or Executive Assessment for future applicants.

We’ll take a deeper look at the Executive Assessment and schools in our next article, but initial feedback seems positive. LBS’ blog touts it as a quality tool because it is “relevant to executives in terms of its content (much more focus on critical thinking, analysis and problem solving, and much less on pure mathematics and grammatical structures).” At Veritas Prep, we’re committed to staying abreast of the latest developments and trends in the graduate business space, and helping candidate identify the best assessment and mode of preparation.

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

By Joanna Graham

Understanding Absolute Values with Two Variables

Quarter Wit, Quarter WisdomWe have looked at quite a few absolute value and inequality concepts. (Check out our discussion on the basics of absolute values and inequalities, here, and our discussion on how to handle inequalities with multiple absolute value terms in a single variable, here.) Today let’s look at an absolute value concept involving two variables. It is unlikely that you will see such a question on the actual GMAT, since it involves multiple steps, but it will help you understand absolute values better.

Recall the definition of absolute value:

|x| = x if x ≥ 0

|x| = -x if x < 0

So, to remove the absolute value sign, you will need to consider two cases – one when x is positive or 0, and another when it is negative.

Say, you are given an inequality, such as |x – y| < |x|. Here, you have two absolute value expressions: |x – y| and |x|. You need to get rid of the absolute value signs, but how will you do that?

You know that to remove the absolute value sign, you need to consider the two cases. Therefore:

|x – y| = (x – y) if (x – y) ≥ 0

|x – y| = – (x – y) if (x – y) < 0

But don’t forget, we also need to remove the absolute value sign that |x| has. Therefore:

|x| = x if x ≥ 0

|x| = -x if x < 0

In all we will get four cases to consider:

Case 1: (x – y) ≥ 0 and x ≥ 0

Case 2: (x – y) < 0 and x ≥ 0

Case 3: (x – y) ≥ 0 and x < 0

Case 4: (x – y) < 0 and x < 0

Let’s look at each case separately:

Case 1: (x – y) ≥ 0 (which implies x ≥ y) and x ≥ 0

|x – y| < |x|

(x – y) < x

-y < 0

Multiply by -1 to get:

y > 0

In this case, we will get 0 < y ≤ x.

Case 2: (x – y) < 0 (which implies x < y) and x ≥ 0

|x – y| < |x|

-(x – y) < x

2x > y

x > y/2

In this case, we will get 0 < y/2 < x < y.

Case 3: (x – y) ≥ 0 (which implies x ≥ y) and x < 0

|x – y| < |x|

(x – y) < -x

2x < y

x < y/2

In this case, we will get y ≤ x < y/2 < 0.

Case 4: (x – y) < 0 (which implies x < y) and x < 0

|x – y| < |x|

-(x – y) < -x

-x + y < -x

y < 0

In this case, we will get x < y < 0.

Considering all four cases, we get that both x and y are either positive or both are negative. Case 1 and Case 2 imply that if both x and y are positive, then x > y/2, and Case 3 and Case 4 imply that if both x and y are negative, then x < y/2. With these in mind, there is a range of values in which the inequality will hold. Both x and y should have the same sign – if they are both positive, x > y/2, and if they are both negative, x < y/2.

Here are some examples of values for which the inequality will hold:

x = 4, y = 5

x = 8, y = 2

x = -2, y = -1

x = -5, y = -6

etc.

Here are some examples of values for which the inequality will not hold:

x = 4, y = -5 (x and y have opposite signs)

x = 5, y = 15 (x is not greater than y/2)

x = -5, y = 9 (x and y have opposite signs)

x = -6, y = -14 (x is not less than y/2)

etc.

As said before, don’t worry about going through this method during the actual GMAT exam – if you do get a similar question, some strategies such as plugging in values and/or using answer choices to your advantage will work. Overall, this example hopefully helped you understand absolute values a little better.

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

Quarter Wit, Quarter Wisdom: The Case of a Correct Answer Despite Incorrect Logic!

Quarter Wit, Quarter WisdomIt is common for GMAT test-takers to think in the right direction, understand what a question gives and what it is asking to be found out, but still get the wrong answer. Mistakes made during the execution of a problem are common on the GMAT, but what is rather rare is going with incorrect logic and still getting the correct answer! If only life was this rosy so often!

Today, we will look at a question in which exactly this phenomenon occurs – we will find the flaw in the logic that test-takers often come up with and then learn how to correct that flaw:

If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did had he driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?

(A) 100

(B) 120

(C) 140

(D) 150

(E) 160

This little gem (and it’s detailed algebra solution) is from our Advanced Word Problems book. We will post its solution here, too, for the sake of a comprehensive discussion:

Method 1: Algebra
Let’s start with the basic “Distance = Rate * Time” formula:

D = R*T ……….(I)

From here, the first theoretical trip can be represented as D + 70 = (R + 5)(T + 1), (the motorist travels for 1 extra hour at a rate of 5 mph faster), which can be expanded to D + 70 = RT + R + 5T +5.

We can then eliminate “D” by plugging in the value of “D” from our equation (I):

RT + 70 = RT + R + 5T + 5, which simplifies to 70 = R + 5T + 5 and then to 65 = R + 5T ……….. (II)

The second theoretical trip can be represented as (R+10)(T+2), which expands to RT + 2R + 10T + 20 (not that we only have an expression since we don’t know what the distance is).

The two middle terms (2R + 10T) can be factored to 2(R+5T), which allows us to use equation (II) here:

RT + 2(R+5T) + 20 = RT + 2(65) + 20 = RT + 150.

Since the original distance was RT, the additional distance is 150 more miles, or answer choice D.

We totally understand that this solution is a bit convoluted – algebra often is. So, understandably, students often look for a more direct logical solution.

Here is one they sometimes employ:

Method 2: Logic (Incorrect)
If the motorist had driven 1 hour longer at a rate 5 mph faster, then his original speed would be 70 miles subtracted by the extra 5 miles he drove in that hour to get 70 – 5 = 65 mph. If he drives at a rate 10 mph faster (i.e. at 65 + 10 = 75) * 2 for the extra hours, he/she would have driven 150 miles extra.

But here is the catch in this logic:

The motorist drove for an average rate of 5 mph extra. So the 70 includes not only the extra distance covered in the last hour, but also the extra 5 miles covered every hour for which he drove. Hence, his original speed is not 65. Now, let’s see the correct logical method of solving this:

Method 3: Logic (Correct)
Let’s review the original problem first. Say, speed is “S” mph – we don’t know the number of hours for which this speed was maintained.

STEP 1:

S + S + S + … + S + S = TOTAL DISTANCE COVERED

In the first hypothetical case, the motorist drove for an extra hour at a speed of 5 mph faster. This means he covered 5 extra miles every hour and then covered another S + 5 miles in the last hour. The underlined distances are the extra ones which all add up to 70.

STEP 2:

S + S + S + … + S + S = TOTAL DISTANCE COVERED

+5 +5 +5 + … + 5 + 5 = +70

In the second hypothetical case, in which the motorist drove for two hours longer at a speed of 10 mph faster,  he adds another 5 mph to his hourly speed and covers yet another distance of “S” in the second extra hour. In addition to S, he also covers another 10 miles in the second extra hour. The additional distances are shown in red  in the third case – every hour, the speed is 10 mph faster and he drove for two extra hours in this case (compared with Step 1).

STEP 3:

S + S + S + … + S + S + S + S = TOTAL DISTANCE COVERED

+5  +5  +5 + …  +5  +5  +5 = +70

+5  +5  +5 + …  +5  +5  +5 + 10 = +70 + 10

Note that the +5s and the S all add up to 70 (as seen in Step 2). We also separately add the extra 10 from the last hour. This is the logic of getting the additional distance of 70 + 70 + 10 = 150. It involves no calculations, but does require you to understand the logic. Therefore, our answer is still D.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: The Biggie Smalls Sufficiency Strategy

GMAT Tip of the WeekIf it’s March, it must be Hip Hop Month in the Veritas Prep GMAT Tip of the Week space, where this week we’ll tackle the most notorious GMAT question type – Data Sufficiency – with some help from hip hop’s most notorious rapper – Biggie Smalls.

Biggie’s lyrics – and his name itself – provide a terrific template for you to use when picking numbers to test whether a statement is sufficient or not. So let’s begin with a classic lyric from “Big Poppa” – you may think Big is describing how he’s approach a young lady in a nightclub, but if you listen closely he’s actually talking directly to you as you attack Data Sufficiency:

“Ask you what your interests are, who you be with. Things to make you smile; what numbers to dial.”

“What numbers to dial” tends to be one of the biggest challenges that face GMAT examinees, so let’s examine the strategies that can take your score from “it was all a dream” to sipping champagne when you’re thirsty.

Biggie Smalls Strategy #1: Biggie Smalls
Consider this Data Sufficiency problem:

What is the value of integer z?

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

2) y is not a prime number

Statistically, more than 50% of respondents in the Veritas Prep practice tests incorrectly choose answer choice A, that Statement 1 alone is sufficient but Statement 2 alone is not sufficient. Why? Because they’re not quite sure “what numbers to dial.” People know that they need to test numbers – Statement 1 is very abstract and difficult to visualize with variables – so they test a few numbers that come to mind:

If y = 5, y – 1 = 4, and the problem is then 5/4 which leads to 1, remainder 1.

If y = 10, y – 1 = 9, so the problem is then 10/9 which also leads to 1, remainder 1.

If they keep choosing random integers that happen to come to mind, they’ll see that pattern hold – the answer is ALMOST always 1 remainder 1, with exactly one exception. If y = 2, then y – 1 = 1, and 2 divided by 1 is 2 with no remainder. This is the only case where z does not equal 1, but that one exception shows that Statement 1 is not sufficient.

The question then becomes, “If there’s only one exception, how the heck does the GMAT expect me to stumble on that needle in a haystack?” And the answer comes directly from the Notorious BIG himself:

You need to test “Biggie Smalls,” meaning that you need to test the biggest number they’ll let you use (here it can be infinite, so just test a couple of really big numbers like 1,000 and 1,000,000) and you need to test the smallest number they’ll let you use. Here, that’s y = 2 and y – 1 = 1, since y – 1 must be a positive integer, and the smallest of those is 1.

The problem is that people tend to simply test numbers that come to mind (again, over half of all respondents think that Statement 1 is sufficient, which means that they very likely never considered the pairing of 2 and 1) and don’t push the limits. Data Sufficiency tends to play to the edge cases – if you get a statement like 5 < x < 12, you can’t just test 8, 9, and 10 – you’ll want to consider 5.00001 and 11.9999. When the GMAT gives you a range, use the entire range – and a good way to remind yourself of that is to just remember “Biggie Smalls.”

Biggie Smalls Strategy #2:  Juicy
In arguably his most famous song, “Juicy”, Biggie spits the line, “Damn right I like the life I live, because I went from negative to positive and it’s all…it’s all good (and if you don’t know, now you know).”

There, of course, Biggie is reminding you that you have to consider both negative and positive numbers in Data Sufficiency problems. Consider this example:

a, b, c, and d are consecutive integers such that the product abcd = 5,040. What is the value of d?

1) d is prime

2) a>b>c>d

This problem exemplifies why keeping Big’s words top of mind is so crucial – difficult problems will often “satisfy your intellect” with interesting math…and then beat you with negative/positive ideology. Here it takes some time to factor 5040 into the consecutive integers 7 x 8 x 9 x 10, but once you do, you can see that Statement 1 is sufficient: 7 is the only prime number.

But then when you carry that over to Statement 2, it’s very, very easy to see 7, 8, 9, and 10 as the only choices and again see that d = 7. But wait! If d doesn’t have to be prime – primes can only be positive – that allows for a possibility of negative numbers: -10, -9, -8, and -7. In that case, d could be either 7 or -10, so Statement 2 is actually not sufficient.

So heed Biggie’s logic: you’ll like the life you live much better if you go from negative to positive (or in most cases, vice versa since your mind usually thinks positive first), and if you don’t know (is that sufficient?) now, after checking for both positive and negative and for the biggest and smallest numbers they’ll let you pick, now you know.

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.

Quarter Wit, Quarter Wisdom: How to Find Composite Numbers on the GMAT

Quarter Wit, Quarter WisdomWe love to talk about prime numbers and their various properties for GMAT preparation, but composite numbers usually aren’t mentioned. Composite numbers are often viewed as whatever is leftover after prime numbers are removed from a set of positive integers (except 1 because 1 is neither prime, nor composite), but it is important to understand how these numbers are made, what makes them special and what should come to mind when we read “composite numbers.”

Principle: Every composite number is made up of 2 or more prime numbers. The prime numbers could be the same or they could be distinct.

For example:

2*2 = 4 (Composite number)

2*3*11 = 66 (Composite number)

5*23 = 115 (Composite number)

and so on…

Look at any composite number. You will always be able to split it into 2 or more prime numbers (not necessarily distinct). For example:

72 = 2*2*2*3*3

140 = 2*2*5*7

166 = 2*83

and so on…

This principle does look quite simple and intuitive at first, but when tested, we could face problems because we don’t think much about it. Let’s look at it with the help of one of our 700+ level GMAT questions:

x is the smallest integer greater than 1000 that is not prime and that has only one factor in common with 30!. What is x?

(A) 1009

(B) 1021

(C) 1147

(D) 1273

(E) 50! + 1

If we start with the answer choices, the way we often do when dealing with prime/composite numbers, we will get stuck. If we were looking for a prime number, we would use the method of elimination – we would find factors of all other numbers and the number that was left over would be the prime number.

But in this question, we are instead looking for a composite number – a specific composite number – and some of the answer choices are probably prime. Try as we might, we will not find a factor for them, and by the time we realize that it is prime, we will have wasted a lot of precious time. Let’s start from the question stem, instead.

We need a composite number that has only one factor in common with 30!. Every positive integer will have 1 as a factor, as will 30!, hence the only factor our answer and 30! will have in common is 1.

30! = 1*2*3*…*28*29*30

30! is the product of all integers from 1 to 30, so all prime numbers less than 30 are factors of 30!.

To make a composite number which has no prime factor in common with 30!, we must use prime numbers greater than 30. The first prime number greater than 30 is 31.

(As an aside, note that if we were looking for the smallest number with no factor other than 1 in common with 31!, we would skip to 37. All integers between 31 and 37 are composite and hence, would have factors lying between 1 and 31. Similarly, if we were looking for the smallest number with no factor other than 1 in common with 50!, 53 would be the answer.)

Let’s get back to our question. If we want to make a composite number without using any primes until 30, we must use two or more prime numbers greater than 30, and the smallest prime greater than 30 is 31. If we use two 31’s to get the smallest composite number, we get 31*31 = 961 But 961 is not greater than 1000, so it cannot be our answer.

So, let’s find the next prime number after 31 – it is 37. Multiplying 31 and 37, we get 31*37 = 1147. This is the smallest composite number greater than 1000 with no prime factors in common with 30! – the only factor it has in common with 30! is 1. Therefore, our 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 FacebookYouTubeGoogle+, 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: Verbal Answers Are Like Donald Trump

GMAT Tip of the WeekIn the winter/spring of 2016, Donald Trump is everywhere – always on your TV screen, all over your social media feeds, on the tip of everyone’s tongue, and, yes, even lurking in the answer choices on your GMAT verbal section.

Why are verbal answer choices like Donald Trump? Is it that they’re only correct 20% of the time? That they’re very often a lot of boastful verbiage about nothing? Hackneyed comedy aside, there’s a very valid reason and it’s one that Ted Cruz and Marco Rubio learned just last night:

Verbal choices, like Donald Trump, simply MUST be attacked. If you saw last night’s debate (or read any coverage of it) you saw how the two closest challengers changed tactics immensely, verbally attacking Trump all night. The rationale there is that if you let Trump go unchecked, he’s going to attack you and he’s going to get away with his own stump speeches all night. The exact same thing is true of GMAT verbal answer choices. If you don’t attack them – if you’re not actively looking for reasons that they’re wrong – they’ll both beat you tactically and wear you down over the test. You simply must be in attack mode throughout the verbal section.

What does that mean? For almost every answer choice, there’s some reason there why someone would pick it (after all, if no one picks it then it’s just a terrible, useless answer choice). And so if you’re looking for reasons to like an answer choice, you’re going to find lots to like (and in doing so pick some wrong answers) and you’re going to get worn down by keeping wrong answer choices in your “maybe” pile too long. But if, instead, you’re more skeptical about each answer choice, actively looking for reasons not to pick them, that discerning approach will help you more efficiently find correct answers.

Consider the example:

If Shero wins the election, McGuinness will be appointed head of the planning commission. But Stauning is more qualified to head it since he is an architect who has been on the planning commission for 15 years. Unless the polls are grossly inaccurate, Shero will win.

Which one of the following can be properly inferred from the information above?

(A) If the polls are grossly inaccurate, someone more qualified than McGuinness will be appointed head of the planning commission.
(B) McGuinness will be appointed head of the planning commission only if the polls are a good indication of how the election will turn out.
(C) Either Shero will win the election or Stauning will be appointed head of the planning commission.
(D) McGuinness is not an architect and has not been on the planning commission for 15 years or more.
(E) If the polls are a good indication of how the election will turn out, someone less qualified than Stauning will be appointed head of the planning commission.

Here there’s a lot to like about a lot of answer choices:

A seems plausible. We know that McGuinness isn’t the most qualified, so there’s a high likelihood that a different candidate could find someone better (maybe even Stauning). B also has a lot to like (and it’s actually ALMOST perfect as we’ll discuss in a second). And so on. But you need to attack these answers:

A is fatally flawed. You don’t know for certain that a different candidate would appoint anyone other than McGuinness, and you really only know that one person is more qualified (and does he even want the job?). This cannot be concluded. B has that dangerous word “only” in it – remove it and the answer is correct, but “only if the polls are a good indication” is way too far to go. What if the polls are flawed and the underdog candidate just appoints McGuinness, too? The same logic invalidates C (there’s nothing guaranteeing that a different candidate wouldn’t pick McGuinness), and the word “and” makes D all the harder to prove (how do you know that McGuinness lacks both qualities?).

The lesson? Much like John Kasich may find on that same stage, the nicer and more accommodating you are, the more the GMAT walks over you. If you want to give each answer a fair chance, you’ll find that many answers have enough reason to be tempting. So follow the new GOP debate strategy and always be attacking. You didn’t sign up for the GMAT to make friends with answer choices; you signed up to “win.”

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

By Brian Galvin.

All You Need to Know About Using Interest Equations on the GMAT

PiggyBankAs an undergraduate, I concentrated in Finance. When I tell people this, they make two unwarranted assumptions: the first is that I work in Finance (I don’t), and the second is that I am a glutton for mathematical punishment (debatable).

The reason people are intimidated by the kinds of compound interest equations we encounter in finance classes is that they look complicated. GMAT test-takers get anxious whenever I introduce this topic in class. But, as with most seemingly abstruse topics, these concepts are far less difficult than they appear at first glance.

Here’s all we really need to know about interest equations: if we’re talking about simple interest, the interest will be the same in every time period, and the equation you assemble will end up being straightforward linear algebra (if you choose to do algebra, that is). If we’re talking about compound interest, we’re really talking about an exponent question. The rest involves a bit of logic and algebraic manipulation.

Look at this official question that many of my students have initially struggled with:

An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to 4000 by earning interest. In how many years after the initial investment was made would the 1000 have increased to 8000 by earning interest at that rate?  

(A) 16
(B) 18
(C) 20
(D) 24
(E) 30

Looking at this question, the first instinct of most test-takers is to start frantically rummaging through their memory banks for that compound interest formula – there’s no need. Take a deep breath and remind yourself that these questions are just exponent questions involving a bit of algebra. With this in mind, let’s call the factor that the principal is multiplied by in each time period “x”. (If you’re accustomed to working with the formula, “x” is basically standing in for your standard (1 + r/100.) If you’re not accustomed to this formula, feel free to retroactively erase this parenthetical from your memory banks.)

If the principal is getting multiplied by “x” each year, then after one year, the investment will be 1000x. After two years the investment will be 1000x^2. After three years, it will be 1000x^3… and so on. In our problem, we’re talking about an investment after 12 years, which would be 1000x^12. If this value is 4000, we get the following equation: 1000x^12 = 4000 (and file away for now that the exponent represents the number of years elapsed).

Ultimately, we want to know what the exponent should be when the investment is at $8000. If you’re looking at the answer choices now and think that 24 seems just a little too easy, your instincts are sound.

We need to work with 1000x^12 = 4000. Let’s simplify:

Divide both sides by 1000 to get x^12 = 4.  Solving for x seems unnecessarily complicated, so let’s consider our options. x^12 = 4 is the same as x^12 = 2^2, so if we take the square root of both sides, we will get x^6 = 2.

Essentially, this means that every 6 years (the exponent) the investment is doubling, or multiplied by 2. But we want to know how long it will take for that initial $1000 to become $8000, or to be multiplied by a factor of 8.

What can we do to x^6 = 2 so that we have an 8 on the right side? We can cube both sides!

(x^6)^3 = 2^3

x^18 = 8

This means that it will take 18 years to increase the investment by a factor of 8. Therefore, our answer is B.

Alternatively, once we see that the investment doubles every 6 years, we can ask ourselves how many times we need to double an investment to go from $1000 to $8000. Doubling once gets us to $2000. Doubling twice gets us to $4000. Doubling a third time gets us to $8000. So if we double the investment every 6 years, and we need the investment to double 3 times, it will take a total of 6*3 = 18 years.

Takeaway: There are plenty of formulas that could come in handy on the GMAT – just know that a little logic and conceptual understanding will allow you to solve many of the questions that seem to require a particular formula. Memorization has limits that logic and mental agility don’t.

*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 follow us on FacebookYouTubeGoogle+ and Twitter!

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

Quarter Wit, Quarter Wisdom: Ratios in GMAT Data Sufficiency

Quarter Wit, Quarter WisdomWe know that ratios are the building blocks for a lot of other concepts such as time/speed, work/rate and mixtures. As such, we spend a lot of time getting comfortable with understanding and manipulating ratios, so the GMAT questions that test ratios seem simple enough, but not always! Just like questions from all other test areas, questions on ratios can be tricky too, especially when they are formatted as Data Sufficiency questions.

Let’s look at two cases today: when a little bit of data is sufficient, and when a lot of data is insufficient.

When a little bit of data is sufficient!
Three brothers shared all the proceeds from the sale of their inherited property. If the eldest brother received exactly 5/8 of the total proceeds, how much money did the youngest brother (who received the smallest share) receive from the sale?

Statement 1: The youngest brother received exactly 1/5 the amount received by the middle brother.

Statement 2: The middle brother received exactly half of the two million dollars received by the eldest brother.

First impressions on reading this question? The question stem gives the fraction of money received by one brother. Statement 1 gives the fraction of money received by the youngest brother relative to the amount received by the middle brother. Statement 2 gives the fraction of money received by the middle brother relative to the eldest brother and an actual amount. It seems like the three of these together give us all the information we need. Let’s dig deeper now.

From the Question stem:

Eldest brother’s share = (5/8) of Total

Statement 1: Youngest Brother’s share = (1/5) * Middle brother’s share

We don’t have any actual number – all the information is in fraction/ratio form. Without an actual value, we cannot find the amount of money received by the youngest brother, therefore, Statement 1 alone is not sufficient.

Statement 2: Middle brother’s share = (1/2) * Eldest brother’s share, and the eldest brother’s share = 2 million dollars

Middle brother’s share = (1/2) * 2 million dollars = 1 million dollars

Now, we might be tempted to jump to Statement 1 where the relation between youngest brother’s share and middle brother’s share is given, but hold on: we don’t need that information. We know from the question stem that the eldest brother’s share is (5/8) of the total share.

So 2 million = (5/8) of the total share, therefore the total share = 3.2 million dollars.

We already know the share of the eldest and middle brothers, so we can subtract their shares out of the total and get the share of the youngest brother.

Youngest brother’s share = 3.2 million – 2 million – 1 million = 0.2 million dollars

Statement 2 alone is sufficient, therefore, the answer is B.

When a lot of data is insufficient!
A department manager distributed a number of books, calendars, and diaries among the staff in the department, with each staff member receiving x books, y calendars, and z diaries. How many staff members were in the department?

Statement 1: The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.

Statement 2: The manager distributed a total of 18 books, 27 calendars, and 36 diaries.

First impressions on reading this question? The question stem tells us that each staff member received the same number of books, calendars, and diaries. Statement 1 gives us the ratio of books, calendars and diaries. Statement 2 gives us the actual numbers. It certainly seems that we should be able to obtain the answer. Let’s find out:

Looking at the question stem, Staff Member 1 recieved x books, y calendars, and z diaries, Staff Member 2 recieved x books, y calendars, and z diaries… and so on until Staff Member n (who also recieves x books, y calendars, and z diaries).

With this in mind, the total number of books = nx, the total number of calendars = ny, and the total number of diaries = nz.

Question: What is n?

Statement 1 tells us that x:y:z = 2:3:4. This means the values of x, y and z can be:

2, 3, and 4,

or 4, 6, and 8,

or 6, 9, and 12,

or any other values in the ratio 2:3:4.

They needn’t necessarily be 2, 3 and 4, they just need the required ratio of 2:3:4.

Obviously, n can be anything here, therefore, Statement 1 alone is not sufficient.

Statement 2 tell us that nx = 18, ny = 27, and nz = 36.

Now we know the actual values of nx, ny and nz, but we still don’t know the values of x, y, z and n.

They could be

2, 3, 4 and 9

or 6, 9, 12 and 3

Therefore, Statement 2 alone is also not sufficient.

Considering both statements together, note that Statement 2 tells us that nx:ny:nz = 18:27:36 = 2:3:4 (they had 9 as a common factor).

Since n is a common factor on left side, x:y:z = 2:3:4 (ratios are best expressed in the lowest form).

This is a case of what we call “we already knew that” – information given in Statement 1 is already a part of Statement 2, so it is not possible that Statement 2 alone is not sufficient but that together Statement 1 and 2 are. Hence, both statements together are not sufficient, and our answer must be E.

A question that arises often here is, “Why can’t we say that the number of staff members must be 9?”

This is because the ratio of 2:3:4 is same as the ratio of 6:9:12, which is same as 18:27:36 (when you multiply each number of a ratio by the same number, the ratio remains unchanged).

If 18 books, 27 calendars, and 36 diaries are distributed in the ratio 2:3:4, we could give them all to one person, or to 3 people (giving them each 6 books, 9 calendars and 12 diaries), or to 9 people (giving them each 2 books, 3 calendars and 4 diaries).

When we see 18, 27 and 36, what comes to mind is that the number of people could have been 9, which would mean that the department manager distributed 2 books, 3 calendars and 4 diaries to each person. But we know that 9 is divisible by 3, which should remind us that the number of people could also be 3, which would mean that the manager distributed 6 books, 9 calendars and 12 diaries to each person. As such, we still don’t know how many staff members there are, and our answer remians E.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: OJ Simpson’s Defense Team And Critical Reasoning Strategy

GMAT Tip of the WeekIf you’re like many people this month, you’re thoroughly enjoying the guilty pleasure that is FX’s series The People v. OJ Simpson. And whether you’re in it to reminisce about the 1990s or for the wealth of Kardashian family history, one thing remains certain (even though, according to the state of California – spoiler alert! – that thing is not OJ’s guilt):

Robert Shaprio, Johnnie Cochran, F. Lee Bailey, Alan Dershowitz, and (yes, even) Robert Kardashian can provide you with the ultimate blueprint for GMAT Critical Reasoning success.

This past week’s third episode focused on the preparations of the prosecutors and of the defense, and showcased some crucial differences between success and failure on GMAT CR:

The prosecution made some classic GMAT CR mistakes, most notably that they went in to the case assuming the truth of their position (that OJ was guilty). On the other hand, the defense took nothing for granted – when they didn’t like the evidence (the bloody glove, for example) they looked for ways that it must be faulty evidence (Mark Fuhrman and the LAPD were racist).

This is how you must approach GMAT Critical Reasoning! The single greatest mistake that examinees make during the GMAT is in accepting that the argument they’re given is valid – like Marcia Clark, you’re a nice, good-natured person and you’ll give the argument the benefit of the doubt. But in law and on the GMAT, bullies like Travolta’s Robert Shapiro win the day. The name of the game is “Critical Reasoning” – make sure that you’re being critical.

What does that look like on the test? It means:

Be Skeptical of Arguments
From the first word of a Strengthen, Weaken, or Assumption question, you’re reading skeptically, and almost angrily so. You’re not buying this argument and you’re searching for holes immediately. Often times these arguments will actually seem pretty valid (sort of like, you know, “OJ did it, based on the glove, the blood in the Brondo, his footprint at the scene, etc.”), but your job is to attack them so you’d better start attacking immediately.

Look for Details That Don’t Match
If an argument says, for example, that “the murder rate is down, so the police department must be doing a better job preventing violent crime…” notice that murder is not the same thing as violent crime, and that even if violent crime is down, you don’t have a direct link to the police department being the catalysts for preventing it. This is part of not buying the argument – when the general flow of ideas suggests “yes,” make sure that the details do, too.

Look for Alternative Explanations
Conclusions on the GMAT – like criminal trial “guilty” verdicts – must be true beyond a reasonable doubt. So even though the premises might make it seem quite likely that a conclusion is true, if there is an alternate explanation that’s consistent with the facts but allows for a different conclusion, that conclusion cannot be logically drawn. This is where the Simpson legal team was so successful: the evidence was overwhelming in its suggestion that Simpson was guilty (as the soon-after civil trial proves), but the defense was able to create just enough suspicion that he could have been framed that the jury was able to acquit.

So whether you’re appalled or enthralled as you watch The People v. OJ Simpson and the defense team shrewdness it portrays, know that the show has valuable insight for you as you attempt to become a Critical Reasoning master. If you want to keep your GMAT verbal score out of jail, you might want to keep up with one particular Kardashian.

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

By Brian Galvin.

Quarter Wit, Quarter Wisdom: Circular Reasoning in GMAT Critical Reasoning Questions

Quarter Wit, Quarter WisdomConsider this argument:

Anatomical bilateral symmetry is a common trait. It follows, therefore, that it confers survival advantages on organisms. After all, if bilateral symmetry did not confer such advantages, it would not be common.

What is the flaw here?

The argument restates rather than proves. The conclusion is a  premise, too – we start out by assuming that the conclusion is true and then state that the conclusion is true.

If A (bilateral symmetry) were not B (confer survival advantages), A (bilateral symmetry) would not be C (common).

A (bilateral symmetry) is C (common) so A (bilateral symmetry) is B (confer survival advantages).

Note that we did not try to prove that “A is C implies A is B”. We did not explain the connection between C and B. For our reasoning, all we said is that if A were not B, it would not be C, so we are starting out by taking the conclusion to be true.

This is called circular reasoning. It is a kind of logical fallacy – a flaw in the logic. You begin with what you are trying to prove, using your own conclusion as one of your premises.

Why is it good to understand circular reasoning for the GMAT? A critical reasoning question that asks you to mimic the reasoning argument could require you to identify such a flawed reasoning and find the argument that mimics it.

Continuing with the previous example:

Anatomical bilateral symmetry is a common trait. It follows, therefore, that it confers survival advantages on organisms. After all, if bilateral symmetry did not confer such advantages, it would not be common.

The pattern of reasoning in which one of the following arguments is most similar to that in the argument above?

(A) Since it is Sawyer who is negotiating for the city government, it must be true that the city takes the matter seriously. After all, if Sawyer had not been available, the city would have insisted that the negotiations be deferred.
(B) Clearly, no candidate is better qualified for the job than Trumbull. In fact, even to suggest that there might be a more highly qualified candidate seems absurd to those who have seen Trumbull at work.
(C) If Powell lacked superior negotiating skills, she would not have been appointed arbitrator in this case. As everyone knows, she is the appointed arbitrator, so her negotiating skills are, detractors notwithstanding, bound to be superior.
(D) Since Varga was away on vacation at the time, it must have been Rivers who conducted the secret negotiations. Any other scenario makes little sense, for Rivers never does the negotiating unless Varga is unavailable.
(E) If Wong is appointed arbitrator, a decision will be reached promptly. Since it would be absurd to appoint anyone other than Wong as arbitrator, a prompt decision can reasonably be expected.

We’ve established that the above pattern of reasoning has a circular reasoning flaw. Let’s consider each answer option to find the one which has similarly flawed reasoning.

(A) Since it is Sawyer who is negotiating for the city government, it must be true that the city takes the matter seriously. After all, if Sawyer had not been available, the city would have insisted that the negotiations be deferred.

Here is the structure of this argument:

If A (Sawyer) were not B (available), C (the city) would have D (insisted on deferring).

Since A (Sawyer) is B (available to the city), C (the city) does E (takes matter seriously).

Obviously, this argument structure is not the same as in the original argument.

(B) Clearly, no candidate is better qualified for the job than Trumbull. In fact, even to suggest that there might be a more highly qualified candidate seems absurd to those who have seen Trumbull at work.

Here is the structure of this argument:

A (people who have seen Trumbull at work) find B (Trumbull is not the best) absurd, therefore B (Trumbull is not the best) is false.

This is not circular reasoning. We have not assumed that B is false in our premises, we are simply saying that people think B is absurd. This is flawed logic too, but it is not circular reasoning.

(C) If Powell lacked superior negotiating skills, she would not have been appointed arbitrator in this case. As everyone knows, she is the appointed arbitrator, so her negotiating skills are, detractors notwithstanding, bound to be superior.

Here is the structure of this argument:

If A (Powell) were not B (had superior negotiating skills), A (Powell) would not have been C (appointed arbitrator).

A (Powell) is C (appointed arbitrator), therefore A (Powell) is B (had superior negotiating skills).

Note that the structure of the argument matches the structure of our original argument – this is circular reasoning, too. We are saying that if A were not B, A would not be C and concluding that since A is C, A is B. The conclusion is already taken to be true in the initial argument, so we can see it is is also an example of circular reasoning.

Hence (C) is the correct answer. Nevertheless, let’s look at the other two options and why they don’t work:

(D) Since Varga was away on vacation at the time, it must have been Rivers who conducted the secret negotiations. Any other scenario makes little sense, for Rivers never does the negotiating unless Varga is unavailable.

Here is the structure of this argument:

If A (Varga) is B (available), C (Rivers) does not do D (negotiate).

A (Varga) was not B (available), so C (Rivers) did D (negotiate).

This logic is flawed – the premise tells us what happens when A is B, however it does not tell us what happens when A is not B. We cannot conclude anything about what happens when A is not B. And because this is not circular reasoning, it cannot be the answer.

(E) If Wong is appointed arbitrator, a decision will be reached promptly. Since it would be absurd to appoint anyone other than Wong as arbitrator, a prompt decision can reasonably be expected.

Here is the structure of this argument:

If A (Wong) is B (appointed arbitrator), C (a decision) will be D (reached promptly).

A (Wong) not being B (appointed arbitrator) would be absurd, so C (a decision) will be D (reached promptly).

Again, this argument uses brute force, but it is not circular reasoning. “A not being B would be absurd” is not a convincing reason, so the argument is not strong as it is, but in any case, we don’t have to worry about it since it doesn’t use circular reasoning.

Take a look at this question for practice:

Dr. A: The new influenza vaccine is useless at best and possibly dangerous. I would never use it on a patient.
Dr. B: But three studies published in the Journal of Medical Associates have rated that vaccine as unusually effective.
Dr. A: The studies must have been faulty because the vaccine is worthless.

In which of the following is the reasoning most similar to that of Dr. A?

(A) Three of my patients have been harmed by that vaccine during the past three weeks, so the vaccine is unsafe.
(B) Jerrold Jersey recommends this milk, and I don’t trust Jerrold Jersey, so I won’t buy this milk.
(C) Wingz tennis balls perform best because they are far more effective than any other tennis balls.
(D) I’m buying Vim Vitamins. Doctors recommend them more often than they recommend any other vitamins, so Vim Vitamins must be good.
(E) Since University of Muldoon graduates score about 20 percent higher than average on the GMAT, Sheila Lee, a University of Muldoon graduate, will score about 20 percent higher than average when she takes the GMAT.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on FacebookYouTubeGoogle+, 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: Marco Rubio, Repetition, and Sentence Correction

GMAT Tip of the WeekLet’s dispel with the fiction that Marco Rubio doesn’t know what he’s doing on Sentence Correction problems. He knows exactly what he’s doing. In his memorable New Hampshire debate performance this past week, Rubio famously delivered the same 25-second speech several times, even in direct response to Chris Christie’s accusation that Rubio only speaks in memorized 25-second speech form.

In doing so, he likely cost himself delegates in New Hampshire and perhaps even cost himself the election (was this his Rick Perry “I can’t remember the third thing” or Howard Dean “Hi-yaaaah!” moment?), but he also provided you with a critical Sentence Correction strategy:

Find what you do well, and keep doing it over and over until you just can’t do it anymore.

This strategy manifests itself in two ways on GMAT Sentence Correction problems:

1) Look for primary Decision Points first.
Rubio came into the debate with one strong talking point, and his first inclination – regardless of the question – was to go straight to that point. On Sentence Correction problems, that is the single most important thing you can do. Much like a debate moderator, the GMAT testmaker will try to get you “off message” by offering you several decisions you could make. And often the decision that comes first is one you’re just not good at, or that actually isn’t a good differentiator. For example, you may think you need to decide between:

“…so realistic as to…” vs. “…so realistic that it…”

“…not unlike…” vs. “…like…”

“…all things antique…” vs. “…all antique things…”

And in any of those cases, you might find that both expressions are actually correct; those are differences between answer choices, but they’re not the difference between correct and incorrect. Idiomatic differences, changes in word choice, etc. may seem to beg your attention, but like Marco Rubio, you should head into each question with your list of points you want to address: modifiers, verbs, pronouns, parallel structure, etc. Look for those primary decision points first and attack them until you’ve exhausted them. Nearly always, you’ll find that doing so eliminates enough answer choices that you never have to deal with the trickier, more obscure, and often irrelevant differences between choices.

Approach each Sentence Correction problem with your scripted and heavily-practiced Decision Points in mind first. Sentence Correction is a task tailor-made for Rubio-bots.

2) Once you identify an error, stay on message as long as you can.
Rubio’s strategy backfired, but that doesn’t mean that it was a poor strategy to begin with – in fact, it’s one that will immensely help you on Sentence Correction problems. He identified a message that resonated, and he decided to do that until he was – quite literally – forced to do something else. This is a critical Sentence Correction tactic: if you find a particular error (say, an illogical modifier), you should then hold each answer choice up to that standard checking for the same error. Nearly always, if you find an error in one answer choice that same type of error will appear in at least one more.

Don’t treat each individual answer choice as a “unique snowflake” that you’ve never seen before. If there’s a verb tense / timeline error in choice B, then immediately scan C, D, and E checking those verb tenses and quickly eliminating any choices with a problem.

For example, consider the problem:

The economic report released today by Congress and the Federal Reserve was bleaker than expected, which suggests that the nearing recession might be even deeper and more prolonged than even the most pessimistic analysts have predicted.

(A) which suggests that the nearing recession might be even deeper and more prolonged than even the most pessimistic analysts have predicted.
(B) which suggests that the nearing recession might be deeper and more prolonged than that predicted by even the most pessimistic analysts.
(C) suggests that the nearing recession might be even deeper and more prolonged than that predicted by even the most pessimistic analysts.
(D) suggesting that the nearing recession might be deeper and more prolonged than that predicted by even the most pessimistic analysts.
(E) a situation that is even more deep and prolonged than even the most pessimistic analysts have predicted.

If you’re attacking this problem like a Rubio-bot, you’ll notice before you ever look at the sentence that the answer choices supply different modifiers. A and B use the relative modifier “which,” D uses the participial phrase “suggesting,” and E uses an appositive “a situation.” Noticing that, you should begin reading the sentence with that Modifier talking point in mind.

When you realize that “which” is used incorrectly in A, you don’t need to read the rest of B to see that it makes the exact same mistake. Since the sentence calls for a modifier (the portion before the comma and underlined is a complete sentence on its own, so the role of the underlined section is to further describe) and the only correct modifier in this situation is the participial “suggesting,” you can eliminate three answer choices (A, B, and E) just with that one Decision Point and quickly arrive at the correct answer, D.

More importantly, remember the overarching strategy: before you attack any Sentence Correction problem, know the grounds upon which you’re hoping to attack it – have your primary Decision Points in mind before you’re ever asked the question. And then when you do find one of those Decision Points that you can use, repeat it ad nauseum until it no longer applies.

Let’s dispel with the fiction that Marco Rubio doesn’t know what he’s doing when he repeats the same talking point over and over again; he knows exactly what he’s doing…it just works better on the GMAT than it does in a presidential debate.

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By Brian Galvin.