Why Logic is More Important Than Algebra on the GMAT

QuestioningOne common complaint I get from students is that their algebra skills aren’t where they need to be to excel on the GMAT. This complaint, invariably, is followed by a request for additional algebra drills.

If you’ve followed this blog for any length of time, you know that one of the themes we stress is that Quantitative Reasoning is not, primarily, a math test. Though math is certainly involved – How could it not be? – logic and reasoning are far more important factors than conventional mathematical facility. I stress this in every class I teach. So why the misconception that we need to hone our algebra chops?

I suspect that the culprit here is the explanations that often accompany official GMAC questions. On the whole, they tend to be biased in favor of purely algebraic solutions.  They’re always technically correct, but often suboptimal for the test-taker who needs to arrive at a solution within two minutes. Consequently, many students, after reviewing these solutions and arriving at the conclusion that they would not have been capable of the hairy algebra proffered in the official solution, think they need to work on this aspect of their prep. And for the most part it isn’t true.

Here’s a good example:

If x, y, and k are positive numbers such that [x/(x+y)]*10 + [y/(x+y)]*20 = k and if x < y, which of the following could be the value of k? 

A) 10
B) 12
C) 15
D) 18
E) 30

A large percentage of test-takers see this question, rub their hands together, and dive into the algebra. The solution offered in the Official Guide does the same – it is about fifteen steps, few of them intuitive. If you were fortunate enough to possess the algebraic virtuosity to solve the question in this manner, you’d likely chew up 5 or 6 minutes, a disastrous scenario on a test that requires you to average 2 minutes per problem.

The upshot is that it’s important for test-takers, when they peruse the official solution, not to arrive at the conclusion that they need to solve this question the same way the solution-writer did. Instead, we can use the same simple strategies we’re always preaching on this blog: pick some simple numbers.

We’re told that x<y, but for my first set of numbers, I like to make x and y the same value – this way, I can see what effect the restriction has on the problem. So let’s say x = 1 and y = 1. Plugging those values into the equation, we get:

(1/2) * 10 + (1/2) * 20  = k

5 + 10 = k

15 = k

Well, we know this isn’t the answer, because x should be less than y. So scratch off C. And now let’s see what the effect is when x is, in fact, less than y. Say x = 1 and y = 2. Now we get:

(1/3) * 10 + (2/3) * 20  = k

10/3 + 40/3 = k

50/3 = k

50/3 is about 17. So when we honor the restriction, k becomes larger than 15. The answer therefore must be D or E. Now we could pick another set of numbers and pay attention to the trend, or we can employ a bit of logic and common sense. The first term in the equation x/(x+y)*10 is some fraction multiplied by 10. So this term, logically, is some value that’s less than 10.

The second term in the equation is y/(x+y)*20, is some fraction multiplied by 20, this term must be less than 20. If we add a number that’s less than 10 to a number that’s less than 20, we’re pretty clearly not going to get a sum of 30. That leaves us with an answer of 18, or D.

(Note that if you’re really savvy, you’ll recognize that the equation is a weighted average. The coefficients in the weighted average are 10 and 20. If x and y were equal, we’d end up at the midway point, 15. Because 20 is multiplied by y, and y is greater than x, we’ll be pulled towards the high end of the range, leading to a k that must fall between 15 and 20 – only 18 is in that range.)

Takeaway: Never take a formal solution to a problem at face value. All you’re seeing is one way to solve a given question. If that approach doesn’t resonate for you, or seems so challenging that your conclusion is that you must purchase a host of textbooks in order to improve your formal math skills, then you haven’t absorbed what the GMAT is really about. Often, the relevant question isn’t, “Can you do the math?” It’s, “Can you reason your way to the answer without actually doing the math?”

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

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

Quarter Wit, Quarter Wisdom: Should You Use the Permutation or Combination Formula?

Quarter Wit, Quarter WisdomA recurring question from many students who are preparing for GMAT is this: When should one use the permutation formula and when should one use the combination formula?

People have tried to answer this question in various ways, but some students still remain unsure. So we will give you a rule of thumb to follow in all permutation/combination questions:

You never NEED to use the permutation formula! You can always use the combination formula quite conveniently. First let’s look at what these formulas do:

Permutation: nPr = n!/(n-r)!
Out of n items, select r and arrange them in r! ways.

Combination: nCr = n!/[(n-r)!*r!]
Out of n items, select r.

So the only difference between the two formulas is that nCr has an additional r! in the denominator (that is the number of ways in which you can arrange r elements in a row). So you can very well use the combinations formula in place of the permutation formula like this:

nPr = nCr * r!

The nCr formula is far more versatile than nPr, so if the two formulas confuse you, just forget about nPr.

Whenever you need to “select,” “pick,” or “choose” r things/people/letters… out of n, it’s straightaway nCr. What you do next depends on what the question asks of you. Do you need to arrange the r people in a row? Multiply by r!. Do you need to arrange them in a circle? Multiply by (r-1)!. Do you need to distribute them among m groups? Do that! You don’t need to think about whether it is a permutation problem or a combination problem at all. Let’s look at this concept more in depth with the use of a few examples.

There are 8 teachers in a school of which 3 need to give a presentation each. In how many ways can the presenters be chosen?

In this question, you simply have to choose 3 of the 8 teachers, and you know that you can do that in 8C3 ways. That is all that is required.

8C3 = 8*7*6/3*2*1 = 56 ways

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

There are 8 teachers in a school of which 3 need to give a presentation each. In how many ways can all three presentations be done?

This question is a little different. You need to find the ways in which the presentations can be done. Here the presentations will be different if the same three teachers give presentations in different order. Say Teacher 1 presents, then Teacher 2 and finally Teacher 3 — this will be different from Teacher 2 presenting first, then Teacher 3 and finally Teacher 1. So, not only do we need to select the three teachers, but we also need to arrange them in an order. Select 3 teachers out of 8 in 8C3 ways and then arrange them in 3! ways:

We get 8C3 * 3! = 56 * 6 = 336 ways

Let’s try another one:

Alex took a trip with his three best friends and there he clicked 7 photographs. He wants to put 3 of the 7 photographs on Facebook. How many groups of photographs are possible?

For this problem, out of 7 photographs, we just have to select 3 to make a group. This can be done in 7C3 ways:

7C3 = 7*6*5/3*2*1 = 35 ways

Here’s another variation:

Alex took a trip with his three best friends and there he clicked 7 photographs. He wants to put 3 of the 7 photographs on Facebook, 1 each on the walls of his three best friends. In how many ways can he do that?

Here, out of 7 photographs, we have to first select 3 photographs. This can be done in 7C3 ways. Thereafter, we need to put the photographs on the walls of his three chosen friends. In how many ways can he do that? Now there are three distinct spots in which he will put up the photographs, so basically, he needs to arrange the 3 photographs in 3 distinct spots, which that can be done in 3! ways:

Total number of ways = 7C3 * 3! = (7*6*5/3*2*1) * 6= 35 * 6 = 210 ways

Finally, our last problem:

12 athletes will run in a race. In how many ways can the gold, silver and bronze medals be awarded at the end of the race?

We will start with selecting 3 of the 12 athletes who will win some position in the race. This can be done in 12C3 ways. But just selecting 3 athletes is not enough — they will be awarded 3 distinct medals of gold, silver, and bronze. Athlete 1 getting gold, Athlete 2 getting silver, and Athlete 3 getting bronze is not the same as Athlete 1 getting silver, Athlete 2 getting gold and Athlete 3 getting bronze. So, the three athletes need to be arranged in 3 distinct spots (first, second and third) in 3! ways:

Total number of ways = 12C3 * 3! ways

Note that some of the questions above were permutation questions and some were combination questions, but remember, we don’t need to worry about which is which. All we need to think about is how to solve the question, which is usually by starting with nCr and then doing any other required steps. Break the question down — select people and then arrange if required. This will help you get rid of the “permutation or combination” puzzle once and for all.

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: Stay In Your Lane (In The Snow And On Sentence Correction)

GMAT Tip of the WeekAs the east coast braces for a historic winter storm (and Weezer fans can’t get “My Name is Jonas” out of their heads), there’s a lesson that needs to be taught from Hanover to Cambridge to Manhattan to Philadelphia to Charlottesville.

When driving in the snow:

  • Don’t brake until you have to.
  • Don’t make sudden turns or lane changes, and only turn if you have to.
  • Stay calm and leave yourself space and time to make decisions.

And those same lessons apply to GMAT Sentence Correction. Approach these questions like you would approach driving in a blizzard, and you may very well earn that opportunity to drive through blustery New England storms as you pursue your MBA. What does that mean?

1) Stay In Your Lane
Just as quick, sudden jerks of the steering wheel will doom you on snowy/icy roads, sudden and unexpected decisions on GMAT Sentence Correction will get you in trouble. Your “lane” consists of the decisions that you’ve studied and practiced and can calmly execute: Modifiers, Verbs (tense and agreement), Pronouns, Comparisons, Parallelism in a Series, etc. It’s when you get out of that lane that you’re prone to skidding well off track. For example, on this problem (courtesy the Official Guide for GMAT Review):

While Jackie Robinson was a Brooklyn Dodger, his courage in the face of physical threats and verbal attacks was not unlike that of Rosa Parks, who refused to move to the back of a bus in Montgomery, Alabama.

(A) not unlike that of Rosa Parks, who refused
(B) not unlike Rosa Parks, who refused
(C) like Rosa Parks and her refusal
(D) like that of Rosa Parks for refusing
(E) as that of Rosa Parks, who refused

Your “lane” here is to check for Modifiers (Is “who refused” correct? Is it required?) and for logical, clear meaning (it is required, because otherwise you aren’t sure who refused to move to the back of the bus). But examinees are routinely baited into “jerking the wheel” and turning against the strange-but-correct structure of “not unlike.” When you’re taken off of your game, you often eliminate the correct answer (A) because you’re turning into a decision you’re just not great at making.

2) Don’t Turn or Brake Until You Have To
The GMAT does test Redundancy and Pronoun Reference (among other things), but those are error types that are dangerous to prioritize – much like it’s dangerous while driving in snow to decide quickly that you need to turn or hit the brakes. Too often, test-takers will slam on the Sentence Correction brakes at their first hint of, “That’s redundant!” (like they would for “not unlike” above) or “There are multiple nouns – that pronoun is unclear!” and steer away from that answer choice.

The problem, as you saw above, is that often this means you’re turning away from the proper path. “Not unlike” may scream “double-negative” or “redundant” to many, but it’s a perfectly valid way to express the idea that the two things aren’t close to identical, but they’re not as different as you might think. And you don’t need to know THAT, as much as you need to know that you shouldn’t ever make redundancy your first decision, because if you’re like most examinees you’re probably not that great at you…AND you don’t have to be, because the path toward your strengths will get you to your destination.

Similarly, this week the Veritas Prep Homework Help service got into an interesting email thread about why this sentence:

Based on his experience in law school, John recommended that his friend take the GMAT instead of the LSAT.

has a pronoun reference error, but this sentence:

Mothers expect unconditional love from their children, and they are rarely disappointed.

does not. And while there likely exists a technical, grammatical reason why, the GMAT reason really comes down to this: Does the problem make you address the pronoun reference? If not, don’t worry about it. In other words, don’t brake or turn until you have to. If you look at those sentences in GMAT problem form, you might have:

Based on his experience in law school, John recommended that his friend take the GMAT instead of the LSAT.

(A) Based on his experience in law school, John

(B) Having had a disappointing experience in law school, John

(C) Given his experience in law school, John

Here, the question forces you to deal with the pronoun problem. The major differences between the choices are that A and C involve a pronoun, and B doesn’t. Here, you have to deal with that issue. But for the other sentence, you might see:

Mothers expect unconditional love from their children, and they are rarely disappointed.

(A) Mothers expect unconditional love from their children, and they are

(B) The average mother expects unconditional love from their children, and are

(C) The average mother expects unconditional love from their children, and they are

(D) Mothers, expecting unconditional love from their children, they are

Here, the only choice that doesn’t include the pronoun “they” is choice B, but that choice commits a glaring pronoun (and verb) agreement error (“the average mother” is singular, but “their children” is plural…and the verb “are” is, too). So you don’t need to worry about the “they” (which clearly refers to “mothers” and not “children,” even though there happen to be two plural nouns in the sentence).

Grammatically, the presence of multiple nouns doesn’t alone make the pronoun itself ambiguous, but strategically for the GMAT, what you really need to know is that you don’t have to hit the brakes at the first sign of “unclear reference.” Wait and see if the answer choices give you a chance to address that, and if they do, then make sure that those choices are free of other, more binary errors first. Don’t turn or brake unless you have to.

3) Stay calm and leave yourself space to make decisions.
Just like a driver in the snow, as a GMAT test-taker you’ll be nervous and antsy. But don’t let that force you into rash decisions! Assess the answer choices before you try to determine whether something outside your 100% confidence interval is right or wrong in the original. You don’t need to make a decision on Choice A right away, just like you don’t need to change lanes simply for the sake of doing so. Have a plan and stick to it, both on the GMAT and on those snowy roads this weekend.

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

By Brian Galvin.

Quarter Wit, Quarter Wisdom: Keeping an Open Mind in Critical Reasoning

Quarter Wit, Quarter WisdomToday we will discuss why it is important to keep an open mind while toiling away on your GMAT studying. Don’t go into test day with biases expecting that if a question tells us this, then it must ask that. GMAC testmakers are experts in surprising you and taking advantage of your preconceived notions, which is how they confuse you and convert a 600-level question to a 700-level one.

We have discussed necessary and sufficient conditions before; we have also discussed assumptions before. This question from our own curriculum is an innovative take on both of these concepts. Let’s take a look.

All of the athletes who will win a medal in competition have spent many hours training under an elite coach. Michael is coached by one of the world’s elite coaches; therefore it follows logically that Michael will win a medal in competition.

The argument above logically depends on which of the following assumptions?

(A) Michael has not suffered any major injuries in the past year.

(B) Michael’s competitors did not spend as much time in training as Michael did.

(C) Michael’s coach trained him for many hours.

(D) Most of the time Michael spent in training was productive.

(E) Michael performs as well in competition as he does in training.

First we must break down the argument into premises and conclusions:

Premises:

  • All of the athletes who will win a medal in competition have spent many hours training under an elite coach.
  • Michael is coached by one of the world’s elite coaches.

Conclusion: Michael will win a medal in competition.

Read the argument carefully:

All of the athletes who will win a medal in competition have spent many hours training under an elite coach.

Are you wondering, “How does one know that all athletes who will win (in the future) would have spent many hours training under an elite coach?”

The answer to this is that it doesn’t matter how one knows – it is a premise and it has to be taken as the truth. How the truth was established is none of our business and that is that. If we try to snoop around too much, we will waste precious time. Also, what may seem improbable may have a perfectly rational explanation. Perhaps all athletes who are competing have spent many hours under an elite coach – we don’t know.

Basically, what this statement tells us is that spending many hours under an elite coach is a NECESSARY condition for winning. What you need to take away from this statement is that “many hours training under an elite coach” is a necessary condition to win a medal. Don’t worry about the rest.

Michael is coached by one of the world’s elite coaches.

It seems that Michael satisfies one necessary condition: he is coached by an elite coach.

Conclusion: Michael will win a medal in competition.

Now this looks like our standard “gap in logic”. To get this conclusion, the necessary condition has been taken to be sufficient. So if we are asked for the flaw in the argument, we know what to say.

Anyway, let’s check out the question (this is usually our first step):

The argument above logically depends on which of the following assumptions?

Note the question carefully – it is asking for an assumption, or a necessary premise for the conclusion to hold.

We know that “many hours training under an elite coach” is a necessary condition to win a medal. We also know that Michael has been trained by an elite coach. Note that we don’t know whether he has spent “many hours” under his elite coach. The necessary condition requires “many hours” under an elite coach.

If Michael has spent many hours under the elite coach then he satisfies the necessary condition to win a medal. It is still not sufficient for him to win the medal, but our question only asks for an assumption – a necessary premise for the conclusion to hold. It does not ask for the flaw in the logic.

Focus on what you are asked and look at answer choice (C):

(C) Michael’s coach trained him for many hours.

This is a necessary condition for Michael to win a medal. Hence, it is an assumption and therefore, (C) is the correct answer.

Don’t worry that the argument is flawed. There could be another question on this argument which asks you to find the flaw in it, however this particular question asks you for the assumption and nothing more.

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: Your MLK Study Challenge (Remove Your Biases)

GMAT Tip of the WeekAs we celebrate Martin Luther King, Jr. this weekend, you may take some of your free time to study for the GMAT. And if you do, make sure to heed the lessons of Dr. King, particularly as you study Data Sufficiency.

If Dr. King were alive today, he would certainly be proud of the legislation he inspired to end much of the explicit bias – you can’t eat here, vote there, etc. – that was part of the American legal code until the 1960s. But he would undoubtedly be dismayed by the implicit bias that still runs rampant across society.

This implicit bias is harder to detect and even harder to “fix.” It’s the kind of bias that, for example, the movie Freaknomics shows; often when the name at the top of a resume connotes some sort of stereotype, it subconsciously colors the way that the reader of that resume processes the rest of the information on it.

While that kind of subconscious bias is a topic for a different blog to cover, it has an incredible degree of relevance to the way that you attack GMAT Data Sufficiency problems. If you’re serious about studying for the GMAT, you’ll probably have long enacted your own versions of the Voting Rights Act and Civil Rights Act well before you get to test day – that is to say, you’ll have figured out how to eliminate the kind of explicit bias that comes from reading a question like:

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

1) x > 0

2) y is a 3 digit number

Here, you’ll likely see very quickly that Statement 1 is not sufficient, and come back to Statement 2 with fresh eyes. You don’t know that x is positive, so you’ll quickly see that y could be 111 and x could be 2, or that y could be -111 and x could be -2, so Statement 2 is clearly also not sufficient. The explicit bias that came from seeing “x is positive” is relatively easy to avoid – you know not to carry over that explicit information from Statement 1 to Statement 2.

But you also need to be just as aware of implicit bias. Try this question, as it is more likely to appear on the actual GMAT:

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

On this version of the problem, people become extremely susceptible to implicit bias. You no longer get to quickly rule out the obvious “x is positive.” Here, the first statement serves to pollute your mind – it is, on its own merit, sufficient (if y is odd and the product of x and y is even, the only prime number x could be is 2, the only even prime), but it also serves to get you thinking about positive numbers (only positive numbers can be prime) and integers (only integers are prime). But those aren’t explicitly stated; they’re just inferences that your mind quickly makes, and then has trouble getting rid of. So as you assess Statement 2, it’s harder for you to even think of the possibilities that:

x could be -2 and y could be -111: You’re not thinking about negatives!

x could be 2/3 and y could be 333: You’re not thinking about non-integers!

On this problem, over 50% of users say that Statement 2 is sufficient (and less than 25% correctly answer A, that Statement 1 alone is sufficient), because they fall victim to that implicit bias that comes from Statement 1 whispering – not shouting – “positive integers.”

Harder problems will generally prey on your more subtle bias, so you need to make sure you’re giving each statement a fresh set of available options. So this Martin Luther King, Jr. weekend, applaud the progress that you have made in removing explicit bias from your Data Sufficiency regimen – you now know not to include Statement 1 directly in your assessment of Statement 2 ALONE – but remember that implicit bias is just as dangerous to your score. Pay attention to the times that implicit bias draws you to a poor decision, and be steadfast in your mission to give each statement its deserved, unbiased attention.

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

By Brian Galvin.

Quarter Wit, Quarter Wisdom: An Interesting Property of Exponents

Quarter Wit, Quarter WisdomToday, let’s take a look at an interesting number property. Once we discuss it, you might think, “I always knew that!” and “Really, what’s new here?” So let me give you a question beforehand:

For integers x and y, 2^x + 2^y = 2^(36). What is the value of x + y?

Think about it for a few seconds – could you come up with the answer in the blink of an eye? If yes, great! Close this window and wait for the next week’s post. If no, then read on. There is much to learn today and it is an eye-opener!

Let’s start by jotting down some powers of numbers:

Power of 2: 1, 2, 4, 8, 16, 32 …

Power of 3: 1, 3, 9, 27, 81, 243 …

Power of 4: 1, 4, 16, 64, 256, 1024 …

Power of 5: 1, 5, 25, 125, 625, 3125 …

and so on.

Obviously, for every power of 2, when you multiply the previous power by 2, you get the next power (4*2 = 8).

For every power of 3, when you multiply the previous power by 3, you get the next power (27*3 = 81), and so on.

Also, let’s recall that multiplication is basically repeated addition, so 4*2 is basically 4 + 4.

This leads us to the following conclusion using the power of 2:

4 * 2 = 8

4 + 4 = 8

2^2 + 2^2 = 2^3

(2 times 2^2 gives 2^3)

Similarly, for the power of 3:

27 * 3 = 81

27 + 27 + 27 = 81

3^3 + 3^3 + 3^3 = 3^4

(3 times 3^3 gives 3^4)

And for the power of 4:

4 * 4 = 16

4 + 4 + 4 + 4 = 16

4^1 + 4^1 + 4^1 + 4^1 = 4^2

(4 times 4^1 gives 4^2)

Finally, for the power of 5:

125 * 5 = 625

125 + 125 + 125 + 125 + 125 = 625

5^3 + 5^3 + 5^3 + 5^3 + 5^3 = 5^4

(5 times 5^3 gives 5^4)

Quite natural and intuitive, isn’t it? Take a look at the previous question again now.

For integers x and y, 2^x + 2^y = 2^(36). What is the value of x + y?

A) 18

(B) 32

(C) 35

(D) 64

(E) 70

Which two powers when added will give 2^(36)?

From our discussion above, we know they are 2^(35) and 2^(35).

2^(35) + 2^(35) = 2^(36)

So x = 35 and y = 35 will satisfy this equation.

x + y = 35 + 35 = 70

Therefore, our answer is E.

One question arises here: Is this the only possible sum of x and y? Can x and y take some other integer values such that the sum of 2^x and 2^y will be 2^(36)?

Well, we know that no matter which integer values x and y take, 2^x and 2^y will always be positive, which means both x and y must be less than 36. Now note that no matter which two powers of 2 you add, their sum will always be less than 2^(36). For example:

2^(35) + 2^(34) < 2^(35) + 2^(35)

2^(2) + 2^(35) < 2^(35) + 2^(35)

etc.

So if x and y are both integers, the only possible values that they can take are 35 and 35.

How about something like this: 2^x + 2^y + 2^z = 2^36? What integer values can x, y and z take here?

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: Make 2016 The Year Of Number Fluency

GMAT Tip of the WeekWhether you were watching the College Football Playoffs or Ryan Seacrest; whether you were at a house party, in a nightclub, or home studying for the GMAT; however you rang in 2016, if 2016 is the year that you make your business school goals come true, hopefully you had one of the following thoughts immediately after seeing the number 2016 itself:

  • Oh, that’s divisible by 9
  • Well, obviously that’s divisible by 4
  • Huh, 20 and 16 are consecutive multiples of 4
  • 2, 0, 1, 6 – that’s three evens and an odd
  • I wonder what the prime factors of 2016 are…

Why? Because the GMAT – and its no-calculator-permitted format for the Quant Section – is a test that highly values and rewards mathematical fluency. The GMAT tests patterns in, and properties of, numbers quite a bit. Whenever you see a number flash before your eyes, you should be thinking about even vs. odd, prime vs. composite, positive vs. negative, “Is that number a square or not?” etc. And, mathematically speaking, the GMAT is a multiplication/division test more than a test of anything else, so as you process numbers you should be ready to factor and divide them at a moment’s notice.

Those who quickly see relationships between numbers are at a huge advantage: they’re not just ready to operate on them when they have to, they’re also anticipating what that operation might be so that they don’t have to start from scratch wondering how and where to get started.

With 2016, for example:

The last two digits are divisible by 4, so you know it’s divisible by 4.

The sum of the digits (2 + 0 + 1 + 6) is 9, a multiple of 9, so you know it’s divisible by 9 (and also by 3).

So without much thinking or prompting, you should already have that number broken down in your head. 16 divided by 4 is 4 and 2000 divided by 4 is 500, so you should be hoping that the number 504 (also divisible by 9) shows up somewhere in a denominator or division operation (or that 4 or 9 does).

So, for example, if you were given a problem:

In honor of the year 2016, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?

(A) 18

(B) 36

(C) 42

(D) 54

(E) 56

You shouldn’t have to spend any time thinking about choices A and B, because you know that 2016 is divisible by 4 and by 9, so it’s definitely divisible by 36 which means it’s also divisible by every factor of 36 (including 18). You don’t need to do long division on each answer choice – your number fluency has taken care of that for you.

From there, you should look at the other numbers and get a quick sense of their prime factors:

42 = 2 * 3 * 7 – You know that 2016 is divisible by 2 and 3, but what about 7?

54 = 2 * 3 * 3 * 3 – You know that 2016 is divisible by that 2 and that it’s divisible by 9, so you can cover two of the 3s. But is 2016 divisible by three 3s?

56 = 2 * 2 * 2 * 7 – You know that two of the 2s are covered, and it’s quick math to divide 2016 by 4 (as you saw above, it’s 504). Since 504 is still even, you know that you can cover all three 2s, but what about 7?

Here’s where good test-taking strategy can give you a quick leg up: to this point, a savvy 700-scorer shouldn’t have had to do any real “work,” but testing all three remaining answer choices could now get a bit labor intensive. Unless you recognize this: for C and E, the only real question to be asked is “Is 2016 divisible by 7?” After all, you’re already accounted for the 2 and 3 out of 42, and you’ve already accounted for the three 2s out of 56.

7 is the only one you haven’t checked for. And since there can only be one correct answer, 2016 must be divisible by 7…otherwise you’d have to say that C and E are both correct.

But even if you’re not willing to take that leap, you may still have the hunch that 7 is probably a factor of 2016, so you can start with choice D. Once you’ve divided 2016 by 9 (here you may have to go long division, or you can factor it out), you’re left with 224. And that’s not divisible by 3. Therefore, you know that 2016 cannot be divided evenly into sets of 54, so answer choice D must be correct. And more importantly, good number fluency should have allowed you to do that relatively quickly without the need for much (if any) long division.

So if you didn’t immediately think “divisible by 4 and 9!” when you saw the year 2016 pop up, make it your New Year’s resolution to start thinking that way. When you see numbers this year, start seeing them like a GMAT expert, taking note of clear factors and properties and being ready to quickly operate on that number.

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

By Brian Galvin.

How to Choose the Right Number for a GMAT Variable Problem

Pi to the 36th digitWhen you begin studying for the GMAT, you will quickly discover that most of the strategies are, on the surface, fairly simple. It will not come as a terribly big surprise that selecting numbers and doing arithmetic is often an easier way of attacking a problem than attempting to perform complex algebra. There is, however, a big difference between understanding a strategy in the abstract and having honed that strategy to the point that it can be implemented effectively under pressure.

Now, you may be thinking, “How hard can it possibly be to pick numbers? I see an “x” and I decide x = 5. Not so complicated.” The art is in learning how to pick workable numbers for each question type. Different questions will require different types of numbers to create a scenario that truly is simpler than the algebra. The harder the problem, the more finesse that will be required when selecting numbers. Let’s start with a problem that doesn’t require much strategy:

If n=4p, where p is prime number greater than 2, how many different positive even divisors does n have, including n? 

(A) 2

(B) 3

(C) 4

(D) 6 

(E) 8 

Okay in this problem, “p” is a prime number greater than 2. So let’s say p = 3. If n = 4p, and 4p = 4*3 = 12. Let’s list out the factors of 12: 1, 2, 3, 4, 6, 12. The even factors here are 2, 4, 6, 12. There are 4 of them. So the answer is C. Not so bad, right? Just pick the first simple number that pops into your head and you’re off to the races. Bring on the test!

If only it were that simple for all questions. So let’s try a much harder question to illustrate the pitfalls of adhering to an approach that’s overly mechanistic:

The volume of water in a certain tank is x percent greater than it was one week ago. If r percent of the current volume of water in the tank is removed, the resulting volume will be 90 percent of the volume it was one week ago. What is the value of r in terms of x?

(A) x + 10

(B) 10x + 1

(C) 100(x + 10)

(D) 100 * (x+10)/(x+100)

(E) 100 * (10x + 1)/(10x+10)

You’ll notice quickly that if you simply declare that x = 10 and r =20, you may run into trouble. Say, for example, that the starting value from one week ago was 100 liters. If x = 10, a 10% increase will lead to a volume of 110 liters. If we remove 20% of that 110, we’ll be removing .20*110 = 22 liters, giving us 110-22 = 88 liters. But we’re also told that the resulting volume is 90% of the original volume! 88 is not 90% of 100, therefore our numbers aren’t valid. In instances like this, we need to pick some simple starting numbers and then calculate the numbers that will be required to fit the parameters of the question.

So again, say the volume one week ago was 100 liters. Let’s say that x = 20%, so the volume, after water is added, will be 100 + 20 = 120 liters.

We know that once water is removed, the resulting volume will be 90% of the original. If the original was 100, the volume, once water is removed, will be 100*.90 = 90 liters.

Now, rather than arbitrarily picking an “r”, we’ll calculate it based on the numbers we have. To summarize:

Start: 100 liters

After adding water: 120 liters

After removing water: 90 liters

We now need to calculate what percent of those 120 liters need to be removed to get down to 90. Using our trusty percent change formula [(Change/Original) * 100] we’ll get (30/120) * 100 = 25%.

Thus, when x = 20, r =25. Now all we have to do is substitute “x” with “20” in the answer choices until we hit our target of 25.

Remember that in these types of problems, we want to start at the bottom of the answer choice options and work our way up:

(E) 100 * (10x + 1)/(10x+10)

100 * (10*20 + 1)/(10*20+10) = 201/210. No need to simplify. There’s no way this equals 25.

(D) 100 * (x+10)/(x+100)

100 * (20+10)/(20+100) = 100 * (30/120) = 25. That’s it! We’re done. The correct answer is D.

Takeaways: Internalizing strategies is the first step in your process of preparing for the GMAT. Once you’ve learned these strategies, you need to practice them in a variety of contexts until you’ve fully absorbed how each strategy needs to be tweaked to fit the contours of the question. In some cases, you can pick a single random number. Other times, there will be multiple variables, so you’ll have to pick one or two numbers to start and then solve for the remaining numbers so that you don’t violate the conditions of the problem. Accept that you may have to make adjustments mid-stream. Your first selection may produce hairy arithmetic. There are no style point on the GMAT, so stay flexible, cultivate back-up plans, and remember that mental agility trumps rote memorization every time.

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

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

Quarter Wit, Quarter Wisdom: Calculating the Probability of Intersecting Events

Quarter Wit, Quarter WisdomWe know our basic probability formulas (for two events), which are very similar to the formulas for sets:

P(A or B) = P(A) + P(B) – P(A and B)

P(A) is the probability that event A will occur.

P(B) is the probability that event B will occur.

P(A or B) gives us the union; i.e. the probability that at least one of the two events will occur.

P(A and B) gives us the intersection; i.e. the probability that both events will occur.

Now, how do you find the value of P(A and B)? The value of P(A and B) depends on the relation between event A and event B. Let’s discuss three cases:

1) A and B are independent events

If A and B are independent events such as “the teacher will give math homework,” and “the temperature will exceed 30 degrees celsius,” the probability that both will occur is the product of their individual probabilities.

Say, P(A) = P(the teacher will give math homework) = 0.4

P(B) = P(the temperature will exceed 30 degrees celsius) = 0.3

P(A and B will occur) = 0.4 * 0.3 = 0.12

2) A and B are mutually exclusive events

If A and B are mutually exclusive events, this means they are events that cannot take place at the same time, such as “flipping a coin and getting heads” and “flipping a coin and getting tails.” You cannot get both heads and tails at the same time when you flip a coin. Similarly, “It will rain today” and “It will not rain today” are mutually exclusive events – only one of the two will happen.

In these cases, P(A and B will occur) = 0

3) A and B are related in some other way

Events A and B could be related but not in either of the two ways discussed above – “The stock market will rise by 100 points” and “Stock S will rise by 10 points” could be two related events, but are not independent or mutually exclusive. Here, the probability that both occur would need to be given to you. What we can find here is the range in which this probability must lie.

Maximum value of P(A and B):

The maximum value of P(A and B) is the lower of the two probabilities, P(A) and P(B).

Say P(A) = 0.4 and P(B) = 0.7

The maximum probability of intersection can be 0.4 because P(A) = 0.4. If probability of one event is 0.4, probability of both occurring can certainly not be more than 0.4.

Minimum value of P(A and B):

To find the minimum value of P(A and B), consider that any probability cannot exceed 1, so the maximum P(A or B) is 1.

Remember, P(A or B) = P(A) + P(B) – P(A and B)

1 = 0.4 + 0.7 – P(A and B)

P(A and B) = 0.1 (at least)

Therefore, the actual value of P(A and B) will lie somewhere between 0.1 and 0.4 (both inclusive).

Now let’s take a look at a GMAT question using these fundamentals:

There is a 10% chance that Tigers will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?

(A) 55%

(B) 60%

(C) 70%

(D) 72%

(E) 80%

Let’s review what we are given.

P(Tigers will not win at all) = 0.1

P(Tigers will win) = 1 – 0.1 = 0.9

P(Federer will not play at all) = 0.2

P(Federer will play) = 1 – 0.2 = 0.8

Do we know the relation between the two events “Tigers will win” (A) and “Federer will play” (B)? No. They are not mutually exclusive and we do not know whether they are independent.

If they are independent, then the P(A and B) = 0.9 * 0.8 = 0.72

If the relation between the two events is unknown, then the maximum value of P(A and B) will be 0.8 because P(B), the lesser of the two given probabilities, is 0.8.

Since 0.8, or 80%, is the greater value, the greatest possibility that the Tigers will win and Federer will play during the season is 80%. 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: Your GMAT New Year’s Resolution

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

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

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

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

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

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

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

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

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

By Brian Galvin.

Quarter Wit, Quarter Wisdom: Basic Operations for GMAT Inequalities

Quarter Wit, Quarter WisdomWe know that we can perform all basic operations of addition, subtraction, multiplication and division on two equations:

a = b

c = d

When these numbers are equal, we know that:

a + c = b + d (Valid)

a – c = b – d (Valid)

a * c = b * d (Valid)

a / c = b / d (Valid assuming c and d are not 0)

When can we add, subtract, multiply or divide two inequalities? There are rules that we need to follow for those. Today let’s discuss those rules and the concepts behind them.

Addition:

We can add two inequalities when they have the same inequality sign.

a < b

c < d

a + c < b + d (Valid)

Conceptually, it makes sense, right? If a is less than b and c is less than d, then the sum of a and c will be less than the sum of b and d.

On the same lines:

a > b

c > d

a + c > b + d (Valid)

Case 2: What happens when the inequalities have opposite signs?

a > b

c < d

We need to multiply one inequality by -1 to get the two to have the same inequality sign.

-c > -d

Now we can add them.

a – c > b – d

Subtraction:

We can subtract two inequalities when they have opposite signs:

a > b

c < d

a – c > b – d (The result will take the sign of the first inequality)

Conceptually, think about it like this: from a greater number (a is greater than b), if we subtract a smaller number (c is smaller than d), the result (a – c) will be greater than the result obtained when we subtract the greater number from the smaller number (b – d).

Note that this result is the same as that obtained when we added the two inequalities after changing the sign (see Case 2 above). We cannot subtract inequalities if they have the same sign, so it is better to always stick to addition. If the inequalities have the same sign, we simply add them. If the inequalities have opposite signs, we multiply one of them by -1 (to get the same sign) and then add them (in effect, we subtract them).

Why can we not subtract two inequalities when they have the same inequality sign, such as when a > b and c > d?

Say, we have 3 > 1 and 5 > 1.

If we subtract these two, we get 3 – 5 > 1 – 1, or -2 > 0 which is not valid.

If instead it were 3 > 1 and 2 > 1, we would get 1 > 0 which is valid.

We don’t know how much greater one term is from the other and hence we cannot subtract inequalities when their inequality signs are the same.

Multiplication:

Here, the constraint is the same as that in addition (the inequality signs should be the same) with an extra constraint: both sides of both inequalities should be non-negative. If we do not know whether both sides are non-negative or not, we cannot multiply the inequalities.

If a, b, c and d are all non negative,

a < b

c < d

a*c < b*d (Valid)

When two greater numbers are multiplied together, the result will be greater.

Take some examples to see what happens in Case 1, or more numbers are negative:

-2 < -1

10 < 30

Multiply to get: -20 < -30 (Not valid)

-2 < 7

-8 < 1

Multiply to get: 16 < 7 (Not valid)

Division:

Here, the constraint is the same as that in subtraction (the inequality signs should be opposite) with an extra constraint: both sides of both inequalities should be non-negative (obviously, 0 should not be in the denominator). If we do not know whether both sides are positive or not, we cannot divide the inequalities.

a < b

c > d

a/c < b/d (given all a, b, c and d are positive)

The final inequality takes the sign of the numerator.

Think of it conceptually: a smaller number is divided by a greater number, so the result will be a smaller number.

Take some examples to see what happens in Case 1, or more numbers are negative.

1 < 2

10 > -30

Divide to get 1/10 < -2/30 (Not valid)

Takeaways: 

Addition: We can add two inequalities when they have the same inequality signs.

Subtraction: We can subtract two inequalities when they have opposite inequality signs.

Multiplication: We can multiply two inequalities when they have the same inequality signs and both sides of both inequalities are non-negative.

Division: We can divide two inequalities when they have opposite inequality signs and both sides of both inequalities are non-negative (0 should not be in the denominator).

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

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

How to Make Rate Questions Easy on the GMAT

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

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

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

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

(A) 26

(B) 33

(C) 36

(D) 44

(E) 48

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

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

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

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

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

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

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

Take the following data sufficiency question:

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

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

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

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

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

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

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

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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

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

Quarter Wit, Quarter Wisdom: Grammatical Structure of Conditional Sentences on the GMAT

Quarter Wit, Quarter WisdomToday, we will take a look at the various “if/then” constructions in the GMAT Verbal section. Let us start out with some basic ideas on conditional sentences (though I know that most of you will be comfortable with these):

A conditional sentence (an if/then sentence) has two clauses – the “if clause” (conditional clause) and the “then clause” (main clause).  The “if clause” is the dependent clause, meaning the verbs we use in the clauses will depend on whether we are talking about a real or a hypothetical situation.

Often, conditional sentences are classified into first conditional, second conditional and third conditional (depending on the tense and possibility of the actions), but sometimes we have a separate zero conditional for facts. We will follow this classification and discuss four types of conditionals:

1) Zero Conditional

These sentences express facts; i.e. implications – “if this happens, then that happens.”

  • If the suns shines, the clothes dry quickly.
  • If he eats bananas, he gets a headache.
  • If it rains heavily, the temperature drops.

These conditionals establish universally known facts or something that happens habitually (every time he eats bananas, he gets a headache).

2) First Conditional

These sentences refer to predictive conditional sentences. They often use the present tense in the “if clause” and future tense (usually with the word “will”) in the main clause.

  • If you come to  my place, I will help you with your homework.
  • If I am able to save $10,000 by year end, I will go to France next year.

3) Second Conditional

These sentences refer to hypothetical or unlikely situations in the present or future. Here, the “if clause” often uses the past tense and the main clause uses conditional mood (usually with the word “would”).

  • If I were you, I would take her to the dance.
  • If I knew her phone number, I would tell you.
  • If I won the lottery, I would travel the whole world.

4) Third Conditional

These sentences refer to hypothetical situations in the past – what could have been different in the past. Here, the “if clause” uses the past perfect tense and the main clause uses the conditional perfect tense (often with the words “would have”).

  • If you had told me about the party, I would have attended it.
  • If I had not lied to my mother, I would not have hurt her.

Sometimes, mixed conditionals are used here, where the second and third conditionals are combined. The “if clause” then uses the past perfect and the main clause uses  the word “would”.

  • If you had helped me then, I would be in a much better spot today.

Now that you know which conditionals to use in which situation, let’s take a look at a GMAT question:

Botanists have proven that if plants extended laterally beyond the scope of their root system, they will grow slower than do those that are more vertically contained.

(A) extended laterally beyond the scope of their root system, they will grow slower than do

(B) extended laterally beyond the scope of their root system, they will grow slower than

(C) extend laterally beyond the scope of their root system, they grow more slowly than

(D) extend laterally beyond the scope of their root system, they would have grown more slowly than do

(E) extend laterally beyond the scope of their root system, they will grow more slowly than do

Now that we understand our conditionals, we should be able to answer this question quickly. Scientists have established something here; i.e. it is a fact. So we will use the zero conditional here – if this happens, then that happens.

…if plants extend laterally beyond the scope of their root system, they grow more slowly than do…

So the correct answer must be (C).

A note on slower vs. more slowly – we need to use an adverb here because “slow” describes “grow,” which is a verb. So we must use “grow slowly”. If we want to show comparison, we use “more slowly”, so the use of “slower” is incorrect here.

Let’s look at another question now:

If Dr. Wade was right, any apparent connection of the eating of highly processed foods and excelling at sports is purely coincidental.

(A) If Dr. Wade was right, any apparent connection of the eating of

(B) Should Dr. Wade be right, any apparent connection of eating

(C) If Dr. Wade is right, any connection that is apparent between eating of

(D) If Dr. Wade is right, any apparent connection between eating

(E) Should Dr. Wade have been right, any connection apparent between eating

Notice the non-underlined part “… is purely coincidental” in the main clause. This makes us think of the zero conditional.

Let’s see if it makes sense:

If Dr. Wade is right, any connection … is purely coincidental.

This is correct. It talks about a fact.

Also, “eating highly processed foods and excelling at sports” is correct.

Hence, our answer must be (D).

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

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

GMAT Tip of the Week: Listen to Yoda on Sentence Correction You Must

GMAT Tip of the WeekSpeak like Yoda this weekend, your friends will. As today marks the release of the newest Star Wars movie, Star Wars Episode VII: The Force Awakens, young professionals around the world are lining up dressed as their favorite robot, wookie, or Jedi knight, and greeting each other in Yoda’s famous inverted sentence structure. And for those who hope to awaken the force within themselves to conquer the evil empire that is the GMAT, Yoda can be your GMAT Jedi Master, too.

Learn from Yoda’s speech pattern, you must.

What can Yoda teach you about mastering GMAT Sentence Correction? Beware of inverted sentences, you should. Consider this example, which appeared on the official GMAT:

Out of America’s fascination with all things antique have grown a market for bygone styles of furniture and fixtures that are bringing back the chaise lounge, the overstuffed sofa, and the claw-footed bathtub.

(A) things antique have grown a market for bygone styles of furniture and fixtures that are bringing
(B) things antique has grown a market for bygone styles of furniture and fixtures that is bringing
(C) things that are antiques has grown a market for bygone styles of furniture and fixtures that bring
(D) antique things have grown a market for bygone styles of furniture and fixtures that are bringing
(E) antique things has grown a market for bygone styles of furniture and fixtures that bring

What makes this problem difficult is the inversion of the subject and verb. Much like Yoda’s habit of putting the subject after the predicate, this sentence flips the subject (“a market”) and the verb (“has grown”). And in doing so, the sentence gets people off track – many will see “America’s fascination” as the subject (and luckily so, since it’s still singular) or “all things antique” as the subject. But consider:

  • Antique things can’t grow. They’re old, inanimate objects (like those Luke Skywalker and Darth Vader action figures that your mom threw away that would now be worth a lot of money).
  • America’s fascination is the reason for whatever is growing. “Out of America’s fascination, America’s fascination is growing” doesn’t make any sense – the cause can’t be its own effect.

So, logically, “a market” has to be the subject. But in classic GMAT style, the testmakers hide the correct answer (B) behind a strange sentence structure. Two, really – people also tend to dislike “all things antique” (preferring “all antique things” instead), but again, that’s an allowable inversion in which the adjective goes after the noun.

Here is the takeaway: the GMAT will employ lots of strange sentence structures, including subject-verb inversion, a la Yoda (but only when it’s grammatically warranted), so you will often need to rely on “The Force” of logic to sift through complicated sentences. Here, that means thinking through logically what the subject of the sentence should be, and also removing modifiers like “out of America’s fascination…” to give yourself a more concise sentence on which to employ that logical thinking (the fascination is causing a market to develop, and that market is bringing back these old types of furniture).

Don’t let the GMAT Jedi mind-trick you out of the score you deserve. See complicated sentence structures, you will, so employ the force of logic, you must.

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

By Brian Galvin.

How I Achieved GMAT Success Through Service to School and Veritas Prep

Service to School Bryan Young served in the United States Army as an enlisted infantryman for five years, with a fifteen month tour in Iraq from 06’-07’. After leaving the military in 2008, he completed a Bachelor’s Degree in Business Administration from the University of Washington. He started his career in the consumer packaged goods industry and is now looking to attend a top tier university to obtain an MBA. Along with help from Veritas Prep, he was able to raise his GMAT score from a 540 to a 690!

How did you hear about Veritas Prep?

I had been thinking about taking the GMAT for the last three years and knew that I would probably need the help of a prep course to be able to get a competitive score. Service to School, a non-profit that helps veterans make the transition from the military to undergraduate and graduate school, awarded me with a scholarship to Veritas Prep.

What was your initial Experience with the GMAT?

During my first diagnostic test, I was pretty overwhelmed. The questions were confusing and the length of the test was intimidating. Finishing the test with a 540 was a wakeup call for me. My goal was to score a 700 or higher and the score I achieved showed me just how much work I was going to need to put into the process.

How did the Veritas Prep Course help prepare you?

The resources that Veritas Prep provides are amazing. The books arrived within a few days and then I was ready to start taking the online classes. After a few classes I realized that I needed to brush up on some of the basics and was able to use their skill builders sections to get back on track. The online class format was great and helped me to learn the strategies and ask questions. Then the homework help line was where I was able to get answers on some of the more tricky questions I encountered.

Tell us about your test day experiences and how you felt throughout the experience?

The first two times I took the test I was still not as prepared as I need to be. The test day started well, but quickly went sour. I ran out of time on the integrated reasoning section and with my energy being low I wound up having my worst verbal performances.

One of the greatest aspects of Veritas Prep is that they allow you to retake the class if you feel like you need to take it again. The second time through the class helped me a lot more since I wasn’t struggling with not knowing some of the basics. This helped me to fully understand the strategies for the quant section and solidify my sentence corrections skills as well. One suggestion of eating a snickers bar (or some sugary snack) made a huge difference for my energy levels and concentration on test day.

After another month and a half of studying I took the GMAT again and was excited to see the 690 with an 8 on the integrated reasoning. The score was in the range I wanted and I couldn’t have been happier to be finished. Veritas Prep helped me so much throughout the year long process of beating the GMAT!

Need help preparing for the GMAT? Join us for one of our FREE online GMAT strategy sessions or sign up for one of our GMAT prep courses, which are starting all the time. And be sure to follow us on FacebookYouTubeGoogle+ and Twitter!

The Patterns to Solve GMAT Questions with Reversed-Digit Numbers

Essay The GMAT asks a fair number of questions about the properties of two-digit numbers whose tens and units digits have been reversed. Because these questions pop up so frequently, it’s worth spending a little time to gain a deeper understanding of the properties of such pairs of numbers. Like much of the content on the GMAT, we can gain understanding of these problems by simply selecting random examples of such numbers and analyzing and dissecting them algebraically.

Let’s do both.

First, we’ll list out some random pairs of two-digit numbers whose tens and units digits have been reversed: {34, 43}; {17, 71}; {18, 81.} Now we’ll see if we can recognize a pattern when we add or subtract these figures. First, let’s try addition: 34 + 43 = 77; 17 + 71 = 88; 18 + 81 = 99. Interesting. Each of these sums turns out to be a multiple of 11. This will be true for the sum of any two two-digit numbers whose tens and units digits are reversed. Next, we’ll try subtraction: 43 – 34 = 9; 71 – 17 = 54; 81 – 18 = 63; Again, there’s a pattern. The difference of each pair turns out to be a multiple of 9.

Algebraically, this is easy enough to demonstrate. Say we have a two-digit number with a tens digit of “a” and a units digit of “b”. The number can be depicted as 10a + b. (If that isn’t clear, use a concrete number to illustrate it to yourself. Let’s reuse “34”. In this case a = 3 and b = 4. 10a + b = 10*3 + 4 = 34. This makes sense. The number in the “tens” place should be multiplied by 10.) If the original number is 10a + b, then swapping the tens and units digits would give us 10b + a. The sum of the two terms would be (10a + b) + (10b + a) = 11a + 11b = 11(a + b.) Because “a” and “b” are integers, this sum must be a multiple of 11. The difference of the two terms would be  (10a + b) – (10b + a) = 9a – 9b = 9(a – b) and this number will be a multiple of 9.

Now watch how easy certain official GMAT questions become once we’ve internalized these properties:

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

A) 6

B) 9

C) 10

D) 11

E) 14

If you followed the above discussion, you barely need to be conscious to answer this question correctly. We just proved that the sum of two-digit numbers whose units and tens digits have been reversed is 11! No need to do anything here. The answer is D. Pretty nice.

Let’s try another, slightly tougher one:

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

A) 3

B) 4

C) 5

D) 6

E) 7

This one is a little more indicative of what we’re likely to encounter on the actual GMAT. It’s testing us on a concept we’re expected to know, but doing so in a way that precludes us from simply relying on rote memorization. So let’s try a couple of approaches.

First, we’ll try picking some numbers. Let’s use the answer choices to steer us. Say we try B – we’ll want two digits that differ by 4. So let’s use the numbers 84 and 48. Okay, we can see that the difference is 84 – 48 = 36. That difference is too big, it should be 27. So we know that the digits are closer together. This means that the answer must be less than 4. We’re done. The answer is A. (And if you were feeling paranoid that it couldn’t possibly be that simple, you could test two numbers whose digits were 3 apart, say, 14 and 41. 41-14 = 27. Proof!)

Alternatively, we can do this one algebraically. We know that if the original two-digit numbers were 10a +b, that the new number, whose digits are reversed, would be 10b + a. If the difference between the two numbers were 27, we’d derive the following equation: (10a + b) – (10b + a) = 27. Simplifying, we get 9a – 9b = 27. Thus, 9(a – b) = 27, and a – b = 3. Also not so bad.

Takeaway: Once you’ve completed a few hundred practice questions, you’ll begin to notice that a few GMAT strategies are applicable to a huge swath of different question types. You’re constantly picking numbers, testing answer choices, doing simple algebra, or applying a basic number property that you’ve internalized. In this case, the relevant number property to remember is that the sum of two two-digit numbers whose units and tens digits have been reversed is always a multiple of 11, and the difference of such numbers is always a multiple of 9. Generally speaking, if you encounter a particular question type more than once in the Official Guide, it’s always worth spending a little more time familiarizing yourself with it.

*Official Guide 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 by him here.

How to Use Difference of Squares to Beat the GMAT

GMATIn Michael Lewis’ Flashboys, a book about the hazards of high-speed trading algorithms, Lewis relates an amusing anecdote about a candidate interviewing for a position at a hedge fund. During this interview, the candidate receives the following question: Is 3599 a prime number? Hopefully, your testing Spidey Senses are tingling and telling you that the answer to the question is going to incorporate some techniques that will come in handy on the GMAT. So let’s break this question down.

First, this is an interview question in which the interviewee is put on the spot, so whatever the solution entails, it can’t involve too much hairy arithmetic. Moreover, it is far easier to prove that a large number is NOT prime than to prove that it is prime, so we should be thinking about how we can demonstrate that this number possesses factors other than 1 and itself.

Whenever we’re given unpleasant numbers on the GMAT, it’s worthwhile to think about the characteristics of round numbers in the vicinity. In this case, 3599 is the same as 3600 – 1. 3600, the beautiful round number that it is, is a perfect square: 602. And 1 is also a perfect square: 12. Therefore 3600 – 1 can be written as the following difference of squares:

3600 – 1 = 602 – 12

We know that x– y= (x + y)(x – y), so if we were to designate “x” as “60” and “y” as “1”, we’ll arrive at the following:

60– 1= (60 + 1)(60 – 1) = 61 * 59

Now we know that 61 and 59 are both factors of 3599. Because 3599 has factors other than 1 and itself, we’ve proven that it is not prime, and earned ourselves a plumb job at a hedge fund. Not a bad day’s work.

But let’s not get ahead of ourselves. Let’s analyze some actual GMAT questions that incorporate this concept.

First:

999,9992 – 1 = 

A) 1010 – 2

B) (106 – 2) 2   

C) 105 (106 -2)

D) 106 (105 -2)

E) 106 (106 -2)

Notice the pattern. Anytime we have something raised to a power of 2 (or an even power) and we subtract 1, we have the difference of squares, because 1 is itself a perfect square. So we can rewrite the initial expression as 999,9992 – 12.

Using our equation for difference of squares, we get:

999,9992 – 12  = (999,999 +1)(999,999 – 1)

(999,999 + 1)(999,999 – 1) = 1,000,000* 999,998.

Take a quick glance back at the answer choices: they’re all in terms of base 10, so there’s a little work left for us to do. We know that 1,000,000 = 106  (Remember that the exponent for base 10 is determined by the number of 0’s in the figure.) And we know that 999,998 = 1,000,000 – 2 = 106 – 2, so 1,000,000* 999,998 = 106 (106 -2), and our answer is E.

Let’s try one more:

Which of the following is NOT a factor of 38 – 28?

A) 97

B) 65

C) 35

D) 13

E) 5

Okay, you’ll see quickly that 38 – 28 will involve same painful arithmetic. But thankfully, we’ve got the difference of two numbers, each of which has been raised to an even exponent, meaning that we have our trusty difference of squares! So we can rewrite 38 – 28 as (34)2 – (24)2. We know that 34 = 81 and 24 = 16, so (34)2 – (24)2 = 812 – 162. Now we’re in business.

812 – 162 = (81 + 16)(81 – 16) = 97 * 65.

Right off the bat, we can see that 97 and 65 are factors of our starting numbers, and because we’re looking for what is not a factor, A and B are immediately out. Now let’s take the prime factorization of 65. 65 = 13 * 5. So our full prime factorization is 97 * 13 * 5. Now we see that 13 and 5 are factors as well, thus eliminating D and E from contention. That leaves us with our answer C. Not so bad.

Takeaways:

  • The GMAT is not interested in your ability to do tedious arithmetic, so anytime you’re asked to find the difference of two large numbers, there is a decent chance that the number can be depicted as a difference of squares.
  • If you have the setup (Huge Number)2 – 1, you’re definitely looking at a difference of squares, because 1 is a perfect square.
  • If you’re given the difference of two numbers, both of which are raised to even exponents, this can also be depicted as a difference of squares, as all integers raised to even exponents are, by definition, perfect squares.

*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 FacebookYouTubeGoogle+ and Twitter!

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

Is Technology Costing You Your GMAT Score?

Veritas Prep GMAT Prep Books on iPadI recently read Sherry Turkle’s Reclaiming Conversation: The Power of Talk in a Digital Age. While the book isn’t about testing advice, per se, its analysis of the costs of technology is so comprehensive that the insights are applicable to virtually every aspect of our lives.

The book’s core thesis – that our smartphones and tablets are fragmenting our concentration and robbing us of a fundamental part of what it means to be human – isn’t a terribly original one. The difference between Turkle’s work and less effective screeds about the evils of technology is the scope of the research she provides in demonstrating how the overuse of our devices is eroding the quality of our education, our personal relationships, and our mental health.

What’s amazing is that these costs are, to some extent, quantifiable. Ever wonder what the impact is of having most of our conversations mediated through screens rather than through hoary old things like facial expressions? College students in the age of smartphones score 40% lower on tests measuring indicators of empathy than college students from a generation ago. In polls, respondents who had access to smartphones by the time they were adolescents reported heightened anxiety about the prospect of face-to-face conversations in general.

Okay, you say. Disturbing as that is, those findings have to do with interpersonal relationships, not education. Can’t technology be used to enhance the learning environment as well? Though it would be silly to condemn any technology as wholly corrosive, particularly in light of the fact that most schools are making a concerted effort to incorporate laptops and tablets in the classroom, Turkle makes a persuasive case that the overall costs outweigh the benefits.

In one study conducted by Pam Mueller and Daniel Oppenheimer, the researchers compared the retention rates of students who took notes on their laptops versus those who took notes by hand. The researchers’ assumption had always been that taking notes on a laptop would be more beneficial, as most of us can type faster than we can write longhand. Much to their surprise, the students who took notes by hand did significantly better than those who took notes on their laptops when tested on the contents of a lecture a week later.

The reason, Mueller and Oppenheimer speculate, is that because the students writing longhand couldn’t transcribe fast enough to record everything, they had to work harder to filter the information they were provided, and this additional cognitive effort allowed them to retain more. The ease of transcription – what we perceive as a benefit of technology – actually proved to be a cost. Even more disturbing, another study indicated that the mere presence of a smartphone – even if the phone is off – will cause everyone in its presence to retain less of a lecture, not just the phone’s owner.

I’ve been teaching long enough that when I first started, it was basically unheard of for a student’s attention to wander because he’d been distracted by a device. Smartphones didn’t exist yet. No one brought laptops to class. Now, if I were to take a poll, I’d be surprised if there were a single student in class who didn’t at least glance at a smartphone during the course of a lesson. One imagines that the same is true when students are studying on their own – a phone is nearby, just in case something important comes up. I’d always assumed the presence of these devices was relatively harmless, but if a phone that’s off can degrade the quality of our study sessions, just imagine the impact of a phone that continually pings and buzzes as fresh texts, emails and notifications come in.

The GMAT is a four-hour test that requires intense focus and concentration, so anything that hampers our ability to focus is a potential drag on our scores. There’s no easy solution here. I’m certainly not advocating that anyone throw away their smartphone – the fact that certain technology has costs associated with it is hardly a reason to discard that technology altogether. There are plenty of well-documented educational benefits: one can use a long train ride as an opportunity to do practice problems or watch a lecture. We can easily store data that can shed light on where we need to focus our attention in future study sessions. So the answer isn’t a draconian one in which we have to dramatically alter our lifestyles. Technology isn’t going anywhere – it’s a question of moderation.

Takeaways: No rant about the costs of technology is going to be terribly helpful without an action plan, so here’s what I suggest:

  • Put the devices away in class and take notes longhand. Whether you’re in a GMAT prep class, or an accounting class in your MBA program, this will benefit both you and your classmates.
  • If you aren’t using your device to study, turn it off, and make sure it’s out of sight when you work. The mere visual presence of a smartphone will cause you to retain less.
  • Give yourself at least 2 hours of device-free time each day. This need not be when you’re studying. It can also be when you’re out to dinner with friends or spending time with family. In addition to improving your interpersonal relationships, conversation actually makes you smarter.

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

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

GMAT Tip of the Week: Movember and Moving Your GMAT Score Higher

GMAT Tip of the WeekOn this first Friday of November, you may start seeing some peach fuzz sprouts on the upper lips of some of your friends and colleagues. For many around the world, November means Movember, a month dedicated to the hopefully-overlapping Venn Diagram of mustaches and men’s health. Why – other than the fact that this is a GMAT blog – do we mention the Venn Diagram?

Because while the Movember Foundation is committed to using mustaches as a way to increase both awareness of and funding for men’s health issues (in particular prostate and testicular cancer), many young men focus solely on the mustache-growth facet of the month. And “I’m growing a mustache for Movember” without the fundraising follow-through is akin to the following quotes:

“I’m growing a mustache for Movember.”

“I’m running a marathon for lymphoma research.”

“I’m dumping a bucket of ice water over my head on Facebook.”

“I’m taking a GMAT practice test this weekend.”/”I’m going to the library to study for the GMAT.”

Now, those are all noble sentiments expressed with great intentions. But another thing they all have in common is that they’re each missing a critical action step in their mission to reach their desired outcome. Growing a mustache does very little to prevent or treat prostate cancer. Running a marathon isn’t what furthers scientists’ knowledge of lymphoma. Dumping an ice bucket over your head is more likely to cause pneumonia than to cure ALS. And taking a practice test won’t do very much for your GMAT score.

Each of those actions requires a much more thorough and meaningful component. It’s the fundraising behind Movember, Team in Training, and the Ice Bucket Challenge that advances those causes. It’s your effort to use your mustache, sore knees, and Facebook video to encourage friends and family to seek out early diagnosis or to donate to the cause. And it’s the follow-up to your GMAT practice test or homework session that helps you increase your score.

This weekend, well over a thousand practice tests will be taken in the Veritas Prep system, many by young men a week into their mustache growth. But the practice tests that are truly valuable will be taken by those who follow up on their performance, adding that extra step of action that’s all so critical. They’ll ask themselves:

Which mistakes can I keep top-of-mind so that I never make them again?

How could I have budgeted my time better? Which types of problems take the most time with the least probability of a right answer, and which types would I always get right if I just took the extra few seconds to double check and really focus?

Based on this test, which are the 2-3 content areas/question types that I can markedly improve upon between now and my next practice test?

How will I structure this week’s study sessions to directly attack those areas?

And then they’ll follow up on what they’ve learned, following the new week’s plan of attack until it’s time to again take the first step (a practice test) with the commitment to take the substantially-more-important follow-up steps that really move the needle toward success.

Taking a practice test and growing a Movember mustache are great first steps toward accomplishing noble goals, but in classic Critical Reasoning form, premise alone doesn’t guarantee the conclusion. So make sure you don’t leave the GMAT test center this November with an ineffective mustache and a dismal score – put in the hard work that has to accompany that first step, and this can be a Movember to Remember.

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

By Brian Galvin.

Manipulating Standard Formulas on the GMAT

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

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

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

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

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

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

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

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

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

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

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

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

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

n(n+1)/2 – (m-1)*m/2

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

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

(A) 47

(B) 48

(C) 49

(D) 50

(E) 51

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

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

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

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

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

We know how to calculate that:

n(n+1)/2 – 40*41/2 = 356

n(n+1) = 2352

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

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

Another method:

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

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

45*7 = 315

45*8 = 360

This brings us very close to the value of 356.

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

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

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

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

raviVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms. He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99thpercentile with the proper techniques and preparation. In this “9 for 99th” video seriesRavi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

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

Lesson Nine: 

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

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

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

By Brian Galvin

3 Ways to Improve Brain Function for Better Studying

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

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

1) Sleep

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

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

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

2) Stop Multi-Tasking

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

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

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

3) Don’t Procrastinate

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

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

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

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

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

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

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

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

raviVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

First, take a look at lessons 1, 2, 3, 4, 5, 6 and 7!

Lesson Eight:

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

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

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

By Brian Galvin

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

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

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

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

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

Take this new question, for example:

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

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

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

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

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

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

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

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

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

Answer choice E:  (4m-12)/[m(m-4)]

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

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

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

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

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

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

raviVeritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms. He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation. In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

First, take a look at lessons 1, 2, 3, 4, 5, and 6!

Lesson Seven:

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

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

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

By Brian Galvin

Is Positive Thinking Enough to Actually Succeed on the GMAT?

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

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

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

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

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

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

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

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

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

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

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

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

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

Master the GMAT by Applying Jedi-like Skills

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Takeaway:

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

*GMATPrep question courtesy of the Graduate Management Admissions Council.

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

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

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

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

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

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

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

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

2. Don’t take too many notes.

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

3. Stay flexible.

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

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

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

By Brian Galvin

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

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

First, take a look at Lessons 1, 2, 3, 4 and 5!

Lesson Six:

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

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

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

By Brian Galvin

5 Reasons That Studying for the GMAT Sucks

GMATLet’s face it. Except for the folks who write the test and prepare you for the test, no one really loves the GMAT. Any anyone who tells you otherwise either scored an 800 with no prep or is lying.

But self-inflicted misery loves company, so in no particular order, let’s take a look at some of the things that suck and more importantly, how to cope:

 

  • Integrated Reasoning (IR) : It was introduced a few years ago, and even though multiple surveys and studies show it does correlate well with skills needed to succeed in business and the corporate world, schools still seem to have varying opinions on its value and how best to use it in the admissions process. For now, think of IR as the appetizer or warm-up. It’s tough, but it’s 30 minutes and can serve as a solid warmup before tackling the tougher ‘main course’ of quant and verbal. You wouldn’t start sprinting out of the gates in a race; treat the GMAT the same way, and if you bank some early points, that can’t hurt either.
  • AWA: Similar to IR, it doesn’t factor into your Total score, and schools differ on how they evaluate the essay. That being said, consider it a pre-pre-warm up, and more importantly, remember that schools can download a copy of your essay when they view your scores. So it’s important to put forth your best effort (now is NOT the time to challenge authority and write what you truly think of the GMAT or B school admissions process) and treat it as another writing sample that schools can use to evaluate your brilliance and creativity under pressure. Also, if English isn’t your first language, it’s absolutely going to be leveraged as an additional writing sample.
  • Data Sufficiency: This isn’t math, at least not in the sense that you’re used to seeing. What happened to the two trains leaving from separate stations and determining where they’ll meet? While that’s more problem solving, data sufficiency is important for schools to gauge your decision making abilities when you have limited or inaccurate information In a perfect world, you could make informed decisions with an infinite amount of time and all of the necessary details. But the world isn’t ideal, and like the cliché says, time is money. So data sufficiency quantifies what schools want to see: can you discern at what point do you have enough information to make an informed decision or at what point do you not have enough information and need to walk away.
  • Getting up early/Staying up late/Giving up Happy Hour aka Time Suck: We’ve all heard of FOMO, or “fear of missing out.” You’re likely going to have to make FOMO your new BFF while you’re preparing. In order to get the score you want, it’s important to put forth the effort. Just like training for a marathon or triathlon, you can’t take shortcuts or it’ll show on race day, and only you truly know the full measure of the effort you’re putting forth. So before you even start studying, make sure you’re mapping out a 3-4 month window where you know you can truly carve out time on a daily (regular!) basis to prepare, and more importantly, dedicate quality time to preparation.
  • Expenses!: The GMAT is expensive! And so is preparation! But if you think about it compared to the investment you’re about to make in your future and your long-term earnings potential, $250 for the test, $20 in bus fare/gas/transportation, and $50 for a celebratory steak after you crush it is a drop in the bucket. In life, there are absolutely times you should clip coupons, look for a better value and skimp on the extras. This is not one of them. Consider the GMAT the first step in a much larger investment in yourself.

It’s not rocket science (if it was, that might be the MCAT, not the GMAT), but it is important to recognize and embrace the challenges of this process. If it was easy, there would be far more individuals taking the GMAT every year (though nearly 250,000 is some decently sized competition). And one day while you’re studying, you’ll realize that while you don’t necessarily love it, the “studying for the GMAT sucks” factor is not quite as strong as it once was.   Take that as your reminder to keep your eye on the end game and keep plugging away. Your former self will thank you down the road.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Joanna Graham

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

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

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

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

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

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

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

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

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

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

By Scott Shrum

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

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

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

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

So then, how do we break this cycle?

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

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

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

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

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

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

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

Are Brain Training Exercises Helpful When Studying for Standardized Tests?

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

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

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

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

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

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

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

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

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

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

Stop Studying: 2 Activities That Will Increase Your GMAT Score

stressed-studentI like to arrive to my Monday evening classes a good half hour early so that I can spend some time talking to my students about how they spent their weekends. It helps me to get to know them, and it allows me to get a sense of the rhythm of their days. Some of my students do interesting things. They travel. They ski in the winters. They rock-climb when it’s warmer. But, unfortunately, they’re a minority.

The most common response is some variation of: I studied for the GMAT. Of course, they should be doing some studying, and I hope that this studying is at times enjoyable. But if an unusually satisfying Data Sufficiency problem is the highlight of your weekend, something is profoundly out of whack in your study-life balance. And yes, at times comments about studying all weekend are exaggerated for comic effect, but I think there is a distressing truth captured in these exchanges: people are so busy and overwhelmed during the week that they end up spending an unhealthy amount of time cramming for the GMAT on the weekends.

This isn’t good.

It isn’t good for the students’ physical or psychological wellbeing; and research is beginning to show that over-studying might be bad for performance as well.

According to one study performed by Stanford University, academic performance for high school students began to deteriorate once the students’ workloads exceeded two hours of homework per night. Now, there’s nothing magic about the figure of two hours – one imagines that people vary in terms of stamina levels, motivation, etc. – but this notion, that doing too much work not only will fail to help you, but also will actively stymie your efforts, is one well worth considering. And though this study involved high school students, there’s no reason to believe that this phenomenon wouldn’t hold for adults preparing for the GMAT. When we overexert ourselves in any capacity, be it physical training, work in the office, or studying, our performance tends to suffer.

I suspect that the most important factor is that if we’re studying too much, there are other beneficial things that we’re not doing. Put another way, if the benefits of additional studying begin to decrease once you’ve been at it for a few hours, wouldn’t it make more sense to use this time to engage in other activities that would not only be more enjoyable but could actually boost your score beyond what more study time could accomplish?

1. Exercise

The first, and most obvious consideration is that when we study, we’re typically inactive. (My apologies to anyone who is reading this at their treadmill desk.) The research on the benefits of aerobic exercise on academic performance is unambiguous. Aerobic exercise prompts the brain to generate, not just fresh neural connections, but new neurons, a phenomenon that was considered a physical impossibility as recently as 20 years ago. Students who exercise do better, on average, than those who don’t. We’ve been touting the benefits of exercise at Veritas Prep for years.  There’s no reason not to have exercise be a part of your routine. (This is to say nothing of the whole feeling better, being healthier, and living longer perk).

2. Conversation

The second, and perhaps more surprising finding, is that socialization can boost intelligence. One study, conducted by the University of Michigan, found that as little as 10 minutes of conversation can boost working memory. Moreover, they found that the total amount of socialization in one’s day was positively correlated with performance on a variety of cognitive tests. (If you’ve been studying for Critical Reasoning, hopefully, you’ve taken a moment to object that correlation isn’t necessarily causation. Yes, you say: it’s possible that socializing causes our brains to work better; but isn’t it also possible that when our brains are functioning optimally, we’re more likely to seek out opportunities for socialization? Not to worry. The experiments were designed to see what happened to a given group that socialized before taking a test, and what happened to that same group when they hadn’t socialized. When controlling for extraneous variables, socialization still had a robust impact on performance.)

Of course, one shouldn’t take any of this research to mean that preparing for this test won’t require a significant time investment. It will. But if you study so much that you stop taking care of yourself and neglect your personal relationships, you will not only make yourself unhappy, you’ll be artificially limiting your intellectual potential. So yes, do those few hours of Data Sufficiency questions. Take a four-hour exam on another day. Just make sure that you’re also taking time to go for a run or to play tennis or to see friends. You’ll be happier and less likely to burn out. And the fact that you’re also likely to do better on the exam with this approach is about as good an ancillary benefit as you’re likely to find.

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

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

Win a Free Veritas Prep GMAT Course!

NSHMBA Thumbnail 1Veritas Prep is excited to announce a scholarship opportunity to help you achieve your target GMAT score! We’ve partnered with the National Society of Hispanic MBAs to offer 100 GMAT preparation courses to qualifying applicants completely free of charge!

A good GMAT score is crucial when applying to business school, and we want to help you succeed. Our GMAT courses are available in over 90 cities worldwide, and also online using new Smartboard technology.

 

Every GMAT course comes with the following:

  • 36 hours of live instruction
  • An instructor who scored in the 99th percentile on the actual GMAT
  • 12 lesson booklets
  • 12 computer-adaptive practice tests
  • Live instructor help seven days a week
  • Veritas Prep GMAT on Demand pre-recorded lesson videos
  • 3,000 GMAT practice problems and solutions

To learn more about this scholarship and how to apply, visit the NSHMBA website. The deadline to apply is May 8th, so if you’re thinking about taking the GMAT, submit your application today!

We’re excited to get you moving on your next step towards graduate school!

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

By Colleen Hill

GMAT Tip of the Week: Prepare for the GMAT Using the Study Plan Rule of Thirds

GMAT Tip of the WeekHere on the first Friday of April, we’ve officially ended the first quarter of the year and fiscal reports are streaming in. But who’s in a hurry to finish 2015?

We’re still firmly entrenched in the first third of the year, and if 2015 is the year that you plan to conquer the GMAT you’re in luck. Why?

Because your GMAT study plan should include three phases:

 

1) Learn

One of the most common mistakes that GMAT studiers make is that they forget that they need to learn before they can execute. Are you keeping an eye on the stopwatch on every question you complete? Are you taking multiple practice tests in your first month of GMAT prep? Have you uttered the phrase “how could I ever do this in two minutes???”? If so, you’re probably not paying nearly enough attention to the learning phase. In the learning phase you should:

  • Review core skills related to the GMAT by DOING them and not just by trying to memorize them. You were once a master of (or maybe a B-student at) factoring quadratics and identifying misplaced modifiers and completing long division. Retrain your mind to do those things well again by practicing those skills.
  • Learn about the GMAT question types and the strategies that will help you attack them efficiently. For this you might consider a prep course or self-study program, or you can always start by reviewing prep books and free online resources.
  • Take as much time as you need to complete and learn from problems. You’ll learn a lot more from struggling through a problem in six minutes than you will from taking two minutes, giving up, and then reading the typewritten solution in the back of the book. Let yourself learn! Again, it’s critical to learn by doing – by actively engaging with problems and talking yourself into understanding – than it is to try to memorize your way to success. The stopwatch is not your friend in the first third of your preparation!
  • Embrace mistakes and keep a positive attitude. The GMAT is a hard test; most people struggle with unfamiliar question formats (Data Sufficiency, anyone?) and challenging concepts (without a calculator, too). Recognize that it will take some time to learn/re-learn these skills, and that making mistakes and thinking about them is one of the best ways to learn.

2) Practice

Regardless of how you’ve studied, you’ll need to complete plenty of practice to make sure you’re comfortable implementing those strategies and using those skills on test day. Once you’ve developed a good sense of what the GMAT is testing and how you need to approach it, it’s time to spend a few weeks devouring practice problems. Among the best sources include:

In this phase, you can start concerning yourself with the stopwatch a little and you’ll want to identify weaknesses and common mistakes so that you can emphasize those. Particularly with GMAT verbal, the more official problems you see the more you develop a feel for the style of them, so it’s important to emphasize practice not just for the conscious skills but also for those subconscious feelings you’ll get on test day from having seen so many ways they’ll ask you a question.

3) Execute

Before you take the GMAT you should have taken several practice tests. Practice tests will help you:

  • Work on pacing and develop a sense for how much time you’ll need to complete each section. From there you can develop a pacing plan.
  • Determine which “silly” mistakes you tend to make under timed pressure and exam conditions, and be hyperaware of them on test day.
  • Develop the kind of mental stamina you’ll need to hold up under a 4-hour test day. Verbal strategies can be much easier to employ in a 60-minute study session than at the end of a several-hour test! Make sure that at least a few times you take the entire test including AWA and IR for the first hour.
  • Continue to see new problems and hone your skills.

While it’s not a terrible idea to take a practice test early in your study regimen and another partway through the Practice phase, most of your tests should come toward the end of your study process. Why? Because the learning and practice phases are so important. You can’t execute until you’ve developed the skills and strategies necessary to do so, and you won’t do nearly as effective a job of gaining and practicing those if you’re not allowing yourself the time and subject-by-subject focus to learn with an open mind.

So be certain to let yourself learn with a natural progression via the GMAT Study Rule of Thirds. Learn first; then focus on practice; then emphasize execution via practice tests. Studying in thirds is the best way to ensure that you get into a school that’s your first choice.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

My Test Prep Journey to Scoring a 710 on the GMAT

Wood Veritas Prep PictureThe Veritas Prep program allowed me to reach my GMAT goals and re-learn all of the quantitative skills that I had forgotten over the past several years. I am an Army veteran, six years out of college, and Veritas Prep was the perfect program to teach me the skills I needed to succeed on the GMAT. I am thankful for the quality of the curriculum, and also very appreciative of the generous scholarship from Veritas Prep through the Service2School organization. Throughout the self-study lessons, I could always count on the on-demand videos to deliver engaging, thoughtful content and guide me through the lesson of the day. I particularly enjoyed Brian’s humorous references (the “alge, brah” joke stands out): The human element to the videos definitely helped me to remember many topics and leverage them on test day.

My goal was a score over 700, and I knew that I needed a structured, high-quality program to help me to get a top 10% score. After looking at several programs, Veritas Prep stood out as the one that would work for me. On day one of the program, I was contacted by Colleen Hill, who told me how to get started and offered her time for any questions I had throughout the course. I have to admit, I did not expect an actual person to contact me; it was a pleasant surprise! Upon receiving my materials in the mail and logging on to check out the online resources, I was again impressed by the quality of the materials. I found that I was more and more excited to begin the course. With everything organized and a thirty-day plan ahead of me, I began the course.

The curriculum was demanding, as I worked through it over a thirty-day period, and well-balanced to where I didn’t feel that I was ever losing ground in either quant or verbal. While working through the lessons, I could also always take comfort in the fact that if I didn’t understand a specific question, I could use the online homework help as a resource. Homework was challenging, which was great, and I found the explanations covered anything that I had missed when it came to why the correct answer was right, and why the wrong answers looked tempting.

When my test day finally came, I felt confident. I felt that the Veritas Prep practice tests had provided a very accurate measure of the difficulty of questions that I faced. Throughout the test, I remembered the lessons, always looking for logical ways to answer the question and leveraging a mastery of the content. I felt calm and confident throughout the test, and when I finished I had a 710. I am ecstatic at that score, especially as it is my first attempt, and I can attribute it to nothing but the exceptional quality of the Veritas Prep curriculum.

For someone who is looking for high-quality, comprehensive preparation for the GMAT, Veritas Prep should definitely be their first choice. I want to give a sincere “thank you” to Colleen and the rest of the Veritas Prep organization; you have helped me get a head start on my journey towards an MBA.

Veritas Prep is a proud sponsor of Service2School.

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

By US Army Captain Chuck Wood

Use Anxiety to Your Advantage on Test Day

GMAT PrepAt some point during the first session of each new class I teach, I’ll write my phone number on the board and mention that I take emergency calls. When I first started doing this, I figured that every now and again I’d get a call from a frantic student the night before the exam because he or she was running through some practice problems and was stumped on a concept that had previously been clear. I could then talk the student through a concept or strategy as a kind of pre-test boost. It turns out, these emergency calls happen far more often than I’d suspected, and they’re never about content. They’re always about anxiety. And the refrain is always the same. “When we’re doing the questions in class, I understand them. When I’m working on my own with no pressure, I’m fine. But when I see the timer…” The implications are clear: the issue often isn’t the content of the question, but the psychological mindset of the test-taker when he encounters it.

In fact, the link between anxiety and standardized testing is so prevalent that a Google search of ‘test anxiety’ yields well over 100,000,000 results. You want to make a parent nervous? Say something about Common Core. Want to freak out a high school student? Invoke the SATs. And if you’re reading this article, you are likely well acquainted with the pernicious effects that the GMAT can have on the ‘ol nervous system. It isn’t hard to see why. These tests not only have tangible academic and professional consequences that can reverberate for years, but they shape our fundamental self-perceptions. Someone who scores in the 98th percentile on a standardized test will, no matter what he says, walk out of that test feeling different about his abilities than someone who scores in the 7th percentile, despite the fact that there are literally dozens of variables in play that have little or nothing to do with underlying intelligence. (And this supposes that there is such a thing as underlying intelligence, as opposed to a host of complexly intersecting domains of intelligence, all of which may be difficult to measure with any kind of accuracy or consistency.) This is all to say that testing anxiety is both real and inevitable. It’s impossible to talk about preparation for an exam like the GMAT without addressing it.

Though this connection isn’t new, much of the science behind how the brain works under pressure is quite novel, and as we learn more, this knowledge will invariably seep into how teachers and tutors prepare their students for the exam.

First, consider the physiological process by which stress makes it make more difficult to perform well on exams. We enter what psychologists call a threat state. Here is a relevant quote from Barry Mendes, an associate professor of psychology from UC San Francisco, culled from a New York Times article on the subject. (The article is itself well worth a read).

The hallmark of a threat state is vasoconstriction — a tightening of the smooth muscles that line every blood vessel in the body. Blood pressure rises; breathing gets shallow. Oxygenated blood levels drop, and energy supplies are reduced. Meanwhile, a rush of hormones amplifies activity in the brain’s amygdala, making you more aware of risks and fearful of mistakes.”

And it turns out that the physiological processes in play are even more complicated than we’ve thought. Recent research has revealed that there is a gene that codes for the speed at which enzymes remove dopamine from various regions in the brain. Some remove dopamine quickly. Others remove it more slowly. In and of itself, this isn’t terrible interesting, but what is fascinating, and relevant to this discussion, is that those who had the gene that coded for the enzymes that removed dopamine more slowly did better than the other group on IQ tests in normal conditions, but worse than the other group on tests with significant time constraints. In other words, the gene that makes you smarter in a low stress environment causes you to underperform in a stressful situation. Suddenly, we have a scientific explanation for the dozens and dozens of students I’ve had over the years who maintained a 3.9 GPA in college, but could not, for the life of them, understand why they struggled on standardized tests!

The implications from the above discussion may sound fairly straightforward. Stress is bad. It can hurt test performance. But it isn’t that simple. It turns out that stress is one of those maddeningly elusive phenomena that we actually alter by focusing our attention on it. (Fans of quantum mechanics will recognize this as a version of the Observer Dilemma. In the quantum world, observing a particle alters the very characteristics we’re attempting to observe, so there’s no way to derive uncontaminated data. Scientists and philosophers have been puzzling over this for the better part of a century, and the phenomenon is no less strange now than it was when it was codified). This is best illustrated by a study conducted at Harvard. Half of the subjects were simply told that the purpose of the study was to examine the effect of anxiety on test-taking. The other students, however, were told that the anxiety during a test could actually boost performance. Sure enough, the group that was told that anxiety could boost performance did significantly better than the control group.

In other words, when we think stress is bad for us, it is. And when we think stress can be beneficial, it is. How we frame the issue in our minds has a direct and material impact on our response to trying conditions.

Moreover, there are things we can do to improve our performance in stressful situations. Pilots, for example, will practice dealing with artificial problems during test runs, and this practice yields benefits when these same problems happen during commercial flights. I’ll often encourage students to create a simulated stressful environment during a practice exam so that if a similar situation should befall the student during the real test, she’ll have an experience to draw on when attempting to adapt. For example, you can allow 10 minutes to elapse during a practice test so that if there is a time crunch on the real test, you’ll have already practiced how to address this potential crisis.

Last, you can practice mindfulness in the weeks leading up to the exam. A study performed last year demonstrated that students who began a mindfulness practice for only two weeks demonstrated improvements in working memory and concentration, benefits that translated to significantly higher scores on standardized tests. (The students in the study took the GRE, but there’s every reason to believe that mindfulness meditation would confer comparable benefits on the GMAT.) Here is an article distilling the main points of the study.

There is no avoiding stress on test day, but there is a lot we can do to reshape how we perceive this stress, and this reshaped perception can actually serve to improve our performance.

Takeaways:

  • Remind yourself that stress is not inherently bad. It can be a source of energy and focus that you can harness. Moreover, your belief in the bracing qualities of stress can be a self-fulfilling prophecy. Repeat that to yourself like mantra: stress can be helpful, but only if we tell ourselves so.
  • Simulate stressful conditions when taking practice tests so that these situations will be less alarming should they happen during the actual exam.
  • Consider starting a consistent mindfulness practice. The research indicating that mindfulness can boost test scores is promising, and the tangential health benefits are enormous.

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

By David Goldstein, a Veritas Prep GMAT instructor based in Boston.

Veritas Prep’s Top-Rated Instructor Comes to India on March 29!

Ravi SreeramaFor some time now, Veritas Prep team member Ravi Sreerama has been regarded as the best GMAT instructor in the industry (see for yourself!) Whether he’s leading GMAT courses in Los Angeles or training students worldwide in our Next-Generation Live Online GMAT Course, Ravi keeps growing his legion of loyal followers. They want to score in the 99th percentile on the GMAT, and Ravi knows how to help them do it.

No, for the first time ever, Ravi will take his show on the road: Starting March 29, Ravi will lead a seven-day Immersion Course in New Delhi! Our Immersion Course format is entirely unique — you cover all 36 hours of the traditional Veritas Prep Full Course GMAT curriculum, but do so over seven straight days. Six of those days feature six hours of GMAT instruction each, with a break in the middle of the week.

The schedule is as follows:

  • Sunday: Foundations of GMAT Logic & Arithmetic
  • Monday: Critical Reasoning, Algebra
  • Tuesday: Sentence Correction, Geometry
  • Wednesday: Review Session and Office Hours
  • Thursday: Reading Comprehension, Data Sufficiency
  • Friday: Advanced Verbal Strategy, Statistics and Combinatorics
  • Saturday: Word Problems, AWA & Integrated Reasoning

Pay special attention to that Wednesday schedule — that day is dedicated to review and to office hours in which you can get one-on-one GMAT coaching from Ravi. Need to catch up? Stuck on a particular area? Have specific questions that you’ve been saving to ask a GMAT expert? Wednesday is when you can take advantage of Ravi being in New Delhi to brush up on the skills that matter most to you.

And, of course, you get all of the other benefits of being in a Veritas Prep Immersion Course, including the camaraderie that comes from spending seven days with a group of like-minded, ambitious GMAT students. You also receive:

  • 36 hours of live, instructor-led class time
  • 12 GMAT lesson booklets
  • 12 computer adaptive practice tests
  • Online student account with study plan
  • 3,000 practice problems and solutions, including video
  • Live homework help 7 days a week for a year
  • Every lesson pre-recorded in HD for review

Hurry… March 29 is coming quickly! Learn more about Ravi Sreerama’s New Delhi GMAT course, and enroll as soon as you can so that you’re ready when class starts on the 29th!

By Scott Shrum

3 Ways to Improve Your Timing on the GMAT

stopwatchThe GMAT presents several challenges for test takers. For many people, the issues are focused around aptitude and the ability to simply get answers right. For others, timing is a big challenge. The GMAT is as much a test of mental endurance as it is an aptitude test.

With over 90 questions in 3+ hours the GMAT requires test takers to not only answer questions correctly, but to also do so quickly. In a vacuum many test takers could answer most GMAT questions correctly under normal conditions but the time constraints imposed by the GMAT make this one of the toughest standardized tests for graduate education.

All hope is not lost however; let’s discuss a few ways to prepare for the GMAT that will pay dividends on the timing front on test day.

Problem Sets

Every practice question you solve should be timed based on the average time you will have per question on the exam. Answering questions under unrealistic time scenarios does little to improve your performance especially if you are already struggling with pacing. Take the questions in sets (1, 5, 10, 20, etc.) and have your phone or stopwatch handy to make sure you are comfortable answering questions in realistic time constraints. If you are a Veritas Prep GMAT student, the Problems tab in your online account allows for the timed answering of homework questions!

Practice Exams

Too often test takers don’t start taking practice exams until too close to their test date. Practice exams are an integral part of your test prep game plan. I recommend taking your practice test at a similar time of day as your test date, if possible. If your test date is Saturday morning make sure you are taking practice tests on Saturday mornings. This is a good way to get your body synced up with the physical and mental side of taking such a long and difficult test. Once you take the test make sure you are including some time for review. Getting a problem wrong can be even more valuable than getting a problem right, focus on learning from your mistakes. You should spend a considerable amount of time figuring out why you got a problem wrong so you will never get a similar problem wrong again.

Problem Recognition

For most test takers who struggle with pacing, you will also want to work on problem recognition. Pacing is about quickly identifying the question type as well as how to approach it and then answering it quickly. Spend some time finding ways to quickly identify different question types and how to approach them. Finally, be able to move on if you realize that you don’t have a strong chance answering the question accurately in a reasonable amount of time. Spending an exorbitant amount of time on a question you will eventually get wrong is a death sentence on the GMAT; so don’t be afraid to move on after making an educated guess.

Incorporate these GMAT prep strategies into your studies and kiss pacing issues goodbye!

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

Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. Find more of his articles here