How to Use Units Digits to Avoid Doing Painful Calculations on the GMAT

StudentDuring the first session of each new class I teach, we do a quick primer on the utility of units digits. Imagine I want to solve 130,467 * 367,569. Without a calculator, we are surely entering a world of hurt. But we can see almost instantaneously what the units digit of this product would be.

The units digit of 130,467 * 367,569 would be the same as the units digit of 7*9, as only the units digits of the larger numbers are relevant in such a calculation. 7*9 = 63, so the units digit of 130,467 * 367,569 is 3. This is one of those concepts that is so simple and elegant that it seems too good to be true.

And yet, this simple, elegant rule comes into play on the GMAT with surprising frequency.

Take this question for example:

If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digit of n^3?

A) three
B) four
C) six
D) nine
E) ten

Surely, you think, the solution to this question can’t be as simple as cubing the easiest possible numbers to see how many different units digits result. And yet that’s exactly what we’d do here.

1^3 = 1

2^3 = 8

3^3 = 27 à units 7

4^3 = 64 à units 4

5^3 = ends in 5 (Fun fact: 5 raised to any positive integer will end in 5.)

6^3 = ends in 6 (Fun fact: 6 raised to any positive integer will end in 6.)

7^3 = ends in 3 (Well 7*7 = 49. 49*7 isn’t that hard to calculate, but only the units digit matters, and 9*7 is 63, so 7^3 will end in 3.)

8^3 = ends in 2 (Well, 8*8 = 64, and 4*8 = 32, so 8^3 will end in 2.)

9^3 = ends in 9 (9*9 = 81 and 1 * 9 = 9, so 9^3 will end in 9.)

10^3 = ends in 0

Amazingly, when I cube all the integers from 1 to 10 inclusive, I get 10 different units digits. Pretty neat. The answer is E.

Of course, this question specifically invoked the term “units digit.” What are the odds of that happening? Maybe not terribly high, but any time there’s a painful calculation, you’d want to consider thinking about the units digits.

Take this question, for example:

A certain stock exchange designates each stock with a one, two or three letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be replaced and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes? 

A) 2,951
B) 8,125
C) 15,600
D) 16,302
E) 18,278 

Conceptually, this one doesn’t seem that bad.

If I wanted to make a one-letter code, there’d be 26 ways I could do so.

If I wanted to make a two-letter code, there’d be 26*26 or 26^2 ways I could do so.

If I wanted to make a three-letter code, there’d be 26*26*26, or 26^3 ways I could so.

So the total number of codes I could make, given the conditions of the problem, would be 26 + 26^2 + 26^3. Hopefully, at this point, you notice two things. First, this arithmetic will be deeply unpleasant to do.  Second, all of the answer choices have different units digits!

Now remember that 6 raised to any positive integer will always end in 6. So the units digit of 26 is 6, and the units digit of 26^2 is 6 and the units digit of 26^3 is also 6. Therefore, the units digit of 26 + 26^2 + 26^3 will be the same as the units digit of 6 + 6 + 6. Because 6 + 6 + 6 = 18, our answer will end in an 8. The only possibility here is E. Pretty nifty.

Takeaway: Painful arithmetic can always be avoided on the GMAT. When calculating large numbers, note that we can quickly find the units digit with minimal effort. If all the answer choices have different units digits, the question writer is blatantly telegraphing how to approach this problem.

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: What is Your Favorite Number?

Quarter Wit, Quarter WisdomFans of The Big Bang Theory will remember Sheldon Cooper’s quote from an old episode on his favorite number:

The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3… and in binary 73 is a palindrome, 1001001, which backwards is 1001001.”

Though Sheldon’s logic is infallible, my favorite number is 1001 because it has a special role in standardized tests.

1001 is 1 more than 1000 and hence, is sometimes split as (1000 + 1). It sometimes appears in the a^2 – b^2 format such as 1001^2 – 1, and its factors are 7, 11 and 13 (not the factors we usually work with).

Due to its unusual factors and its convenient location (right next to 1000), it could be a part of some tough-looking GMAT questions and should be remembered as a “special” number. Let’s look at a question to understand how to work with this  number.

Which of the following is a factor of 1001^(32) – 1 ?

(A) 768
(B) 819
(C) 826
(D) 858
(E) 924

Note that 1001 is raised to the power 32. This is not an exponent we can easily handle. If  we try to use a binomial here and split 1001 into (1000 + 1), all we will achieve is that upon expanding the given expression, 1 will be cancelled out by -1 and all other terms will have 1000 in common. None of the answer choices are factors of 1000, however, so we must look for some other factor of 1001^(32) – 1.

Without a calculator, it is not possible for us to find the factors of 1001^(32) – 1, but we do know the prime factors of 1001 and hence, the prime factors of 1001^32. We may not be able to say which numbers are factors of 1001^(32) – 1, but we will be able to say which numbers are certainly not factors of this!

Let me explain:

1001 = 7 * 11 * 13 (Try dividing 1001 by 7 and you’ll get 143. 143 is divisible by 11, giving you 13.)

1001^32 = 7^32 * 11^32 * 13^32

Now, what can we say about the prime factors of 1001^(32) – 1? Whatever they are, they are certainly not 7, 11 or 13 – two consecutive integers cannot have any common prime factor (discussed here and continued here).

Now look at the answer choices and try dividing each by 7:

(A) 768 – Not divisible by 7

(B) 819 – Divisible by 7

(C) 826 – Divisible by 7

(D) 858 – Not divisible by 7

(E) 924 – Divisible by 7

Options B, C and E are eliminated. They certainly cannot be factors of 1001^(32) – 1 since they have 7 as a prime factor, and we know 1001^(32) – 1 cannot have 7 as a prime factor.

Now try dividing the remaining options by 11:

(A) 768 – Not divisible by 11

(D) 858 – Divisible by 11

D can also be eliminated now because it has 11 as a factor. By process of elimination, the answer is A; it must be a factor of 1001^(32) – 1.

I hope you see how easily we used the factors of 1001 to help us solve this difficult-looking question. And yes, another attractive feature of 1001 – it is a palindrome in the decimal representation itself!

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: How to Avoid GMAT (and Pokemon Go) Traps

GMAT Tip of the WeekIn seemingly the most important development in world history since humans learned to create fire, Pokemon Go has arrived and is taking the world by storm. Rivaling Twitter and Facebook for mobile phone attention and battling the omnipresent selfie as a means of death-by-mobile-phone, Pokemon Go is everywhere you want to be…and often in places you don’t.

And that is why Pokemon Go is responsible for an ever-important GMAT lesson.

Perhaps most newsworthy about Pokemon Go these days is the dangerous and improper places that it has led its avid users. On the improper side,  such solemn and dignified places as the national Holocaust Museum and Arlington National Cemetery have had to actively prohibit gamers from descending upon mourners/commemorators while playing the game. And as for danger, there have been several instances of thieves luring gamers into traps and therefore robbing them of valuable (if you’re playing the game, you definitely have a smartphone) items.

And the GMAT can and will do the same thing.

How?

If you’re reading this on our GMAT blog, you’ve undoubtedly already learned that, on Data Sufficiency problems, you cannot assume that a variable is positive, or that it is an integer. But think about what makes Pokemon Go users so vulnerable to being lured into a robbery or to losing track of basic human decency. They’re so invested in the game that they lose track of the situations they’re being lured into.

Similarly, the most dangerous GMAT traps are those for which you should absolutely know better, but the testmaker has gotten your mind so invested in another “game” that you lose track of something basic. Consider the example:

If y is an odd integer and the product of x and y equals 222, what is the value of x? 

(1) x is a prime number
(2) y is a 3 digit number

Statement 1 is clearly sufficient. Since y is odd, and an integer, and the product of integers x and y is an even integer, that means that x must be even. And since x also has to be prime (which is how you know it’s an integer, too), the only even prime is 2, making x = 2.

From there your mind is fixated on the game. You can quickly see that in that case y = 111 and x = 2. Which you then have to forget about as you attack Statement 2. But here’s the reason that less than 25% of users in the Veritas Prep Question Bank get this right, while nearly half incorrectly choose D. Statement 1 has gotten your mind fixated on the even/odd/prime game, meaning that you may only be thinking about integers (and positive integers at that) at this point.

That y is a 3-digit number DOES NOT mean that it has to be 111. It could be -111 (making x = -2) or 333 (making x = 2/3). So only Statement 1 alone is sufficient, but the larger lesson is more important. Just like Pokemon Go has the potential to pollute your mind and have you see the real world through its “enhanced reality” lens, so does a statement that satisfies your intellect (“Ah, 2 is the only even prime number!”) give you just enough tunnel vision that you make poor decisions and fall for traps.

The secret here is that almost no one scoring above a 500 carries over all of Statement 1 (“Oh, well I already know that x = 2!”) – a total rookie mistake. It’s that Statement 1 got you fixated on definitions of types of integers (prime, even, odd) and therefore got your mind looking through the “enhanced reality” of integers-only.

The lesson? Much like Pokemon Go, the GMAT has tools to get you so invested in a particular facet of a game that you lose your universal awareness of your surroundings. Know that going in – that you have to consciously step back from that enhanced reality you’ve gained after Statement 1 and look at the whole picture. So take a lesson from Pokemon Go and know when to stop and step back.

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 Approach Difficult GMAT Problems

SAT/ACTMy students have a hard time understanding what makes a difficult GMAT question difficult. They assume that the tougher questions are either testing something they don’t know, or that these problems involve a dizzying level of complexity that requires an algebraic proficiency that’s simply beyond them.

One of my main goals in teaching a class is to persuade everyone that this is not, in fact, how hard questions work on this test. Hard questions don’t ask you do to something you don’t know how to do. Rather, they’re cleverly designed to provoke an anxiety response that makes it difficult to realize that you do know exactly how to solve the problem.

Take this official question, for example:

Let a, b, c and d be nonzero real numbers. If the quadratic equation ax(cx + d) = -b(cx +d) is solved for x, which of the following is a possible ratio of the 2 solutions?

A) –ab/cd
B) –ac/bd
C) –ad/bc
D) ab/cd
E) ad/bc

Most students see this and panic. Often, they’ll start by multiplying out the left side of the equation, see that the expression is horrible (acx^2 + adx), and take this as evidence that this question is beyond their skill level. And, of course, the question was designed to elicit precisely this response. So when I do this problem in class, I always start by telling my students, much to their surprise, that every one of them already knows how to do this. They’ve just succumbed to the question writer’s attempt to convince them otherwise.

So let’s start simple. I’ll write the following on the board: xy = 0. Then I’ll ask what we know about x or y. And my students shrug and say x or y (or both) is equal to 0. They’ll also wonder what on earth such a simple identity has to do with the algebraic mess of the question they’d been struggling with.

I’ll then write this: zx + zy = 0. Again, I’ll ask what we know about the variables. Most will quickly see that we can factor out a “z” and get z(x+y) = 0. And again, applying the same logic, we see that one of the two components of the product must equal zero – either z = 0 or x + y = 0.

Next, I’ll ask if they would approach the problem any differently if I’d given them zx = -zy – they wouldn’t.

Now it clicks. We can take our initial equation in the aforementioned problem: ax(cx +d) = -b(cx+d), and see that we have a ‘cx + d’ on both sides of the equation, just as we’d had a “z” on both sides of the previous example. If I’m able to get everything on one side of the equation, I can factor out the common term.

Now ax(cx +d) = -b(cx+d) becomes ax(cx +d) + b(cx+d) = 0.

Just as we factored out a “z” in the previous example, we can factor out “cx + d” in this one.

Now we have (cx + d)(ax + b) = 0.

Again, if we multiply two expressions to get a product of zero, we know that at least one of those expressions must equal 0. Either cx + d = 0 or ax + b = 0.

If cx + d = 0, then x = -d/c.

If ax + b = 0, then x = -b/a.

Therefore, our two possible solutions for x are –d/c and –b/a. So, the ratio of the two would simply be (-d/c)/(-b/a). Recall that dividing by a fraction is the equivalent of multiplying by the reciprocal, so we’re ultimately solving for (-d/c)(-a/b). Multiplying two negatives gives us a positive, and we end up with da/cb, which is equivalent to answer choice E.

Takeaway: Anytime you see something on the GMAT that you think you don’t know how to do, remind yourself that the question was designed to create this false impression. You know how to do it – don’t hesitate to dive in and search for how to apply this knowledge.

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: Attacking Gerunds on the GMAT!

Quarter Wit, Quarter WisdomA few weeks back, we talked about participles and how they are used on the GMAT. In that post, we had promised to discuss gerunds more in depth at another time. So today, as promised, we’ll be looking at gerunds. Before we do that, however, let’s examine Verbals.

A Verbal is a verb that acts as a different part of speech – not as a verb.

There are three types of verbals:

  • Infinitives – these take the form of “to + verb”
  • Gerunds – these are the “-ing” form of the verb
  • Participles – these can take the “-ing,” “-ed,” “-en” etc. forms

Gerunds end in “-ing” and act as nouns in the sentence. They can act as a subject, direct object, subject complement or object of a preposition. For example:

Running a marathon is very difficult. – Subject
I love swimming. – Direct object
The activity I enjoy the most is swimming. – Subject complement
She thanked me for helping her. – Object of a preposition

You don’t have to identify the part of speech the gerund represents in a sentence; you just need to identify whether a verb’s “-ing” form is being used as a gerund and evaluate whether it is being used correctly.

A sentence could also use a gerund phrase that begins with a gerund, such as, “Swimming in the morning is exhilarating.”

Let’s take a look at a couple of official questions now:

A recent study has found that within the past few years, many doctors had elected early retirement rather than face the threats of lawsuits and the rising costs of malpractice insurance.

(A) had elected early retirement rather than face
(B) had elected early retirement instead of facing
(C) have elected retiring early instead of facing
(D) have elected to retire early rather than facing
(E) have elected to retire early rather than face

Upon reading the original sentence, we see that there is a gerund phrase here – “rising costs of malpractice insurance” – which is parallel to the noun “threat of lawsuits.”

The two are logically parallel too, since there are two aspects that the doctors do not want to face: rising costs and the threat of lawsuits.

Note, however, that they are not logically parallel to “face.” Hence, the use of the form “facing” would not be correct, since it would put “facing” and “rising” in parallel. So answer choices B, C and D are incorrect.

Actually, “retire” and “face” are logically parallel so they should be grammatically parallel, too. Answer choice E has the two in parallel in infinitive form – to retire and (to is implied here) face are in parallel.

Obviously, there are other decision points to take note of here, mainly the question of “had elected” vs. “have elected.” The use of “had elected” will not be correct here, since we are not discussing two actions in the past occurring at different times. Therefore, the correct answer is E.

Take a look at one more:

In virtually all types of tissue in every animal species dioxin induces the production of enzymes that are the organism’s trying to metabolize, or render harmless, the chemical that is irritating it.

(A) trying to metabolize, or render harmless, the chemical that is irritating it
(B) trying that it metabolize, or render harmless, the chemical irritant
(C) attempt to try to metabolize, or render harmless, such a chemical irritant
(D) attempt to try and metabolize, or render harmless, the chemical irritating it
(E) attempt to metabolize, or render harmless, the chemical irritant

Notice the use of the gerund “trying” in answer choice A. “Organism’s” is in possessive form and acts as an adjective for the noun verbal “trying.” Usually, with possessives, a gerund does not work. We need to use a noun only. With this in mind, answer choices A and B will not work.

The other three options replace “trying” with “attempt” and hence correct this error, however options C and D use the redundant “attempt to try.” The use of “attempt” means “try,” so there is no need to use both. Option E corrects this problem, so it is our correct answer.

Unlike participles, which can be a bit confusing, gerunds are relatively easy to understand and use. Feeling more confident about them now?

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 Reach a 99th Percentile GMAT Score Using No New Academic Strategies

Pump UpLast week I received an email from an old student who’d just retaken the GMAT. He was writing to let me know that he’d just received a 770. Of course, I was ecstatic for him, but I was even more excited once I considered what his journey could mean for other students.

His story is a fairly typical one: like the vast majority of GMAT test-takers, he enrolled in the class looking to hit a 700. His scores improved steadily throughout the course, and when he took the test the first time, he’d received a 720, which was in line with his last two practice exams. After he finished the official test, he called me – both because he was feeling pretty good about his score but also because a part of him was sure he could do better.

My feeling at the time was that there really wasn’t any pressing need for a retake: a 720 is a fantastic score, and once you hit that level of success, the incremental gains of an improvement begin to suffer from the law of diminishing returns. Still, when you’re talking about the most competitive MBA programs, you want any edge you can get. Moreover, he’d already made up his mind. He wanted to retake.

Part of his decision was rooted in principle. He was sure he could hit the 99th percentile, and he wanted to prove it to himself. The problem, he noted, was that he’d already mastered the test’s content. So if there was nothing left for him to learn, how did he jump to the 99th percentile?

The answer can be found in the vast body of literature enumerating the psychological variables that influence test scores. We like to think of tests as detached analytic tools that measure how well we’ve mastered a given topic. In reality, our mastery of the content is one small aspect of performance.

Many of us know this from experience – we’ve all had the experience of studying hard for a test, feeling as though we know everything cold, and then ending up with a score that didn’t seem to reflect how well we’d learned the material. After I looked at the research, it was clear that the two most important psychological variables were 1) confidence and 2) how well test-takers managed test anxiety. (And there’s every reason to believe that those two variables are interconnected.)

I’ve written in the past about how a mindfulness meditation practice can boost test day performance. I’ve also written about how perceiving anxiety as excitement, rather than as a nefarious force that needs to be conquered, has a similarly salutary effect. Recently I came across a pair of newer studies.

In one, researchers found that when students wrote in their journals for 10 minutes about their test-taking anxiety the morning of their exams, their scores went up substantially. In another, the social psychologist Amy Cuddy found that body language had a profound impact on performance in all sorts of domains. For example, her research has revealed that subjects who assumed “power poses” for two minutes before a job interview projected more confidence during the interview and were better able to solve problems than a control group that assumed more lethargic postures. (To see what these power poses look like, check out Cuddy’s fascinating Ted talk here.) Moreover, doing power poses actually created a physiological change, boosting testosterone and reducing the stress hormone Cortisol.

Though her research wasn’t targeted specifically at test-takers, there’s every reason to believe that there would be a beneficial effect for students who practiced power poses before an exam. Many teachers acquainted with Cuddy’s research now recommend that their students do this before tests.

So the missing piece of the puzzle for my student was simply confidence. His strategies hadn’t changed. His knowledge of the core concepts was the same. The only difference was his psychological approach. So now I’m recommending that all of my students do the following to cultivate an ideal mindset for producing their best possible test scores:

  1. Perform mindfulness meditation for the two weeks leading up to the exam.
  2. Reframe test-day anxiety as excitement.
  3. Spend 10 minutes the morning of the test writing in a journal.
  4. Practice two minutes of power poses in the waiting room before sitting for the exam and between the Quant and Verbal 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 David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.

How to Go From a 48 to 51 in GMAT Quant – Part VII

Quarter Wit, Quarter WisdomBoth a test-taker at the 48 level and one at the 51 level in the GMAT Quant section, are conceptually strong – given an unlimited time frame, both will be able to solve most GMAT questions correctly. The difference lies in the two things a test-taker at the 51 level does skillfully:

  1. Uses holistic, big-picture methods to solve Quant questions.
  2. Handles questions he or she finds difficult in a timely manner.

We have been discussing holistic methods on this blog for a long time now and will continue discussing them. (Before you continue reading, be sure to check out parts I, II, III, IVV and VI of this series.)

Today we will focus on “handling the hard questions in a timely manner.” Note that we do not say “solving the hard questions in a timely manner.” Occasionally, one might be required to make a quick call and choose to guess and move on – but again, that is not the focus of this post. We are actually going to talk about the “lightbulb” moment that helps us save on time. There are many such moments for the 51 level test-taker – in fact, the 51 scorers often have time left over after attempting all these questions.

Test takers at the 48 level will also eventually reach the same conclusions but might need much more time. That will put pressure on them the next time they look at the ticking clock, and once their cool is lost, “silly errors” will start creeping in. So it isn’t about just that one question – one can end up botching many other questions too.

There are many steps that can be easily avoided by a lightbulb moment early on. This is especially true for Data Sufficiency questions.

Let’s take an official example:

Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?

Statement 1: She has $282 worth of packages.

Statement 2: She has twice as many packages of corn as of rice.

A high scorer will easily recognize that this question is based on the concept of “integral solutions to an equation in two variables.” Since, in such real world examples, x and y cannot be negative or fractional, these equations usually have a finite number of solutions.

After we find one solution, we will quickly know how many solutions the equation has, but getting the first set of values that satisfy the equation requires a little bit of brute force.

The good thing here is that this is a Data Sufficiency question – you don’t need to find the actual solution. The only thing we need is to establish that there is a single solution only. (Obviously, there has to be a solution since Pam does own $282 worth of packages.)

So, the test-taker will start working on finding the first solution (using the method discussed in this post). We are told:

Price of a packet of corn = $17
Price of a packet of rice = $13

Say Pam has “x” packets of corn and “y” packets of rice.

Statement 1: She has $282 worth of packages

Using Statement 1, we know that 17x + 13y = 282.

We are looking for the integer values of x and y.

If x = 0, y will be 21.something (not an integer)
If x = 1, y = 20.something
If x = 2, y = 19.something
If x = 3, y = 17.something

This is where the 51 level scorer stops because they never lose sight of the big picture. The “lightbulb” switches on, and now he or she knows that there will be only one set of values that can satisfy this equation. Why? Because y will be less than 17 in the first set of values that satisfies this equation. So if we want to get the next set that satisfies, we will need to subtract y by 17 (and add 13 to x), which will make y negative.

So in any case, there will be a unique solution to this equation. We don’t actually need to find the solution and hence, nothing will be gained by continuing these calculations. Statement 1 is sufficient.

Statement 2: She has twice as many packages of corn as of rice.

Statement 2 gives us no information on the total number of packages or the total amount spent. Hence, we cannot find the total number of packages of corn using this information alone. Therefore, our answer is A.

I hope you see how you can be alert to what you want to handle these Quant questions in a timely manner.

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 Overly Specific Question Stem

GMAT Tip of the WeekFor most of our lives, we ask and answer relatively generic questions: “How’s it going?” “What are you up to this weekend?” “What time do the Cubs play tonight?”

And think about it, what if those questions were more specific: “Are you in a melancholy mood today?” “Are you and Josh going to dinner at Don Antonio’s tonight and ordering table-side guacamole?” “Do the Cubs play at 7:05 tonight on WGN?” If someone is asking those questions instead, you’re probably a bit suspicious. Why so specific? What’s your angle?

The same is true on the GMAT. Most of the question stems you see are relatively generic: “What is the value of x?” “Which of the following would most weaken the author’s argument?” So when the question stem get a little too specific, you should become a bit suspicious. What’s the test going for there? Why so specific?

The overly-specific Critical Reasoning question stem is a great example. Consider the problem:

Raisins are made by drying grapes in the sun. Although some of the sugar in the grapes is caramelized in the process, nothing is added.
Moreover, the only thing removed from the grapes is the water that evaporates during the drying, and water contains no calories or nutrients.
The fact that raisins contain more iron per food calorie than grapes do is thus puzzling.

Which one of the following, if true, most helps to explain why raisins contain more iron per calorie than do grapes?

(A) Since grapes are bigger than raisins, it takes several bunches of grapes to provide the same amount of iron as a handful of raisins does.
(B) Caramelized sugar cannot be digested, so its calories do not count toward the food calorie content of raisins.
(C) The body can absorb iron and other nutrients more quickly from grapes than from raisins because of the relatively high water content of grapes.
(D) Raisins, but not grapes, are available year-round, so many people get a greater share of their yearly iron intake from raisins than from grapes.
(E) Raisins are often eaten in combination with other iron-containing foods, while grapes are usually eaten by themselves.

Look at that question stem: a quick scan naturally shows you that you need to explain/resolve a paradox, but the question goes into even more detail for you. It reaffirms the exact nature of the paradox – it’s not about “iron,” but instead that that raisins contain more iron per calorie than grapes do. By adding that extra description into the question stem, the testmaker is practically yelling at you, “Make sure you consider calories…don’t just focus on iron!” And therefore, you should be prepared for the correct answer B, the only one that addresses calories, and deftly avoid answers A, C, D, and E, which all focus only on iron (and do so tangentially to the paradox).

Strategically speaking, if a Critical Reasoning question stem gets overly specific, you should pay particular attention to the specificity there…it’s most likely directing you to the operative portion of the argument.

Overly specific questions are most helpful in Data Sufficiency questions (and that same logic will help on Problem Solving too, as you’ll see). The testmaker knows that you’ve trained your entire algebraic life to solve for individual variables. So how can a question author use that lifetime of repetition against you? By asking you to solve for a specific combination that doesn’t require you to find the individual values. Consider this example, which appears courtesy the Official Guide for GMAT Quantitative Review:

If x^2 + y^2 = 29, what is the value of (x – y)^2?

(1) xy = 10
(2) x = 5

Two major clues should stand out to you that you need to Leverage Assets on this problem. For one, using both statements together (answer choice C) is dead easy. If xy = 10 and x = 5 then y = 2 and you can solve for any combination of x and y that anyone could ever ask for. But secondly and more subtly, the question stem should jump out as a classic way-too-specific, Leverage Assets question stem. They asked for a really, really specific value: (x – y)^2.

Now, immediately upon seeing that specificity you should be thinking, “That’s too specific…there’s probably a way to solve for that exact value without getting x and y individually.” That thought process alone tells you where to spend your time – you want to really leverage Statement 1 to try to make it work alone.

And if you’re still unconvinced, consider what the specificity does: the “squared” portion removes the question of negative vs. positive from the debate, removing one of the most common reasons that a seemingly-sufficient statement just won’t work. And, furthermore, the common quadratic (x – y)^2 shares an awful lot in common with the x^2 and y^2 elsewhere in the question stem. If you expand the parentheses, you have “What is x^2 – 2xy + y^2?” meaning that you’re already 2/3 of the way there (so to speak), since they’ve spotted you the sum x^2 + y^2.

The important strategy here is that the overly-specific question stem should scream “LEVERAGE ASSETS” and “You don’t need to solve for x and y…there’s probably a way to solve directly for that exact combination.” Since you know that you’re solving for the expanded x^2 – 2xy + y^2, and you already know that x^2 + y^2 = 29, you’re really solving for 29 – 2xy. Since you know from Statement 1 that xy = 20, then 29 – 2xy will be 29 – 2(10), which is 9.

Statement 1 alone is sufficient, even though you don’t know what x and y are individually. And one of the major signals that you should recognize to help you get there is the presence of an overly specific question stem.

So remember, in a world of generic questions, the oddly specific question should arouse a bit of suspicion: the interrogator is up to something! On the GMAT, you can use that to your advantage – an overly specific Critical Reasoning question usually tells you exactly which keywords are the most important, and an overly specific Data Sufficiency question stem begs for you to leverage assets and find a way to get the most out of each statement.

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.

Don’t Swim Against the Arithmetic Currents on the GMAT Quant Section

MalibuWhen I was a child, I was terrified of riptides. Partially, this was a function of having been raised by unusually neurotic parents who painstakingly instilled this fear in me, and partially this was a function of having inherited a set of genes that seems to have predisposed me towards neuroticism. (The point, of course, is that my parents are to blame for everything. Perhaps there is a better venue for discussing these issues.)

If there’s a benefit to fears, it’s that they serve as potent motivators to find solutions to the troubling predicaments that prompt them. The solution to dealing with riptides is to avoid struggling against the current. The water is more powerful than you are, so a fight is a losing proposition – rather, you want to wait for an opportunity to swim with the current and allow the surf to bring you back to shore. There’s a profound wisdom here that translates to many domains, including the GMAT.

In class, whenever we review a strategy, my students are usually comfortable applying it almost immediately. Their deeper concern is about when to apply the strategy, as they’ll invariably find that different approaches work with different levels of efficacy on different problems. Moreover, even if one has a good strategy in mind, the way the strategy is best applied is often context-dependent. When we’re picking numbers, we can say that x = 2 or x = 100 or x = 10,000; the key is not to go in with a single approach in mind. Put another way, don’t swim against the arithmetic currents.

Let’s look at some questions to see this approach in action:

At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women, and children at the picnic, how many men were there, in terms of x?

A) x/2
B) x/3
C) x/4
D) x/5
E) x/6

The moment we see “x,” we can consider picking numbers. The key here is contemplating how complicated the number should be. Swim with the current – let the question tell you. A quick look at the answer choices reveals that x could be something simple. Ultimately, we’re just dividing this value by 2, 3, 4, 5, or 6.

Keeping this in mind, let’s think about the first line of the question. If there are 3 times as many adults as children, and we’re keeping things simple, we can say that there are 3 adults and 1 child, for a total of 4 people. So, x = 4.

Now, we know that among our 3 adults, there are twice as many women as men. So let’s say there are 2 women and 1 man. Easy enough. In sum, we have 2 women, 1 man, and 1 child at this picnic, and a total of 4 people. The question is how many men are there? There’s just 1! So now we plug x = 4 into the answers and keep going until we find x = 1. Clearly x/4 will work, so C is our answer. The key was to let the question dictate our approach rather than trying to impose an approach on the question.

Let’s try another one:

Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in February, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. On which month were sales closes to the sales in January?

A) February
B) March
C) April
D) May
E) June

Great, you say. It’s a percent question. So you know that picking 100 is often a good idea. So, let’s say sales in January were 100. If we want the month when sales were closest to January’s level, we want the month when sales were closest to 100, Sales in February were 10% greater, so February sales were 110. (Remember that if sales increase by 10%, we can multiply the original number by 1.1. If they decrease by 10% we could multiply by 0.9, and so forth.)

So far so good. Sales in March were 15% less than in February. Well, if sales in Feb were 110, then the sales in March must be 110*(0.85). Hmm… A little tougher, but not insurmountable. Now, sales in April were 20% greater than they were in March, meaning that April sales would be 110*(0.85)*1.2. Uh oh.  Once you see that sales are 10% less in May than they were in April, we know that sales will be 110*(0.85)*1.2*0.9.

Now you need to stop. Don’t swim against the current. The arithmetic is getting hard and is going to become time-consuming. The question asks which month is closest to 100, so we don’t have to calculate precise values. We can estimate a bit. Let’s double back and try to simplify month by month, keeping things as simple as possible.

Our February sales were simple: 110. March sales were 110*0.85 – an unpleasant number. So, let’s try thinking about this a little differently. 100*0.85 = 85.  10*0.85 = 8.5. Add them together and we get 85 + 8.5 = 93.5.  Let’s make life easier on ourselves – we’ll round up, and call this number 94.

April sales are 20% more than March sales. Well, 20% of 100 is clearly 20, so 20% of 94 will be a little less than that. Say it’s 18. Now sales are up to 94 + 18 = 112. Still not close to 100, so we’ll keep going.

May sales are 10% less than April sales. 10% of 112 is about 11. Subtract 11 from 112, and you get 101. We’re looking for the number closest to 100, so we’ve got our answer – it’s D, May.

Takeaway: Don’t try to impose your will on GMAT questions. Use the structural clues of the problems to dictate how you implement your strategy, and be prepared to adjust midstream. The goal is never to conquer the ocean, but rather, to ride the waves to calmer waters.

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.

Help! My Practice Test Score Seems Wrong!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Compounding that is:

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

And then of course there is the fact that:

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

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

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

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

What does that mean for you?

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

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

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

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

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

By Brian Galvin and Scott Shrum.

Quarter Wit, Quarter Wisdom: Using Prepositional Phrases on the GMAT

Quarter Wit, Quarter WisdomIn previous posts, we have already discussed participles as well as absolute phrases. Today, let’s take a look at another type of modifier – the prepositional phrase.

A prepositional phrase will begin with a preposition and end with a noun, pronoun, gerund, or clause – the “object” of the preposition. The object of the preposition might have one or more modifiers to describe it.

Here are some examples of prepositional phrases (with prepositions underlined):

  • along the ten mile highway…
  • with a cozy blanket…
  • without worrying…
  • about what he likes…

A prepositional phrase can function as an adjective or an adverb. As an adjective, it answers the question, “Which one?” while as an adverb it can answer the questions, “How?” “When?” or “Where?”.

For example:

  • The book under the table belongs to my mom. Here, the prepositional phrase acts as an adjective and tells us “which one” of the books belongs to my mom.
  • We tried the double cheeseburger at the new burger joint. Here, the prepositional phrase acts as an adverb and tells us “where” we tried the cheeseburger.

Like other modifiers, a prepositional modifier should be placed as close as possible to the thing it is modifying.

Let’s take a look at a couple of official GMAT questions to see how understanding prepositional phrases can help us on this exam:

The nephew of Pliny the Elder wrote the only eyewitness account of the great eruption of Vesuvius in two letters to the historian Tacitus.

(A) The nephew of Pliny the Elder wrote the only eyewitness account of the great eruption of Vesuvius in two letters to the historian Tacitus.
(B) To the historian Tacitus, the nephew of Pliny the Elder wrote two letters, being the only eyewitness accounts of the great eruption of Vesuvius.
(C) The only eyewitness account is in two letters by the nephew of Pliny the Elder writing to the historian Tacitus an account of the great eruption of Vesuvius.
(D) Writing the only eyewitness account, Pliny the Elder’s nephew accounted for the great eruption of Vesuvius in two letters to the historian Tacitus.
(E) In two letters to the historian Tacitus, the nephew of Pliny the Elder wrote the only eyewitness account of the great eruption of Vesuvius.

There are multiple prepositional phrases here:

  • of the great eruption of Vesuvius (answers “Which eruption?”)
  • in two letters (tells us “where” he wrote his account)
  • to the historian Tacitus (answers “Which letters?”)

Therefore, the phrase “to the historian Tacitus” should be close to what it is describing, “letters,” which makes answer choices B and C incorrect.

Also, “in two letters to the historian Tacitus” should modify the verb “wrote.” In options A and D, “in two letters to the historian Tacitus” seems to be modifying “eruption,” which is incorrect. (There are other errors in answer choices B, C and D as well, but we will stick to the topic at hand.)

Option E corrects the prepositional phrase errors by putting the modifier close to the verb “wrote,” so therefore, E is our answer.

Let’s try one more:

Defense attorneys have occasionally argued that their clients’ misconduct stemmed from a reaction to something ingested, but in attributing criminal or delinquent behavior to some food allergy, the perpetrators are in effect told that they are not responsible for their actions.

(A) in attributing criminal or delinquent behavior to some food allergy
(B) if criminal or delinquent behavior is attributed to an allergy to some food
(C) in attributing behavior that is criminal or delinquent to an allergy to some food
(D) if some food allergy is attributed as the cause of criminal or delinquent behavior
(E) in attributing a food allergy as the cause of criminal or delinquent behavior

This sentence has two clauses:

Clause 1: Defense attorneys have occasionally argued that their clients’ misconduct stemmed from a reaction to something ingested,

Clause 2: in attributing criminal or delinquent behavior to some food allergy, the perpetrators are in effect told that they are not responsible for their actions.

These two clauses are joined by the conjunction “but,” and the underlined part is a prepositional phrase in the second clause.

Answer choices A, C and E imply that the perpetrators are attributing their own behaviors to food allergies. That is not correct – their defense attorneys are attributing their behavior to food allergies, and hence, all three of these options have modifier errors.

This leaves us with B and D. Answer choice D uses the phrase “attributed as,” which is grammatically incorrect – the correct usage should be “X is attributed to Y,” rather than “X attributed as Y.” Therefore, option B is our answer.

As you can see, the proper placement of prepositional phrases is instrumental in creating a sentence with a clear, logical meaning.  Since that type of clear, logical meaning is a primary emphasis of correct Sentence Correction answers, you should be prepared to look for prepositional phrases (here we go…) *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: Exit the GMAT Test Center…Don’t Brexit It

GMAT Tip of the WeekAcross much of the United Kingdom today, referendum voters are asking themselves “wait, did I think that through thoroughly?” in the aftermath of yesterday’s Brexit vote. Some voters have already admitted that they’d like a do-over, while evidence from Google searches in the hours immediately following the poll closures show that many Brits did a good deal of research after the fact.

And regardless of whether you side with Leave or Stay as it corresponds to the EU, if your goal is to Leave your job to Stay at a top MBA program in the near future, you’d be well-served to learn a lesson from those experiencing Brexit Remorse today.

How can the Brexit aftermath improve you GMAT score?

Pregrets, Not Regrets (Yes, Brexiters…we can combine words too.)
The first lesson is quite simple. Unlike those who returned home from the polls to immediately research “What should I have read up on beforehand?” you should make sure that you do your GMAT study before you get to the test center, not after you’ve (br)exited it with a score as disappointing as this morning’s Dow Jones.

But that doesn’t just mean, “Study before the test!” – an obvious tip. It also means, “Anticipate the things you’ll wish you had thought about.” Which means that you should go into the test center with list of “pregrets” and not leave the test center with a list of regrets.

Having “pregrets” means that you already know before you get to the test center what your likely regrets will be, so that you can fix them in the moment and not lament them after you’ve seen your score. Your list of pregrets should be a summary of the most common mistakes you’ve made on your practice tests, things like:

  • On Data Sufficiency, I’d better not forget to consider negative numbers and nonintegers.
  • Before I start doing algebra, I should check the answer choices to see if I can stop with an estimate.
  • I always blank on the 30-60-90 divisibility rule, so I should memorize it one more time in the parking lot and write it down as soon as I get my noteboard.
  • Reading Comprehension inferences must be true, so always look for proof.
  • Slow down when writing 4’s and 7’s on scratchwork, since when I rush they tend to look too much alike.
  • Check after every 10 questions to make sure I’m on a good pace.

Any mistakes you’ve made more than once on practice tests, any formulas that you know you’re apt to blank on, any reminders to yourself that “when X happens, that’s when the test starts to go downhill” – these are all items that you can plan for in advance. Your debriefs of your practice tests are previews of the real thing, so you should arrive at the test center with your pregrets in mind so that you can avoid having them become regrets.

Much like select English voters, many GMAT examinees can readily articulate, “I should have read/studied/prepare for _____” within minutes of completing their exam, and very frequently, those elements are not a surprise. So anticipate in the hour/day before the test what your regrets might be in the hours/days immediately following the test, and you can avoid that immediate remorse.

Double Cheque Your Work
Much like a Brexit vote, you only get one shot at each GMAT problem, and then the results lead to consequences. But the GMAT gives you a chance to save yourself from yourself – you have to both select your answer and confirm it. So, unlike those who voted and then came home to Google asking, “Did I do the right thing?” you should ask yourself that question before you confirm your answer. Again, your pregrets are helpful. Before you submit your answer, ask yourself:

  • Did I solve for the proper variable?
  • Does this number make logical sense?
  • Does this answer choice create a logical sentence when I read it back to myself?
  • Does this Inference answer have to be true, or is there a chance it’s not?
  • Am I really allowed to perform that algebraic operation? Let me try it with small numbers to make sure…

There will, of course, be some problems on the GMAT that you simply don’t know how to do, and you’ll undoubtedly get some problems wrong. But for those problems that you really should have gotten right, the worst thing that can happen is realizing a question or two later that you blew it.

Almost every GMAT examinee can immediately add 30 points to his score by simply taking back those points he would have given away by rushing through a problem and making a mistake he’d be humiliated to know he made. So, take that extra 5-10 seconds on each question to double check for common mistakes, even if that means you have to burn a guess later in the section. If you minimize those mistakes on questions within your ability level, that guess will come on a problem you should get wrong, anyway.

Like a Brexit voter, the best you can do the day before and day of your important decision-making day is to prepare to make the best decisions you can make. If you’re right, you’re right, and if you’re wrong, you’re wrong, and you may never know which is which (the GMAT won’t release your questions/answers and the Brexit decision will take time to play out). The key is making sure that you don’t leave with immediate regrets that you made bad decisions or didn’t take the short amount of time to prepare yourself for better ones. Enter the test center with pregrets; don’t Brexit it with regrets.

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 Simplify Percent Questions on the GMAT

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

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

Take the following question, for example:

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

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

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

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

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

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

24 min. 18 sec. = 0.90t

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

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

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

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

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

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

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

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

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

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

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

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

Quarter Wit, Quarter Wisdom: Some GMAT Questions Using the “Like” vs. “As” Concept

Quarter Wit, Quarter WisdomToday we will look at some official GMAT questions testing the “like” vs. “as” concept we discussed last week.

(Review last week’s post – if you haven’t read it already – before you read this one for greater insight on this concept.)

Take a look at the following GMAT Sentence Correction question:

As with those of humans, the DNA of grape plants contains sites where certain unique sequences of nucleotides are repeated over and over.

(A) As with those of humans, the DNA of grape plants contains sites where
(B) As human DNA, the DNA of grape plants contain sites in which
(C) As it is with human DNA, the DNA of grape plants, containing sites in which
(D) Like human, the DNA of grape plants contain sites where
(E) Like human DNA, the DNA of grape plants contains sites in which

Should we use “as” or “like”? Well, what are we comparing? We’re comparing the DNA of humans to the DNA of grape plants. Answer choice E compares these two properly – “Like human DNA, the DNA of grape plants…” DNA is singular, so it uses the singular verb “contains”.

All other options are incorrect. Answer choice A uses “those of” for DNA, but DNA is singular, so this cannot be right. B uses “as” to compare the two nouns, which is also incorrect. C is a sentence fragment without a main verb. And D compares “human” to “DNA”, which is not the “apples-to-apples” comparison we need to make this sentence correct. Therefore, our answer must be E.

Let’s try another one:

Like Auden, the language of James Merrill is chatty, arch, and conversational — given to complex syntactic flights as well as to prosaic free-verse strolls.

(A) Like Auden, the language of James Merrill
(B) Like Auden, James Merrill’s language
(C) Like Auden’s, James Merrill’s language
(D) As with Auden, James Merrill’s language
(E) As is Auden’s the language of James Merrill

Here, we’re comparing Auden’s language to James Merrill’s language. Answer choice C correctly uses the possessive “Auden’s” to show that language is implied. “Like Auden’s language, James Merrill’s language …” contains both parallel structure and a correct comparison.

Answer choices A, B and D incorrectly compare “Auden” to “language,” rather than “Auden’s language” to “language,” so those options are out. The structure of answer choice E is not parallel – “Auden’s” vs. “the language of James Merrill”. Therefore, the answer must be C.

Let’s try something more difficult:

More than thirty years ago Dr. Barbara McClintock, the Nobel Prize winner, reported that genes can “jump,” as pearls moving mysteriously from one necklace to another.

(A) as pearls moving mysteriously from one necklace to another
(B) like pearls moving mysteriously from one necklace to another
(C) as pearls do that move mysteriously from one necklace to others
(D) like pearls do that move mysteriously from one necklace to others
(E) as do pearls that move mysteriously from one necklace to some other one

This is a tricky question – it’s perfect for us to re-iterate how important it is to focus on the meaning of the given sentence. Do not try to follow grammar rules blindly on the GMAT!

Is the comparison between “genes jumping” and “pearls moving”? Do pearls really move mysteriously from one necklace to another? No! This is a hypothetical situation, so we must use “like” – genes are like pearls. Answer choices B and D are the only ones that use “like,” so we can eliminate our other options. D uses a clause with “like,” which is incorrect. In answer choice B, “moving from …” is a modifier – “moving” doesn’t act as a verb here, so it doesn’t need a clause. Hence, answer choice B is correct.

Here’s another one:

According to a recent poll, owning and living in a freestanding house on its own land is still a goal of a majority of young adults, like that of earlier generations.

(A) like that of earlier generations
(B) as that for earlier generations
(C) just as earlier generations did
(D) as have earlier generations
(E) as it was of earlier generations

Note the parallel structure of the comparison in answer choice E – “Owning … a house… is still a goal of young adults, as it was of earlier generations.” It correctly uses “as” with a clause.

Answer choice A uses “that” but its antecedent is not very clear; there are other nouns between “goal” and “like,” and hence, confusion arises. None of the other answer choices give us a clear, parallel comparison, so our answer is E.

Alright, last one:

In Hungary, as in much of Eastern Europe, an overwhelming proportion of women work, many of which are in middle management and light industry.

(A) as in much of Eastern Europe, an overwhelming proportion of women work, many of which are in
(B) as with much of Eastern Europe, an overwhelming proportion of women works, many in
(C) as in much of Eastern Europe, an overwhelming proportion of women work, many of them in.
(D) like much of Eastern Europe, an overwhelming proportion of women works, and many are.
(E) like much of Eastern Europe, an overwhelming proportion of women work, many are in.

Another tricky question. The comparison here is between “what happens in Hungary” and “what happens in much of Eastern Europe,” not between “Hungary” and “much of Eastern Europe.” A different sentence structure would be required to compare “Hungary” to “much of Eastern Europe” such as “Hungary, like much of Eastern Europe, has an overwhelming …”

With prepositional phrases, as with clauses, “as” is used. So, we have two relevant options – A and C. Answer choice A uses “which” for “women,” and hence, is incorrect. Therefore, our answer is C.

Here are some takeaways to keep in mind:

  • You should be comparing “apples” to “apples”.
  • Parallel structure is important.
  • Use “as” with prepositional phrases.

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 Least Helpful Waze To Study

GMAT Tip of the WeekIf you drive in a large city, chances are you’re at least familiar with Waze, a navigation app that leverages user data to suggest time-saving routes that avoid traffic and construction and that shave off seconds and minutes with shortcuts on lesser-used streets.

And chances are that you’ve also, at some point or another, been inconvenienced by Waze, whether by a devout user cutting blindly across several lanes to make a suggested turn, by the app requiring you to cut through smaller streets and alleys to save a minute, or by Waze users turning your once-quiet side street into the Talladega Superspeedway.

To its credit, Waze is correcting one of its most common user complaints – that it often leads users into harrowing and time-consuming left turns. But another major concern still looms, and it’s one that could damage both your fender and your chances on the GMAT:

Beware the shortcuts and “crutches” that save you a few seconds, but in doing so completely remove all reasoning and awareness.

With Waze, we’ve all seen it happen: someone so beholden to, “I must turn left on 9th Street because the app told me to!” will often barrel through two lanes of traffic – with no turn signal – to make that turn…not realizing that the trip would have taken the exact same amount of time, with much less risk to the driver and everyone else on the road, had he waited a block or two to safely merge left and turn on 10th or 11th. By focusing so intently on the app’s “don’t worry about paying attention…we’ll tell you when to turn” features, the driver was unaware of other cars and of earlier opportunities to safely make the merge in the desired direction.

The GMAT offers similar pitfalls when examinees rely too heavily on “turn your brain off” tricks and techniques. As you learn and practice them, strategies like the “plumber butt” for rates and averages may seem quick, easy, and “turn your brain off” painless. But the last thing you want to do on a higher-order thinking test like the GMAT is completely turn your brain off. For example, a “turn your brain off” rate problem might say:

John drives at an average rate of 45 miles per hour. How many miles will he drive in 2.5 hours?

And using a Waze-style crutch, you could remember that to get distance you multiply time by rate so you’d get 112.5 miles. That may be a few seconds faster than performing the algebra by thinking “Rate = Distance over Time”; 45 = D/2.5; 45(2.5) = D; D = 112.5.

But where a shortcut crutch saves you time on easier problems, it can leave you helpless on longer problems that are designed to make you think. Consider this Data Sufficiency example:

A factory has three types of machines – A, B, and C – each of which works at its own constant rate. How many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

(1) 7 Machine As and 11 Machine Bs can produce 250 widgets per hour

(2) 8 Machine As and 22 Machine Cs can produce 600 widgets per hour

Here, simply trying to plug the information into a simple diagram will lead you directly to choice E. You simply cannot separate the rate of A from the rate of B, or the rate of B from the rate of C. It will not fit into the classic “rate pie / plumber’s butt” diagram that many test-takers use as their “I hate rates so I’ll just do this trick instead” crutch.

However, those who have their critical thinking mind turned on will notice two things: that choice E is kind of obvious (the algebra doesn’t get you very close to solving for any one machine’s rate) so it’s worth pressing the issue for the “reward” answer of C, and that if you simply arrange the algebra there are similarities between the number of B and of C:

7(Rate A) + 11(Rate B) = 250
8(Rate A) + 22(Rate C) = 600

Since 11 is half of 22, one way to play with this is to double the first equation so that you at least have the same number of Bs as Cs (and remember…those are the only two machines that you don’t have “together” in either statement, so relating one to the other may help). If you do, then you have:

14(A) + 22(B) = 500
8(A) + 22(C) = 600

Then if you sum the questions (Where does the third 22 come from? Oh, 14 + 8, the coefficients for A.), you have:

22A + 22B + 22C = 1100

So, A + B + C = 50, and now you know the rate for one of each machine. The two statements together are sufficient, but the road to get there comes from awareness and algebra, not from reliance on a trick designed to make easy problems even easier.

The lesson? Much like Waze, which can lead to lack-of-awareness accidents and to shortcuts that dramatically up the degree of difficulty for a minimal time savings, you should take caution when deciding to memorize and rely upon a knee-jerk trick in your GMAT preparation.

Many are willing (or just unaware that this is the decision) to sacrifice mindfulness and awareness to save 10 seconds here or there, but then fall for trap answers because they weren’t paying attention or become lost when problems are more involved because they weren’t prepared.

So, be choosy in the tricks and shortcuts you decide to adopt! If a shortcut saves you a minute or two of calculations, it’s worth the time it takes to learn and master it (but probably never worth completely avoiding the “long way” or knowing the general concept). But if its time savings are minimal and its grand reward is that, “Hey, you don’t have to understand math to do this!” you should be wary of how well it will serve your aspirations of scores above around 600.

Don’t let these slick shortcut waze of avoiding math drive you straight into an accident. Unless the time savings are game-changing, you shouldn’t make a trade that gains you a few seconds of efficiency on select, easier problems in exchange for your awareness and understanding.

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.

Why Take a Language Test in Addition to the GMAT or GRE?

FAQMany international applicants are curious as to why graduate schools require an English language test along with the GMAT or the GRE. The latter tests are quite challenging and are already conducted in English, so why take TOEFL or IELTS, in addition?

Well, the reason is actually quite simple. Although the GMAT and GRE are administered in English, they do not truly test language proficiency.

Language vs. Aptitude Tests
Test-takers should be fluent in English to take GMAT and GRE, but these exams are just reasoning tests. The GMAT and GRE measure your aptitude for graduate school success by assessing your analytical thinking, quantitative skills, comprehension of complex texts, ability to identify arguments, etc.

These tests do require fluency in English because this is the language of the test. As such, you will need to brush-up your knowledge of standard English grammar and upgrade your vocabulary to an academic level to cope with the Verbal Sections and the Analytical Writing assessments. In addition, the GMAT and GRE will both require a refresher of high school and college math skills.

What language skills do you use on the GMAT and GRE?
1) Reading Comprehension
Both the GRE and GMAT are conducted entirely in English, so you should be able to comprehend all instructions and test questions, as well as be able to read quickly and understand what you are reading in detail.

The vocabulary in some parts of these tests can be at a very high academic level, or can be highly specialized in a certain field. On the GMAT, for example, you can find texts about history, biology and chemistry with very specific terminology. Don’t be surprised – the GMAT opens the door to business school, which prepares future managers. Managers have to be able to make decisions in any industry, not necessarily knowing all the details and terminology in the field.

Reading long, specialized text is essential for success in graduate school, but the GMAT and GRE do not test other equally important language skills such as your listening, comprehension and speaking abilities.

2) Applying Grammar Rules
Mastery of grammar rules and having an experienced eye for tiny details is essential for the Verbal Sections of the GRE and GMAT. Your grammar expertise will help you with, for example, GMAT Sentence Correction questions. Let’s look at how you can work on this using the following practice question; you have to choose which of the five answer choices is correct in order to replace the underlined part of the sentence:

SARS coronavirus – the virus that causes Sudden Acute Respiratory Syndrome – does not seem to transmit easily from person to person, though in China it has infected the family members and health care personnel taking care of them.

(A) it has infected the family members and health care personnel taking care of them
(B) it has infected the family members and health care personnel who had taken care of them
(C) the virus has infected the family members and health care personnel who have taken care of them
(D) the virus had infected the family members and health care personnel who took care of victims
E) it has infected the family members and health care personnel taking care of victims

Can you see how having a knowledge of grammar rules and a decision-point strategy can help you find the right answer? Veritas Prep experts explain:

In the original sentence, you will probably not notice the error with “them” at the end until you see the choice of “victims” in (D) and (E). The “them” in (A), (B), and (C) has no antecedent in the sentence. When you say “has infected THE family members and health personnel taking care of them” you need to have something for “them” to refer back to (it is not referring to family members or health personnel as that would be illogical – they are THE people doing the taking care of). In (D) the past perfect “had infected” is illogical as the virus did not infect the people BEFORE they took care of the people with the virus (the victims). (E) gets everything correct – it uses the proper, logical tense and uses “victims” instead of “them”. Answer is (E).

3) Writing and Style
Both the GMAT and the GRE have writing components. For the GRE, you are required to write two essays – Analysis of an Argument and Analysis of a Statement. The GMAT has only one essay – Analysis of the Argument. Although the focus of this part of the test is on your analytical skills, your presentation, use of correct grammar, level of vocabulary, structure and writing style will also count towards your score.

What language skills do the TOEFL and IELTS test?
The TOEFL (Test of English as a Foreign Language) and IELTS (International English Language Testing System) are the most well-known English proficiency tests required by universities. Although there are a number of differences between these tests, they both check all English language skills. In this way, university Admissions Committees make sure that prospective applicants can freely communicate in English in an academic environment, as well as make the most of their extracurricular activities and social life while at school.

The TOEFL and IELTS both assess:

1) Listening Comprehension
During these tests, you will listen to recordings of native speakers talking about different topics. Some of them are related to university life, such as lectures, class discussions, and talks between professors and students or among students. These tests reflect the variety of native English accents around the world, just as most of the international university classrooms do.

2) Reading Comprehension
You will have to read (within a specified time) large chunks of text on different topics. Vocabulary is at an academic level here, and the topics are from various fields of study and everyday situations. Your understanding of these texts will be verified in different ways.

3) Grammar
As with the GMAT and GRE, you will have questions that require a mastery of standard English grammar. You will have to find the best answer for certain Verbal questions, or decide whether a sentence is correct or incorrect (and how to correct it).

4) Writing
Both the IELTS and TOEFL exams have a written section. During this part of the test, you will have to write an essay – vocabulary used, clarity of expression, grammar, style, structure and focus on the topic are all considered in evaluating your essay.

5) Speaking
Oral communication is essential in graduate school, especially when the teaching methodology focuses on class discussion, group projects, presentations, and networking. While the Oral Section tests listening comprehension again, its primary purpose is to assess your ability to express yourself orally. For the TOEFL exam, the Oral Section, like the rest of the test, is carried out on a computer – you will listen to the instructions and then record your oral presentation. For the IELTS exam, your oral ability is assessed though a live, face-to-face conversation with the examiners.

Can language tests be waived?
Some universities will waive the requirement for a language test for international applicants who have recently completed a Bachelor’s Degree course studied entirely in English. In rare cases, some business schools will not require applicants to take the IELTS or TOEFL, since they will have the chance to evaluate candidates’ language skills during the admissions interview. This does not mean that all schools requiring an admission interview will waive the TOEFL/IELTS requirement, however, so it is best to check with the schools you are applying to for their policies on the matter.

Now you can clearly see how these two types of tests differ, and why most universities and business schools require both an aptitude test (the GMAT and GRE) and a language proficiency test. Admissions Committees require evidence that you have the potential to succeed with your studies, and that neither your language nor reasoning skills will be barriers.

By Iliana Bobova, from our partners at PrepAdviser.

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!

Quarter Wit, Quarter Wisdom: Using “Like” vs. “As” on the GMAT Verbal Section

Quarter Wit, Quarter WisdomIf you have seen the Veritas Prep curriculum, then you know we frequently highlight the strategy of “Think like the Testmaker” to answer GMAT questions. Recently, we had a student question the grammatical validity of this construct – this brought the “like” vs. “as” debate to mind, so we decided to tackle it this week.

When should you use “like” and when should you use “as” in a sentence?

Both words can be used in comparisons, however the structure of the sentence will be different in the two cases. This is because traditionally, “like” is a preposition and “as” is a conjunction – a preposition takes the form of an object while a conjunction takes the form of a clause. Therefore:

Using “like,” we compare nouns/pronouns (including gerunds). Usually, a single verb will be used.

Using “as,” we compare actual actions. There will be two verbs used when we compare using “as.”

So, this is how we are going to compare “like” and “as”:

  • He runs like a madman. – A single verb, “runs.”
  • He runs as a madman does. – Two verbs, “runs” and “does” (which is equivalent to “does run”).

In the same way, both of the following sentences are correct:

  • Think like the Testmaker.
  • Think as the Testmaker does.

But beware – “as” used with a noun or pronoun alone does not mean that this usage is incorrect. “As” can also be used to show a role or capacity. For example, in the sentence, “She works as a consultant,” the word “as” means that she works in the capacity of a consultant. There is no comparison here, but the sentence is still grammatically correct.

Also, we usually use “like” in the case of hypothetical comparisons. Take, for instance, the sentence, “She screams like a banshee.” Here, it would be odd to say, “She screams as a banshee does,” because we don’t really know how a banshee screams.

Let’s look at a few GMAT Sentence Correction questions now:

Like many self-taught artists, Perle Hessing did not begin to paint until she was well into middle age.

(A) Like
(B) As have
(C) Just as with
(D) Just like
(E) As did

In this sentence, the word “like” is correctly comparing “Perle Hessing” to “many self taught artists.” There is no clause after “like” and we are using a single verb. Hence, the use of “like” is correct and our answer is A.

Not too bad, right? Let’s try another question:

Based on recent box office receipts, the public’s appetite for documentary films, like nonfiction books, seems to be on the rise. 

(A) like nonfiction books 
(B) as nonfiction books 
(C) as its interest in nonfiction books 
(D) like their interest in nonfiction books 
(E) like its interest in nonfiction books

This sentence also has a comparison, and it is between “appetite” and “interest” and how they are both are on a rise. Answer choice E compares “appetite” to “interest” using “like” as a single verb. None of the answer choices have “as” with a clause so the answer must be E.

These were two simple examples of “like” vs. “as.” Now let’s look at a higher-level GMAT question:

During an ice age, the buildup of ice at the poles and the drop in water levels near the equator speed up the Earth’s rotation, like a spinning figure skater whose speed increases when her arms are drawn in

(A) like a spinning figure skater whose speed increases when her arms are drawn in 
(B) like the increased speed of a figure skater when her arms are drawn in 
(C) like a figure skater who increases speed while spinning with her arms drawn in 
(D) just as a spinning figure skater who increases speed by drawing in her arms 
(E) just as a spinning figure skater increases speed by drawing in her arms

There is a comparison here, but between which two things? Answer choice A seems to be comparing “Earth’s rotation” to “spinning figure skater,” but these two things are not comparable. Option E is the correct choice here – it compares “speed up Earth’s rotation” to “skater increases speed.” Therefore, our answer is 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: The Curry Twos Remind You To Keep The GMAT Simple

GMAT Tip of the WeekHappy Friday from Veritas Prep headquarters, where we’re actively monitoring the way that Twitter is reacting to UnderArmour’s release of the new Steph Curry shoes. What’s the problem with the Curry Twos? Essentially they’re too plain and buttoned up – much more Mickelson than Michael, son.

OK, so what? The Curry 2s are more like the Curry 401(k)s. Why should that matter for your GMAT score?

Because on the GMAT, you want to be as simple and predictable as a Steph Curry sneaker.

What does that mean? One of the biggest study mistakes that people make is that once they’ve mastered a core topic like “factoring” or “verb tenses,” they move on to more obscure topics and spend their valuable study time on those.

There are two major problems with this: 1) the core topics appear much more often and are much more repeatable, and 2) in chasing the obscure topics later in their study regimen, people spend the most valuable study time – that coming right before the test – feverishly memorizing things they probably won’t see or use at the expense of practicing the skills and strategies that they’ll need to use several times on test day.

Consider an example: much like Twitter is clowning the Curry Twos, a handful of Veritas Prep GMAT instructors were laughing this time last week about an explanation in a practice test (by a company that shall remain nameless…) for a problem similar to:

Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 30 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?

(A) 3:5
(B) 9:25
(C) 5:3
(D) 25:9
(E) Cannot be determined from the information provided

Now, the “Curry Two” approach – the tried and true, “don’t-overcomplicate-this-for-the-sake-of-overcomplicating-it” method – is to recognize that the distance around any circle (a wheel, a gear, etc.) is its circumference. And circumference is pi * diameter. So, if each gear travels the same circumferential distance, that distance for any given period of time is “circumference * number of revolutions.” That then means that the circumference of A times the number of revolutions of A is equal to the circumference of B times the number of revolutions for B, and you know that’s:

30π * A = 50π * B (where A = # of revolutions for A, and B = # of revolutions for B). Since you want the ratio of A:B, divide both sides by B and by 30, and you have A/B = 50/30, or A:B = 5:3 (answer choice C).

Why were our instructors laughing? The explanation began, “There is a simple rule for interconnected gears…” Which is great to know if you see a gear-based question on the test or become CEO of a pulley factory, but since the GMAT officially tests “geometry,” you’re much better off recognizing the relationship between circles, circumferences, and revolutions (for questions that might deal with gears, wheels, windmills, or any other type of spinning circles) than you are memorizing a single-use rule about gears.

Problems like this offer the “Curry Two” students a fantastic opportunity to reinforce their knowledge of circles, their ability to think spatially about shapes, etc. But, naturally, there are students who will add “gear formula” to their deck of flashcards and study that single-use rule (which 99.9% of GMAT examinees will never have the opportunity to use) with the same amount of time/effort/intensity as they revisit the Pythagorean Theorem (which almost everyone will use at least twice).

Hey, the Curry Twos are plain, boring, and predictable, as are the core rules and skills that you’ll use on the GMAT. But simple, predictable, and repeatable are what win on this test, so heed this lesson. As 73 regular season opponents learned this basketball season, Curry Twos lead to countless Curry 3s, and on the GMAT, “Curry Two” strategies will help you curry favor with admissions committees by leading to Curry 700+ scores.

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 Use Pronoun Substitution to Answer GMAT Sentence Correction Questions

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

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

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

Take the following question, for example:

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

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

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

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

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

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

Let’s try another one:

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

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

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

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

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

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

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

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

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

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

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

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

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

Quarter Wit, Quarter Wisdom: Are Official Answers Debatable on the GMAT?

Quarter Wit, Quarter WisdomLet’s begin with the bottom line: no, they are not. If you are thinking along the lines of, “This official answer cannot be correct! How can the answer be A? It must be C, or C is at least just as valid as A,” then you are wasting your time. The answer given is never debatable. What you should be thinking instead is, “The answer given is A, but  I thought it was C. I must find out where I made a mistake.”

The point is that since you are going to take GMAT, you must learn to think like the GMAT testmakers. The answers they give for these questions are the correct answers, so need to accept that – this way, the next step of figuring out the gap in your understanding will be far easier. Today, let’s take a look at an official question that is often debated:

The average hourly wage of television assemblers in Vernland has long been significantly lower than that in neighboring Borodia. Since Borodia dropped all tariffs on Vernlandian televisions three years ago, the number of televisions sold annually in Borodia has not changed. However, recent statistics show a drop in the number of television assemblers in Borodia. Therefore, updated trade statistics will probably indicate that the number of televisions Borodia imports annually from Vernland has increased.

Which of the following is an assumption on which the argument depends?

(A) The number of television assemblers in Vernland has increased by at least as much as the number of television assemblers in Borodia has decreased.
(B) Televisions assembled in Vernland have features that televisions assembled in Borodia do not have.
(C) The average number of hours it takes a Borodian television assembler to assemble a television has not decreased significantly during the past three years.
(D) The number of televisions assembled annually in Vernland has increased significantly during the past three years.
(E) The difference between the hourly wage of television assemblers in Vernland and the hourly wage of television assemblers in Borodia is likely to decrease in the next few years.

First, let’s look at the premises of the argument:

  • The hourly wage of assemblers in Vernland is much lower than that in Borodia.
  • 3 years ago, Borodia dropped all tariffs on TVs imported from Vernland.
  • The number of TVs sold annually in Borodia is same.
  • However, the number of assemblers in Borodia has decreased.

The conclusion is that the trade statistics will probably indicate that the number of televisions Borodia imports annually from Vernland has increased.

This conclusion might look logical, but it is full of assumptions.

Why does this conclusion seem so logical? Wages in Vernland are lower, so it would seem like TVs should be cheaper here. Borodia dropped all tariffs on imported TVs, which means there will be no artificial inflation of Vernland TV prices. Finally, the number of TVs sold in Borodia has not dropped, but number of assemblers in Borodia has dropped, which makes it look like fewer TVs are getting made in Borodia.

An onlooker might conclude that Borodia is importing more TVs from Vernland because they are cheaper, but here are some assumptions that come to mind:

  • The cost of a TV in Vernland is lower because assembler’s wage is lower. What if the raw material cost is higher in Vernland? Or other costs are higher? The cost to produce a Vernland TV could actually be higher than the cost to produce a Borodia TV.
  • Fewer TVs are getting made in Borodia, but that does not mean that Borodian assemblers have not become more productive. What if fewer assemblers are needed because they can actually complete the assembly process much faster? The number of TVs sold is the same, however, if each assembler is doing more work, fewer assemblers will be needed. In this case, the number of TVs made in Borodia might not have changed even though the number of producers dropped.

Coming to our question now: Which of the following is an assumption on which the argument depends?

We are looking for an assumption, i.e. a NECESSARY premise. We have already identified some assumptions, so let’s see if any of the answer choices gives us one of those:

(A) The number of television assemblers in Vernland has increased by at least as much as the number of television assemblers in Borodia has decreased.

This is the most popular incorrect answer choice. Test takers keep trying to justify why it makes perfect sense, but actually, it is not required for the conclusion to hold true.

The logic of test takers that pick this answer choice is often on the lines of, “If the number of workers from Borodia decreased, in order for Borodia to show an increased number of imports from Vernland, Vernland must have increased their number of workers by at least as much as the number of workers that left Borodia.”

Note that although this may sound logical, it is not necessary to the argument. There are lots of possible situations where this may not be the case:

Perhaps number of TVs being manufactured in Vernland is the same and, hence, the number of assemblers is the same, too. It is possible that out of the fixed number of TVs manufactured, fewer are getting locally bought and more are getting exported to Borodia. So, it is not necessarily true that number of TV assemblers in Vernland has increased.

(B) Televisions assembled in Vernland have features that televisions assembled in Borodia do not have.

This is also not required for the conclusion to hold – the TVs could actually be exactly the same, but the TVs assembled in Vernland could still be cheaper than the TVs assembled in Borodia due to a potentially lower cost of assembly in Vernland.

(C) The average number of hours it takes a Borodian television assembler to assemble a television has not decreased significantly during the past three years.

This is one of the assumptions we discussed above – we are assuming that the reduction in the number of assemblers must not be due to an increase in the productivity of the assemblers because if the assemblers have got more productive, then the number of TVs produced could be the same and, hence, the number of TVs imported would not have increased.

(D) The number of televisions assembled annually in Vernland has increased significantly during the past three years.

This is not required for the conclusion to hold. Perhaps the number of TVs being sold in Vernland has actually reduced while more are getting exported to Borodia, so the overall number of TVs being made is the same.

(E) The difference between the hourly wage of television assemblers in Vernland and the hourly wage of television assemblers in Borodia is likely to decrease in the next few years.

This is also not required for the conclusion to hold. What happens to the hourly wages of assemblers in Vernland and Borodia in the future doesn’t concern this argument – we are only concerned about what has been happening in the last 3 years.

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!

How to Go From a 48 to 51 in GMAT Quant – Part VI

Quarter Wit, Quarter WisdomToday’s post the next part in our “How to Go From 48 to 51 in Quant” series. Again, we will learn a technique that can be employed by the test-taker at an advanced stage of preparation – requiring one to understand the situations in which one can use this simplifying technique.

(Before you continue reading, be sure to check out parts I, II, III, IV, and V of this series.)

We all love to use the plug-in method on GMAT Quant questions. We have an equation given, and if the answer choices are the possible values of x, we just plug in these values to find the one that satisfies the equation.

But what if the answer choices are all complicated values? What if it seems that five times the calculation (in the worst case) will be far more time consuming than actually solving the given equation? Then one is torn between using the favorite plug-in method and using algebra. Let’s take an example to review the methods we can use to solve the question and learn how to simplify the plug-in process by approximating the five available options:

If |4x−4|=|2x+30|, which of the following could be a value of x?

(A) –35/3
(B) −21/2
(C) −13/3
(D) 11/5 
(E) 47/5

This question is an ideal candidate for the “plug-in” method. Here, you have the absolute value equation with the potential values of x given in the answer choices. The problem is that the values of x given are fractional. Of course, if we do plan to solve the equation rather than “plug-in”, we can still solve it using our holistic approach rather than pure algebra. Let’s take a look at that now, and later we will discuss the trick to making the answer choices easier for us to plug in.

Method 1:
|4x – 4| = |2x + 30|

4 * |x – 1| = 2 * |x + 15|

2 * |x – 1| = |x + 15|

This is how we rephrase the equation in our words: twice the distance of x from 1 should be equal to the distance of x from -15.

——————(-15) —————————————————(0)——(1)——————

There are two ways to find the value of x:

Case 1: x could be between -15 and 1 such that the distance between them is split in the ratio 2:1.

or

Case 2: x could be to the right of 1 such that the distance between x and -15 is twice the distance between x and 1.

Let’s examine both of these cases in further detail:

Case 1: The distance from -15 to 1 is of 16 units – this can be split into 3 sections of 16/3 units each. So, the distance of x from 1 should be 16/3, which would make the distance of x from -15 two times 16/3, i.e. 32/3.

So, x should be at a point 16/3 away from 1 toward the left.

x = 1 – 16/3 = -13/3

This is one of our answer choices and, hence, the correct answer. Normally, we would just move on to the next question at this point, but had we not found -13/3 in the answer options, we would have moved on to Case 2:

Case 2: The distance between -15 and 1 is 16 units. x should be an additional 16 units to the right of 1, so the distance between x and 1 is 16 and the distance between x and -15 is two times 16, i.e. 32. This means that x should be 16 units to the right of 1, i.e. x = 17. If you would not have found -13/3 in the answer choices, then you would have found 17.

Now let’s move on to see how we can make the plug-in method work for us in this case by examining each answer choice we are given:

Method 2:
|4x – 4| = |2x + 30|

2 * |x – 1| = |x + 15|

(A) -35/3

It is difficult to solve for x = -35/3 to see if both sides match. Instead, let’s solve for the closest integer, -12.

2 * |-12 – 1| = |-12 + 15|

On the left-hand side, you will get 26, but on the right-hand side, you will get 3.

These values are far away from each other, so x cannot be -35/3.  As the value of x approaches the point where the equation holds – i.e. where the two sides are equal to each other – the gap between the value of the two sides keeps reducing. With such a huge gap between the value of the two sides in this case, it is unlikely that a small adjustment of -35/3 from -12 will bring the two sides to be equal.

(B) -21/2

For this answer choice, let’s solve for the nearest integer, x = -10.

2 * |-10 – 1| = |-10 + 15|

On the left-hand side, you will get 22; on the right-hand side, you will get 5.

Once again, these values are far away from each other and, hence, x will not be -21/2.

(C) -13/3

For this answer choice, let’s solve for x = -4.

2 * |-4 -1| = |-4 + 15|

On the left-hand side, you will get 10; on the right-hand side, you will get 11.

Here, there is a possibility that x can equal -13/3, as the two sides are so close to one another – plug in the actual value of -13/3 and you will see that the left-hand side of the equation does, in fact, equal the right-hand side. Therefore, C is the correct answer.

Basically, we approximated the answer choices we were given and shortlisted the one that gave us very close values. We checked for that and found that it is the answer.

We can also solve this question using pure algebra (taking positive and negative signs of absolute values) but in my opinion, the holistic Method 1 is almost always better than that. Out of the two methods discussed above, you can pick the one you like better, but note that Method 2 does have limited applications – only if you are given the actual values of x, can you use it. Method 1 is far more generic for absolute value 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!

What to Do When You Find a Weighted Average Question In the Verbal Section of the GMAT

No MathWeighted averages show up everywhere on the GMAT. Most test-takers are prepared to see them on the Quantitative Section, but they’ll show up on the Integrated Reasoning and Verbal Sections, as well.  Because it is such an exam staple, we want to make sure that we have a thorough, intuitive understanding of the concept.

In class, I’ll typically start with a simple example. Say you have two solutions, A and B. A is 10% salt and B is 20% salt. If we combine these two solutions to get a composite solution that is 14% salt, do we have more A or B in this composite solution? Most students eventually see that we’ll have more of solution A, but it doesn’t always feel instinctive. If we had had equal quantities of both solutions, the combined solution would have been 15% salt – equidistant from 10% and 20%. So, if there is 14% salt, the average skews closer to A than B, and thus, there must be more of solution A.

I’ll then give another example. Say that there is an intergalactic party in which both humans and aliens are present. The humans, on average, are 6 feet tall. The aliens, on average, are 100 feet tall. If the average height at the party is 99 feet, who is dominating the party? It isn’t so hard to see that this party is packed with aliens and that the few humans present would likely spend the evening cowering in some distant corner of the room. The upshot is that it’s easier to feel the intuition behind a weighted average question when the numbers are extreme.

Take this tough Critical Reasoning argument for example:

To be considered for inclusion in the Barbizon Film Festival, a film must belong either to the category of drama or of comedy. Dramas always receive more submissions but have a lower acceptance rate than comedy. All of the films are either foreign or domestic. This year, the overall acceptance rate for domestic films was significantly higher than that for foreign films. Within each category, drama and comedy, however, the acceptance rate for domestic films was the same as that for foreign films.

From the cited facts it can be properly concluded that

(A) significantly fewer foreign films than domestic films were accepted.
(B) a higher proportion of the foreign than of the domestic films submitted were submitted as dramas.
(C) the rate of acceptance of foreign films submitted was the same for drama as it was for comedies.
(D) the majority of the domestic films submitted were submitted as comedies.
(E) the majority of the foreign films submitted were submitted as dramas.

Okay. We know that dramas had a lower acceptance rate than comedies, and we know that the overall acceptance rate for domestic films was significantly higher than the acceptance rate for foreign films. So, let’s assign some easy numbers to try and get a handle on this information:

Say that the acceptance rate for dramas was 1% and the acceptance rate for comedies was 99%.

We’ll also say that the acceptance rate for domestic films was 98% and the acceptance rate for foreign films was 2%.

The acceptance rate within both domestic and foreign films is a weighted average of comedies and dramas. If only dramas were submitted, clearly the acceptance rate would be 1%. If only comedies were submitted, the acceptance rate would be 99%. If equal amounts of both were submitted, the acceptance rate would be 50%.

What do our numbers tell us? Well, if the acceptance rate for domestic films was 98%, then almost all of these films must have been comedies, and if the acceptance rate for foreign films was 2%, then nearly all of these films must have been dramas. So, domestic films were weighted towards comedies and foreign films were weighted towards drama. (An unfair stereotype, perhaps, but this is GMAC’s question, not mine.)

We can see that answer choice A is out, as we only have information regarding rates of acceptance, not absolute numbers. C is also out, as it violates a crucial premise of the question stem – we know that the acceptance rate for dramas is lower than for comedies, irrespective of whether we’re talking about foreign or domestic films.

That leaves us with answer choices B, D and E. So now what?

Let’s pick another round of values, but see if we can invalidate two of the three remaining options.

What if the acceptance rate for domestic films was 3% and the acceptance rate for foreign films was still 2%? (We’ll keep the acceptance rate for dramas at 1% and the acceptance rate for comedies at 99%.) Now domestic films would be mostly dramas, so option D is out – the majority of domestic films would not be comedies, as this  answer choice states.

Similarly, what if the acceptance rate for domestic films was 98% and the rate for foreign films was 97%? Now the foreign films would be mostly comedies, so option E is also out – the majority of foreign films would not be dramas, as this answer choice states.

Because the acceptance rate is lower for dramas than it is for comedies, and foreign films have a lower acceptance rate than do domestic films, the foreign films must be weighted more heavily towards dramas than domestic films are. This analysis is perfectly captured in option B, which is, in fact, the correct answer.

Takeaway: certain concepts, such as weighted averages, are such exam staples that will appear in both Quant and Verbal questions. If you see one of these examples in the Verbal Section, assigning extreme values to the information you are given can help you get a handle on the underlying logic being tested.

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.

Help! 100% of the GMAT Sentence Correction Question is Underlined!

MBA Interview QuestionsImagine, you are plugging along in your Verbal Section on the GMAT, and then it pops up – the dreaded Sentence Correction question where every single word is underlined. The golden strategy for Sentence Correction is typically to evaluate decision points, as in determining what two or three spots in the sentence are evaluated in the answer choices. Consider a question where not all of the sentence is underlined:

A recent research study of worldwide cellular penetration finds that there are now one mobile phone for every two people, more than twice as many than there were in 2005.

(A) there are now one mobile phone for every two people, more than twice as many than there were
(B) there is now one mobile phone for every two people, more than twice as many than there were
(C) there is now one mobile phone for every two people, more than twice as many as there were
(D) every two people now have one mobile phone, more than twice as many than there were
(E) every two people now has one mobile phone, more than twice as many as there were

The first step we take is to cut away the junk, getting to the core of the Sentence Correction question – by ignoring “of worldwide cellular penetration,” we uncover that the subject of the sentence, “a study finds that,” makes it clear with the usage of “that” that the second portion of the sentence it set up to be a new clause with its own subject/verb relationship. This is the first decision point.

We should also know that there “is,” not “are,” one phone, which definitely puts answer choice A out of the running. Another decision point is our comparison phrase – it should be “twice as many as,” not “twice as many than,” which eliminates options B and D. Quickly, with these decision points, we are down to two remaining answers. E seems to inference that two people share one mobile phone (seems a little tough logistically, right?) aka, an illogical structure to the sentence. That leaves us with the correct answer, C.

Easy enough, right? But what do we do if everything is, indeed, underlined?

Our strategy is not going to be all that different, but instead, we will need to focus more on decision points from the answer choices and then use process of elimination when it is not entirely apparent what needs adjusting within the question sentence itself. Take a similar example (but one that is completely underlined):

Unlike cellular phones and personal computers, there is a difficulty on the part of many people to adapt to other modern technologies.

(A) Unlike cellular phones and personal computers, there is a difficulty on the part of many people to adapt to other modern technologies.
(B) Unlike cellular phones and personal computers, which many people are comfortable using, they have difficulty adapting to other modern technologies.
(C) Unlike cellular phones and personal computers, other modern technologies bring out a difficulty for many people to adapt to them.
(D) Many people, though comfortable using cellular phones and personal computers, have difficulty adapting to other modern technologies.
(E) Many people have a difficulty in adapting to other modern technologies, while they are comfortable using cellular phones and personal computers.

Looking at our answer choices, a clear decision point is “unlike” versus “many.” “Unlike” ends up comparing people to cellular phones and personal computers, and while Apple’s Siri can be pretty wise, there are (at least, for now) huge differences between people and those technologies. “Unlike” doesn’t work, and now we’ve have quickly narrowed it down to two answer choices: D and E. “Difficulty in adapting” gives us another decision choice in option E, leaving us with D as the correct answer.

When coming across completely underlined Sentence Correction questions, the first course of action is to not freak out. Stick with the strategy, and the correct answer will come easier than you think.

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.

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.