GMAT Tip of the Week: No News Is Good News

GMAT Tip of the WeekWe all have a laundry list of answers to the question “what makes Data Sufficiency difficult?” — it’s a unique question type; the math skills involved can be quite tricky; subtle phrasing and precision-in-wording can make huge differences; the situations are often abstract and difficult to conceptualize. But what about a better question – “what makes Data Sufficiency easier?” There are actually quite a few examples of this, and many relate to the Veritas Prep mindset “Think Like the Testmaker”. We can even break it down to one word:

Clues.

In all actuality, business schools don’t much care whether you can list all the factors of 224 or whether you know that the diameter and tangent of a circle are perpendicular at that point of tangency. What they do care about, though, is your ability to see opportunity – or danger – where others do not; your ability to recognize trends and use them to make decisions; your ability to read your opponent, whether a competitor or a negotiator, and come out on top. And so a great many “difficult” Data Sufficiency questions are written so that they embed clues to help astute test-takers – those with the abilities prized by business schools and employers – avoid trap answers and make good decisions.

One such clue comes in the form of what we’ll call “No News is Good News”, meaning that if the two statements in a Data Sufficiency question provide the exact same information:

-The answer can only be D or E (one can’t be sufficient without the other, and if they say the same thing then there’s no benefit to using both together)
-You now have twice as much time to invest in “the work” on one statement, since that work will cover both statements
-You have an opportunity to save yourself from a bad decision

Let’s investigate all three of those points, but particularly the last one, with an example:

All attendees at a university gathering are faculty or alumni of the university. Are any of the attendees both faculty and alumni?

(1) 3/5 of the attendees are members of the university faculty

(2) 40% of the attendees are not members of the university faculty

Now, many test takers (about half in the Veritas Prep Question Bank, as well as a couple of admittedly-distracted VP staffers seeing this question for the first time) will go through the following progression:

1) 3/5 = 60%, so I see what’s going on here…statement 1 says 60% and statement 2 says 40%

2) (and this is incorrect…more on that in a second) Well if 60% are faculty and 40% are “something else”, and there are only faculty and alumni and no one at this event is “neither”, then it looks like it’s 60% faculty and 40% alumni with no overlap, so the answer must be C, both statements together.

Which isn’t horrible logic, even though it’s incorrect. It’s a relatively understandable progression – but here’s where “No News is Good News” can help. If you really think about it, statements 1 and 2 basically say the same thing. If someone were to ask “what percent of people are not faculty” after statement 1, you’d have to say “well if 60% are, then 40% are not”. So if you think about it, statement 2 doesn’t tell you anything new. So how could the answer be C?

This is your clue to go back and re-investigate and save yourself. Statement 2 doesn’t mean “exactly 40% are alumni”, it only means “40% are not faculty”. So those 40% have to be alumni, but alumni isn’t limited to 40%. That 40% is just “alumni who are not faculty”. Consider the hypothetical that, out of 100 attendees, 60 are faculty, 50 are alumni, and 10 are therefore “both”. That’s perfectly consistent with the statements but doesn’t give you the same number for “both” that you would have had had you picked C.

So the answer is E, but the lesson is probably more important – the fact that the two statements gave you the exact same information was your clue that had you initially thought “C” you had to go back and do some work. When the two statements each tell you the same thing, the answer has to be D or E, and usually that means you have to put in a little due diligence to make sure you choose wisely.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Thinking Like the Testmaker

GMAT Tip of the WeekEarlier this week, in creating a blog post for our friends at Poets & Quants, we wanted to punctuate the Data Sufficiency lesson in the post with a fairly-basic sample problem that would have these four characteristics:

– More than half of users would get it wrong

– Of those users, the vast majority would pick the trap answer that corresponded with one particular mistake, the subject of the post

– After reading the rest of the post, they’d easily understand the mistake they made

– Naturally, the question had to be perfectly valid and the trap answer couldn’t be a “dirty trick” but rather had to be a valuable lesson

Now, you’d think it might be hard to get more than half of users – those who are taking additional time to study for the GMAT, so they’re clearly taking things seriously and putting in the work…this isn’t a late night Leno or Kimmel sketch in which we find the least-educated, least-worldly tourists on Hollywood Blvd. to answer a current events question! – to get a fairly basic question wrong. But in all actuality? It took less than 5 minutes to come up with a question that would end up hitting all those metrics. Upon creating the question we posted it in the Veritas Prep Question Bank and 60% of users to date have gotten it wrong, with just over 50% of users picking the prescribed trap answer. The lesson?

Writing GMAT questions that smart people get wrong is easy, because GMAT test-takers are extremely predictable.

That’s the point of the Veritas Prep “Think Like the Testmaker” theme that reappears through our lessons. The GMAT can bait you into trap answers over and over again, because your mind is predictable. A standardized test lends itself quite well to a standardized set of mistakes. The questions themselves will very often seem unique to you, but the same blueprints come up over and over again for the testmaker. “How do I trap 60% of users? Well, let me dig into my playbook, which includes:

  • Hide a valuable piece of information in the question stem of a Data Sufficiency question. For added effect, make one of the statements just algebra-intensive enough that people have to spend 45 seconds on it and it steals their attention away from that juicy nugget in the question…they’ll have totally forgotten about it.
  • Use a strange – but correct – grammatical structure as the first 5-7 words of the correct Sentence Correction answer, and people will eliminate it quickly and end up choosing between two incorrect answers that both passed the “I prefer this phrasing” test up front.
  • Set up a calculation for a word problem that leads people to solve for an intermediate step first, then make that number – the number they get right before they should take one more step – an answer choice, and prey on those who aren’t keeping track of which question was actually asked.
  • Create a problem that seems like it’s just testing a concept that everyone memorizes via flashcards, but make that memorized concept only one of two correct options.
  • Use a modifier or qualifier to eat up the first 7-10 words of the correct Critical Reasoning answer, knowing that impatient test-takers will quickly make their decision that it’s “out of scope” before reading the whole thing.

These testmaker traps – and more – come up very frequently on the GMAT, but test taker who are paying attention can learn to sniff them out before they fall into them. That’s the payoff to Thinking Like the Testmaker – if you get a geometry question wrong, it’s not necessarily that you don’t know the geometry (although most people will jot down “study more triangles” as their takeaway), as it could very well be that the testmaker beat you by knowing how you think instead.

For example, the lesson in the aforementioned blog post was “make sure you note important information in the question stem of a Data Sufficiency question”. Why? We see it all the time – students are in such a hurry to start “doing math” that they quickly skim through the question stem, then hustle to the statements. And this blueprint will get around half of test-takers just about every time even if the math isn’t that hard:

1) Embed a piece of information in the question stem; make it something that isn’t obvious…that the student will have to think about just a little to make it “actionable”

2) Make one of the statements require multiple steps and “satisfy the intellect” of the test-taker once they’ve finished those steps

3) Make it so that the question stem piece of information is critical

So our question:

If the product xy is not equal to 0, what is the value of x?

(1) y(x^2) + 4xy + 4y = 0

(2) y = 6

How does this fit the blueprint?

1) That “xy is not equal to 0” line requires just a bit of unpacking. For xy to not be 0, neither x nor y can equal 0.

2) In order to unravel the quadratic in statement 1, you have to do a few steps of factoring:

Factor the common ys: y(x^2 + 4x + 4) = 0
Notice that the x terms form a common quadratic – it’s (x + 2)^2 —> y(x + 2)(x + 2) = 0

By this point, many have forgotten about the fact that y can’t be 0. They may still look at this and say “either x = -2 or y = 0”, and the stats show that more than half of users don’t think this is sufficient. The main reason? They haven’t unpacked that question stem – had they, they could eliminate y = 0 as a possibility (meaning x must be -2) or they’d have just divided both sides by y in the original (you can’t do that if y might equal 0, but since we know it can’t you can divide it out) and been done with y forever. Most people (52% or so) pick C, and several pick E (perhaps not seeing that there’s only one solution for x).

The bigger lesson? It pays to not just see your mistakes in terms of content – those who picked C on this problem do not have a major problem with quadratics! In order to pick C, you have to be able to factor out statement 1 and realize that there’s only one value of x. If you picked C – as most do – you didn’t get beaten on content, you got beaten because the GMAT knew it could sneak xy isn’t 0 past you in the question stem. So as you study, pay attention to your mistakes and Think Like the Testmaker. The more you recognize these blueprints for trap answers, the bigger you’ll smile when you see the GMAT setting you up for them.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Why Johnny Manziel Would Beat the GMAT (but maybe not Bama)

GMAT Tip of the WeekHeading into this weekend’s giant Alabama vs. Texas A&M game, college football fans are probably as sick of hearing about Johnny Manziel as aspiring MBAs are of studying for the GMAT. But both, at least to some degree, are necessary evils – Manziel represents the best chance that football fans have of seeing someone other than Alabama playing for the national championship, and the GMAT is essential to a well-rounded MBA application. And there’s an overlap between the two – Manziel’s playing style can help you learn to beat the daunting GMAT the same way that he’s the only recent QB to beat that daunting Alabama defense. Here’s how summoning your inner Johnny Football can help you become Johnny (or Jenny) GMAT:

1) He can improvise

Manziel is most dangerous when the play breaks down and he has to create on his own outside of “the system”. He can check out of the assigned play call, scramble backward, decide to run and change his mind at the last minute when a receiver is open, or decide to pass and then at the last minute see that cornerback closing and tuck the ball to run like crazy for the pylon. Like any good GMAT test-taker, Manziel knows how to stick to the playbook when the first option is there, but he’s able to change gears when it becomes clear that the defense – or the question – has shifted into something entirely different.

The GMAT requires you to improvise, to realize on the fly that your first inclination might not work but that there’s another angle you can try. The GMAT rewards flexibility and the ability to almost make a mistake but learn from it in the moment. On quant questions, the algebra may lead you down a path that actually gets messier, and you might realize that it’s time to plug in some answer choices. Or your first sentence correction decision point may leave you with two flawed answers, and you’ll need to go reinvestigate answers you’ve eliminated. Hard GMAT questions will often force you to use a second strategy – those who have practiced with flexibility will have the advantage.

2) He’s not afraid to push the limits when it comes to rules

Manziel spent most of the summer testing authority and pushing the limits of the rules. And by doing so he was able to see just how far he could push the limits and get away with it, whether it was signing autographs for money (allegedly) or doing a little underage drinking / drug-experimentation on his rivals’ campus in Austin (also allegedly). He’s no worse for the wear – the NCAA helped keep him healthy by resting him during the Rice game – and showed you an important strategy for the GMAT…you have to push the limits when it comes to the rules. Like Manziel, the GMAT loves to play to the edges.

When a GMAT question gives the stipulation that “x is positive”, it’s up to you to push the limits – how small can you go? 0.00001? How high can you go? Infinity? Pushing boundaries is the key on many Data Sufficiency questions, like:

Is y > x?

(1) y = x^3

(2) x > 0

In your investigation of statement 1, you might quickly recognize “sure, if x = 2, then y’s bigger…but what about a negative? If x = -2, then y = -8, so negatives are the gamechangers.” And then with statement 2 (which should clearly be insufficient on its own), a lesser Man might say “oh, well together they’re sufficient because I can’t use negatives anymore”. But a full-fledged Manziel would push the limits a little: x can’t be negative, but what if it’s only hair over 0, like 1/4. 1/4 to the third power is 1/64, which is smaller. So y could still be smaller than x if we push the limits and go as small as the statements will let us go – the answer is E, but you have to get there by challenging the statements as far as they’ll let you.

3) He’s cocky

Manziel wasn’t intimidated running out the tunnel in Tuscaloosa last year, playing the defending national champions with a massive NFL-bound defensive line in front of a rabid fanbase. And he wouldn’t be intimidated by having his palm scanned and his digital photograph taken at the Pearson/VUE GMAT test center, either. Manziel is confident – to a fault, many college football enthusiasts would argue, but confident nonetheless. He trusts his instincts and like all good quarterbacks he’s able to leave a bad play behind him to focus on the next play.

To succeed on the GMAT, you need to be able to do that, too – to not be intimidated by convoluted-looking questions (start with what you know) and to not let one bad question unravel your confidence for the next question. Confidence is important, but you don’t have to be an impossibly cocky quarterback to summon the practical things that Manziel does well:

  • Know that everyone misses several questions. A mistake or two won’t kill your score, so stay upbeat and trust yourself.
  • Remember that if you’re nervous, that’s just your body’s adrenalin preparing you for peak performance. Nerves and anxiety are a biological response to the expectation of success – no one gets nervous buying a lottery ticket or Tweeting their celebrity crush, but you do get nervous when you’re asking for a promotion you think you deserve or when you’re asking out that girl from the coffee shop who has been flirting with you.
  • Don’t let what looks like an “easy” question seem like an indicator that you’re not doing well. Maybe it’s just easy for you, maybe it’s experimental, or maybe it’s harder than it looks. There are plenty of explanations for why that question might look easy even though you’re doing extremely well.
  • Don’t let hard questions get you down. You’ve earned them by doing well!
  • Don’t be afraid to guess. Like Manziel, sometimes you have to throw it out of bounds on second down to avoid the sack and make for a manageable third down. On the GMAT, spending 4-5 minutes on an impossible problem can leave you rushing later on, making silly mistakes that hurt your score a lot more. Guessing is ok – in many cases it’s strategically the right move.

Whether you’re an avid member of Texas A&M’s 12th Man, you greet people every morning with “Roll Tide”, or you’re somewhere in between, you can use the hype for this weekend’s Alabamanziel-apalooza to your advantage, studying how Johnny Manziel’s demeanor and ability can help you conquer the GMAT.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Get Exxxtreeeme!!!! on Logic-Based Math Questions

GMAT Tip of the WeekWhat do Mountain Dew, Tough Mudder, and Data Sufficiency have in common? Maybe they’re your plans for this weekend, but more universally they all lend themselves to the mentality, lifestyle, and even spelling of the eXXtreme!! And while we could fill this space with extreme-to-the-max tips about Mountain Dew (please don’t drink it for breakfast, high school students) and Tough Mudder (bring your wallet…their marketing is as extreme as the event itself), it’s more helpful to show you how taking it to the extreme can help you succeed on logic-based quant questions.

The name if the game with Data Sufficiency is “must be true”, as in “you have sufficient information to answer the question if the same answer must be true in all allowable cases”. So if you get a question like:

Is x^2 greater than 16?

With a statement like:

(1) x < 4

While the “obvious” values of x might be 3 (which squared is 9, so “no”) and 2 (which squared is 4, so also “no”), you’ll be rewarded for thinking of more-extreme answers allowed by the facts (what about a really, really negative number like -100: its square root will be very big and very positive, so that can give you your “yes”, making this statement not sufficient).

The GMAT likes to play to the extremes when it gives you limits on Data Sufficiency and “must be true” Problem Solving problems. When they give you the stipulation that x > 0, a wise test taker won’t start thinking only at 1 (what about a tiny fraction like 1/10?) and won’t stop thinking at 9 or 10 (what about a million?). The GMAT will reward you for pushing the limits of the possible range of values, and by that same token punish you if you stay within the typical comfort zone.

Consider this example:

If a, b, and c are consecutive odd positive integers and a < b < c, which of the following must be true?

I. at least one of the three numbers is prime
II. ab > c
III. a + b + c = 3b

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

For this question, most test-takers realize quickly that statement III must be true, as for consecutive odd integers, c will equal b + 2 and a will equal b – 2, so they’ll net out to 3b.

Statement II can be eliminated by going to the lower extreme: 1(3) is not greater than 5, but for all other versions (3*5 is greater than 7; 5*7 is greater than 9, etc.) the answer is “yes”. You have to go to the low extreme to eliminate statement II.

Statement I is the crux of this problem – about 70% of all respondents to this question in the Veritas Prep Question Bank see statement I as definitely true, when in fact it’s not. Their mistake? They don’t go to extremes. With two-digit numbers, at least one of every three odds in a row is prime. But that’s just because there aren’t enough numbers to be divisible by. There are only 14 multiples of 7 and 9 multiples of 11 within that set, meaning that you’re leaning extremely heavily on factors of 3 and 5 to find odd numbers that aren’t prime. But by the time you hit triple digits, there are plenty of potential factors, and prime numbers become much more rare. Consider 121, 123, and 125 – none are prime. If you go high enough in your search – with some logic behind it – you can fairly easily prove statement 1 not to be true. And the technique for doing so is to recognize that it’s easy to find multiples of 5 (if a number ends in 5, it’s an odd multiple of 5) and multiples of 3 (if the sum of the digits of a number is a multiple of 3, that number is divisible by 3). So you want to find multiples of 7 or 11 that don’t end in 5 and make those your starting point. 11-squared works perfectly – it’s only divisible by 11 – and then you can check two odds in either direction to see if they pass the 3s and 5s tests. 217 is another great one – you know that 210 and 7 are both divisible by 7, and then next to that you can find 215 (divisible by 5) and 213 (divisible by 3).

The problem with this problem is that people don’t look to the extremes. They’re relatively happy to check 3-4 sets of one and two digit numbers and feel that they’ve proven a trend, whereas on Must Be True questions it pays to get extreme.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Spend Your Labor Day Making Quant Problems Less Labor-Intensive

GMAT Tip of the WeekSo it’s Labor Day weekend, and hopefully you’ll celebrate by relaxing. But wait – Harvard’s admissions deadline is only about two weeks away, and Stanford’s is soon to follow, and within the next six weeks most top 20 programs will begin reviewing Round One applications.

So maybe you can’t afford to put your feet up just yet – maybe you do have to use your day off on Labor Day to start working toward your next career. But if you do decide to do some GMAT labor on Labor Day, keep in mind that you can still honor the spirit of the holiday, a day for the working man to celebrate the fruits of his labor by resting. You can practice GMAT math in the least labor-intensive way possible.

Two of the most common ways to reduce your workload on GMAT quant problems are:

  • Recognize “number properties”. If you can note that the correct answer must be negative (vs. positive) or odd (vs. even) or end in a certain digit, often you can avoid doing all the math and just follow the pattern to the correct answer.
  • Use the answer choices. If you can get away with an estimate, or eliminate certain answer choices for not having the right characteristics, or plug answer choices back into the problem (“backsolve”) to avoid doing the algebra, you can let the answer choices guide you away from hard labor.

So let’s look at an example of a problem for which the two above strategies can help us avoid some excess workload:

What is the square root of (x^2 * y^2) if x < 0 and y > 0?

(A) -xy
(B) xy
(C) -(absolute value of (xy))
(D) (absolute value of y)(x)
(E) Cannot be determined

Now, this problem can be solved using algebra but it may look a little intimidating that way, too. And algebra can lead to labor if you’re not careful. But you have clues:

*The presence of “x < 0”, “y > 0”, and two absolute value signs in the answer choices should indicate that this is a positive/negative number properties problem. The actual values of x and y don’t matter much (there are no actual values given anywhere in the problem) as long as you can figure out whether the right answer needs to be negative or positive, and whether each answer choice gives you that correctly. So in a case like this, you can avoid strange, conceptual algebra by picking numbers consistent with the stipulations in the problem:

x must be negative, so let’s call it -2
y must be positive, so let’s call it 3
Note: by avoiding 1 and -1 we avoid numbers with really unique problems, and since we’re squaring/rooting numbers by using a different base (2 vs. 3) for each we can more easily track the importance of each variable.

With x = -2 and y = 3, then inside the radical we have (-2)^2 * (3)^2 = 4 * 9 = 36. And the square root of 36 is 6, so we know that in our situation the result of that operation is 6. Now we can plug those numbers into the answer choices to see if we get 6:

(A) -(-2)(3) = 6, so A could work

(B) -2(3) = -6, so B is wrong

(C) The absolute value of -2(3) is 6, so -(6) = -6 and C is wrong

(D) The absolute value of 3 is 3, so it’s (3)(-2) = -6, so D is wrong

So of those answer choices, only A works, so A is correct.

More important is the takeaway – on this problem, if you can see that actual numbers aren’t as important as the number property, positive vs. negative, you can avoid having to do all the algebraic work in search of a solution and instead you can test numbers to see what type of positive/negative you need. Heeding these kinds of clues and using the answer choices to your advantage can help you avoid plenty of undue labor. So if you’re working on the GMAT this Labor Day, keep these strategies in mind and you’ll be able to avoid too much hard work on Test Day, a holiday that at least this year might matter all the more.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

Tales From the Question Bank: Pros Before Idio-es

GMAT Tip of the WeekThe Veritas Prep Question Bank offers unique insights in to the habits of GMAT test-takers; while students from around the world answer free GMAT practice questions, the Question Bank tracks patterns in the answers that the world selects, and in this series we’ll highlight valuable lessons that you can learn from the statistical analysis of how people choose their answers.

For this post, we’ll tackle the Sentence Correction question below. Try your hand at this question, and below we’ll reveal the user statistics and break down what we can learn from them.

The data being collected in the current geological survey are providing a strong warning for engineers as they consider the new dam project, but their greatest importance might lie in how they influence the upcoming decision by those same engineers on whether to retrofit 75 bridges in the survey zone.

(A) The data being collected in the current geological survey are providing a strong warning for engineers as they consider the new dam project, but their greatest importance

(B) The data being collected in the current geological survey provide a strong warning for engineers as they consider the new dam project, but its greatest importance

(C) The data collected in the current geological survey is providing a strong warning for engineers as they consider the new dam project, but their greatest importance

(D) The data collected in the current geological survey provides a strong warning for engineers in consideration of the new dam project, but its greatest importance

(E) The data collected in the current geological survey provide a strong warning for engineers in consideration for the new dam project, but the greatest importance

Savvy test-takers will note a couple major differences between the answer choices:

-Two answer choices use the word “being” in “being collected”, and three do not (they simply omit that)
-Two answer choices use the pronoun “its” toward the end, and two use “their” (one omits the pronoun completely)

How did people tackle these decision points? Let’s take a look at the data:

A few noteworthy stats:

-Over 75% of users avoided the word “being”, which is *usually* incorrect on the GMAT (but then again it is an actual word, so it has to be used correctly in some function of speech, right?)
-About half of users went for “its” and a little more than a quarter for “their”

And the correct answer? It uses “being” and “their”, the two most unpopular decisions. So what can you learn from this?

It appears that most users made their first decision to eliminate “being”, which has a reputation in the GMATsphere for *being* (intentional) wrong. But here’s the thing – “being” can be correctly used as a present-tense verb, a noun (as in “human being”), and other contexts. Ain’t ain’t a word, but being is. There are a handful of these pieces of GMAT wisdom (that often start with the phrase “the GMAT prefers” or “the GMAT doesn’t like”) that actually aren’t terrible advice, they’re just awful first decisions. If you’re down between two answers and the only striking difference you see is that one of them uses “being”, odds are you should eliminate that one. But as a primary decision you can do better.

For the next decision, it appears that people attempt the “data…its” vs. “data…their” distinction by trying to determine whether data is singular or plural. Which isn’t a bad strategy – but when singular/plural decisions are to be made and appear tricky (words like “data”, “deer”, “fish”, etc. can be both), the GMAT very often cleverly hides a controlling word away from the underline. And here they do that – look at “…how they influence” a few words after the underline. That “they” can only apply to “data” (“engineers” are referred to separately in that same thought). So there is a binary decision point here – data is set by that outside-the-underline pronoun to be “their”, which eliminates B and D (the most popular answer). Then with choice C mixing singular/plural (“their” but “is providing”), you’re left with a tougher decision between A and E.

Here’s where “being” is perfectly okay and consistent – if the data are “being collected” and “are providing” valuable information about an “upcoming decision”, that present-tense “being” completely works. And it’s actually more specific and clear than the wording in choice E – in E “the greatest importance” is ambiguous…what’s important? In A, we know the data have one primary significance, and we also get a clear sense of the timeline – they are currently being collected and continuing to provide value.

So A is correct, but more important is what you can learn from the stats taken from your peers:

1) Pronoun decisions are much more binary and concrete than “idiomatic” decisions like “being” and others. In this question, many users missed it because they made that “being” decision first and eliminated the right answer immediately.

2) When making singular/plural decisions that seem more difficult than they should be, look past the underlined portion to see if there’s a smoking gun elsewhere – a fixed pronoun or verb that removes all doubt.

Remember, also, that the official GMAT complies this type of data and much, much more, so the authors of GMAT questions know that test-takers have certain exploitable tendencies. You can be certain that the GMAT is paying attention to data like this; make sure that you learn from your mistakes (and those of others) to gameplan for the test.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: What Does the Median Mean?

GMAT Tip of the WeekStatistics-based GMAT questions can be tricky, particularly for those who haven’t been formally trained in stats or for those whose knowledge of statistics is more incomplete than they realize. One concept for which many students have blind spots is that of the median, so let’s take a moment to identify and explain a few of these common knowledge gaps.

For starters, everyone taking the GMAT likely knows that the median is the “middle number” in a set of data, and that to find that middle number you have to first sort the values in order. So for a set:

{2, 5, 1, 3, 4}

The median isn’t 1, the middle number as it’s displayed above, but rather 3, the middle number once the data set has been sorted in order as: {1, 2, 3, 4, 5}.

Further, everyone likely knows that if there are an even number of terms, the median is the average of the two middle terms. So in the set {2, 4, 6, 8, 10, 12}, the median is the average of 6 and 8, which is 7.

But here are a few things that people who flip through that section of their prep book and think “median, yeah that’s easy” often tend to overlook and miss:

1) The median doesn’t have to be BETWEEN two other numbers

Take the set {7, 10, 12, x, 17, 19, 22}, in which x is defined as the median. You might look at that and think “oh, x has to be between 12 and 17”. But that’s not necessarily true. If x were 12, the set would list as: {7, 10, 12, (x =) 12, 17, 19, 22} and 12 would still be the 4th out of 7 numbers. x could match either 12 or 17.

This can be extremely important on Data Sufficiency questions. If the question were “Is x > 12?” and you were told that x is the median of that set, you’d be very much tempted to say that it has to be greater than 12. But remember – the median of a 7 term set doesn’t have to be between the 3rd and 5th terms; it could match one of those.

2) The median also means “an equal number of terms above and below”

This definition works with “the middle number” but it adds another level of conceptual understanding that can help you on challenging problems. Consider the problem:

Sets A, B, and C are combined together to create set J. What is the median of set J?

1. The medians of sets A, B, and C are all 25
2. Sets A, B, and C each have the same number of terms

You might very well be tempted to think that you need statement 2, but as it turns out statement 1 is sufficient alone based on that extra definition above. If sets A, B, and C each equally divide their terms above and below 25, then 25 will remain the median of the new combined set. You can see it with numbers:

Set A: {21, 23, 25, 27, 29} — two terms below 25, two terms above 25, one term is exactly 25
Set B: {24, 26} — one term below 25, one term above 25

Just seeing this, you should note that the new set will now have three terms below 25, three terms above 25, and the middle term is 25. Or if all the sets had an even number of values:

Set B: {24, 26}
Set C: {10, 20, 30, 40}

Note that when you combine them, the “innermost” pair of numbers that will form the middle two both come from Set B, keeping the median at 25. Any way you do this, the average will stay at 25.

So remember – in addition to “the middle term”, median also means “an equal number of values above and below”.

3) In an evenly spaced set, the median equals the mean

When a set is evenly spaced (such as “consecutive even numbers” or “consecutive multiples of 7”, the median and the mean will be the same. So in a set like:

{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}

if you want to find the average, you don’t actually have to add up all 15 values and divide by 15, you can instead just find the 8th value and that will be the average. The average will be 16.

Where this can be extremely helpful is when you’re asked to determine the sum of a set of evenly spaced values, such as in the question:

What is the sum of all the even numbers between 0 and 100, inclusive?

You can here use the average calculation that Average = Sum of values / Number of values, solving for the sum. You know that the average will be the middle number, 50, so then you just have to find the number of values (which is 51, calculated as the range (100) divided by 2 (since you only want every other number), plus one for “inclusive”). The answer is then 51*50, or 2550.

Knowing that you can use the median to your advantage this way can save you valuable time.

In summary, don’t let your knowledge of Median stop at just “the middle number”. It’s more than that, and savvy test takers can raise their score well above the GMAT’s median value by taking advantage of a more thorough understanding.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Trial, Error, and Success

GMAT Tip of the WeekOne of the most fascinating parts of being a GMAT instructor is getting to watch successful adults relive the math they did as kids. In many cases, an instructor can actually see that concept or point in time when the student stopped trying to really understand the math and just started relying on that combination of memorization and partial credit to get their Bs in math and search for a career path that would include no more of it. How many students decided at some point in junior high or high school that they just weren’t a “math person”?

While that’s sad on so many levels, it’s a particular challenge for many GMAT students in that somewhere down the line the binary nature of math – there’s always exactly one right answer, as opposed to an essay that you can write and back up your opinion of “To Kill A Mockingbird” in English – taught them that there wasn’t much value in trial and error. You either had the right answer or you didn’t, but for many math was never a discussion or a process. And so directly related to the GMAT the lesson that many students never embraced is this:

On the GMAT quant section, it’s okay to try and fail. And actually it’s more than okay – it’s absolutely necessary on some questions.

GMAT math is often not about “how DO I do this problem?” but much more about “how MIGHT I do this problem?”. There’s no one blueprint for most questions, but rather you need to be able to try out a concept and see if your reasoning holds up. Consider an example:

If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

(A) 51
(B) 54
(C) 72
(D) 162
(E) 50! + 2

Now, this is a unique problem structure – were you to see this problem on the test, you wouldn’t likely have seen a problem written all that closely to it before, so you probably don’t have a direct method to be able to solve it. For most of us, the thought process will have to include some trial and error. You may just have to have a conversation with yourself, thinking of numbers and trying to determine whether or not they’ll work:

-How about 51…I know that all the numbers 1 through 50 are factors of 50!. But wait – 51 is 3*17, and so both of those are factors of 50! so 51 doesn’t wok.
-How about 52 – well, no, that’s even and can quickly be broken down into 2*26, both factors of 50!.
-53 is prime and it’s bigger than all the individual components of 1*2*3*4*…49*50, so it would work. But wait – the question specifically says that it can’t be prime.
-If you keep going with other numbers like 54 (27*2) and 55 (5*11), if they’re not prime they’ll have smaller factors that fit within 50!, and if they are prime, well, the definition of the problem says they don’t work. So how do I lean on that smallest prime number of 53?
-Oh, I can make it “not prime” by multiplying it by the smallest possible number, 2, and then I have 106. It’s not a factor of 50! and that’s as small as you can get. So factor it out: 1, 106, 2, 53, and the sum is 162, answer choice D.

Now the takeaway from this – very few people will have a system to pick up that 106 is that number in question, but by thinking through several “wrong” numbers and finding out why they don’t work, you can incrementally develop a better understanding of the framework and lead yourself to the right number. Math is a conversation in many cases. So if a problem looks complicated and you don’t have a formula or system ready to go, start trying things and holding them up to logic until you realize that you’ve stumbled on the method. GMAT math requires a lot of trial and error. Often you need to fail in order to succeed on that very same question.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Avoid (Carlos) Danger on the GMAT

“A rose by any other name would smell as sweet.” – Juliet / William Shakespeare

Carlos Danger is Anthony Weiner. And a creep by any other name would be just as creepy. This week the New York mayoral candidate, notorious for tweeting his last name all across the internet, put his campaign into his fake last name by doing the same thing under an alias. And in doing so, he taught many of you who aspire to live under his intended jurisdiction – as students at NYU-Stern or Columbia, or as bankers or marketers or hip-hop moguls after graduation – a valuable lesson about the GMAT:

Problems that look dangerous are often just the same old suspects in disguise.

Your job on the GMAT is often to see through the illusion of danger, to see the familiar amidst the unfamiliar, to know that the more unique a problem looks the more valuable it is to find something tried-and-true about it. Consider an example:

Let the superfactorial of a number n be denoted S[n] and represent the product of the first n factorial numbers. For example, S[4] = (4!)(3!)(2!)(1!) = (24)(6)(2)(1) = 288. Which of the following is equivalent to 11S[10} divided by S[11]?

(A) 1/10!
(B) 10/11
(C) 1
(D) S[10]
(E) S[11]

As with most function/sequence/awkward-notation problems, this problem is much more Anthony Weiner than Carlos Danger – it’s a fairly standard problem (it’s a factors/fractions problem in disguise) made up to look like something it’s not. Your clues? In large part it’s the answer choices, of which particularly A through C should give you insight – your job is to take a really complex fraction and reduce it to something simpler. And that typically comes from stacking the fraction and cancelling repetitive terms that multiply on both the top and bottom. So take a look:

Numerator: 11 * 10! * 9! * 8! * 7! * 6! * 5! * 4! * 3! * 2! * 1
Denominator: 11! * 10! * 9! * 8!… (you should see by now – all these factorials 10 and below will cancel)

So if you’re ready to cancel repetitive terms on top and bottom, this thing quickly simplifies to 11/11!. And so now what you really have is:

Numerator: 11
Denominator: 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 (or 11 * 10!)

So the 11s cancel, and you’re left with 1/10!, answer choice A.

The bigger takeaway? Even though this problem looked like a lot of exotic danger with the “superfactorial” definition, it was really a more common concept being tested. This question was all about reducing fractions, a pretty accessible skill just made to look a lot trickier by putting fancy names like “superfactorial” on top of it. Like the New York press, you’re smarter than that – you know that there’s usually a familiar suspect behind all that smoke, mirrors, and Carlos Danger. Keep that in mind, and your GMAT score report will be an image you’re proud to Twitpic to the world.

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Stop Counting Rights and Wrongs in Your Practice Tests!

A common question we get from students who have just completed our free GMAT practice goes something like this: “I just got a score of X, but I see that I got Y questions right and Z questions wrong… How can my score be so low/high?” Embedded in this question is a bit of a lack of understanding of how a computer-adaptive test (CAT) works. Let’s dig in…

How A Computer-Adaptive Test Works
CATs such as the GMAT are built on algorithms that use something called Item Response Theory, or IRT. The IRT system has two main functions — item administration (determining which questions to give you) and ability estimation (calculating your score). And each system informs the other. Once the ability estimate feels confident that you’re above average, for example, it delivers questions that are most likely to help it determine “just how far above average?” — which means that you’ll miss several questions even if you’re in the 90th percentile, because it’s trying to determine whether you’re above that level and the only way to know is to continue testing your upper limit.

Now, that is a simplified explanation, and it strips out a good amount of IRT nuance and basically says this: Once the system has narrowed in on your ability you should theoretically get half the remaining questions wrong; if your true ability level puts you at the 60th percentile among all GMAT test takers, you should get all the 70th-percentile questions wrong and all the 50th-percentile questions right, and the system will keep bouncing you between those levels. That’s a pretty simplistic description of how it works (you will sometimes get really easy questions wrong and super hard ones right, after all), but it’s close enough for a good understanding of the scoring system.

Getting Questions Wrong Means the System Is Working
So what does all of that bouncing around mean? Once the test has a close read on your true ability level, AND assuming that the test has in its arsenal enough questions to keep challenging you at that level, you should then start to miss a lot of questions. After all, if you’re still getting a lot of questions right, then the system must not have you pegged at the right ability level. Or — and you will see this with a lot of practice tests available on the market — it knows your ability level, but it doesn’t have enough questions at that ability level to keep challenging you.

And get this: According to IRT theory, it doesn’t take too long to get there — within just six or seven questions the system usually has a pretty good feel for your ability level. So, if you take the Quant section of a GMAT practice test and the system figures you out after about seven questions, then you should spend the next 30 questions bouncing around your ability level. Of course your answer sequence from that point forward won’t perfectly be “right, wrong, right, wrong…” but you will probably start to get a good percentage of questions wrong. Or, you’ll spend an unreasonable amount of time on questions trying to get them right, and then you’ll pay the price at the end of the test when you run out of time, in which case you will have a bunch of “wrong” responses recorded at the end of the test section.

This Is Where the Math Gets Fancy
What’s really happening with the ability estimation is that it’s calculating the probability of someone with your responses having each score. And here’s where conventional wisdom in online GMAT forums tends to miss the nuance of IRT: We see “You get a question right it gives you a harder question / You get it wrong it gives you an easier one,” but that’s still too simplistic. What the system is really doing after each response is using all of your responses to date to estimate the probability of your having each score, and not all questions carry equal weight.

Again, the IRT system heavily relies on probability — some questions are much more potent at determining whether you’re above or below a certain threshold and others are a little less telling. The system takes these weights into account, particularly as your score moves. These weights also have to account for content delivery. The system might want to ask you a “more potent” (meaning it will give the system a lot of information about you based on how you respond) Sentence Correction question, but need to deliver you another Reading Comprehension passage, and so those RC questions might not carry the same weight as the questions before it. All of this is constantly happening in the background as you move through the GMAT.

So, the next time you hear someone recounting the number or percentage of questions they got right in their last practice test, just smile and nod. They probably don’t know much about CATs or Item Response Theory. We’ll let you decide whether to let them in on it or not!

Plan on taking the GMAT soon? Try our own new, 100% computer-adaptive GMAT practice test and see how you do. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

GMAT Tip of the Week: Three Essential Steps To Learning From Mistakes

“You can learn a lot more from a few seconds of pain than from a few hours of glory.”

We all want to breeze through our GMAT homework getting every question right in under two minutes, but absolutely no one does that. And if you’re in a GMAT class, do you really want to get every answer right the first time? Sure, that might mean that “you’re great”, but in reality what it probably means is that the class is going through problems that are too easy. The beauty of mistakes – and the reason that Veritas Prep classes emphasize “Learning by Doing” with challenge-level problems throughout – is that they’re the best learning opportunities out there. Every time you make a mistake, you’re adding another lesson to the pile and finding a new hole to plug. Every mistake you make in practice is a chance to make sure you learn to avoid that mistake for when it really matters.

But mistakes should sting – your goal is perfection even while your reality is flawed. So the lesson here isn’t “everyone makes mistakes” but instead “everyone makes mistakes, but those who learn from them are the ones who become great”. And the more pertinent GMAT lesson is that there are three essential steps you should take every time you miss a GMAT question:

1) Understand why your wrong answer was wrong.

2) Understand why the right answer was right.

3) Understand why your wrong answer was tempting.

And note – if you happened to guess correctly after narrowing it down to two answer choices, you should still go through these steps.

Let’s take a look at a Data Sufficiency problem from the Veritas Prep Question Bank as an example of using this strategy:

What is the area of right triangle XYZ?

(1) Side YZ is 9 inches long.

(2) Side XZ is 15 inches long.

Here’s the thought process that about 50% of all test-takers use to answer this question:

“I memorized that a common side ratio for right triangles is 3-4-5, and since 9 is (3)(3) and 15 is (3)(5), the middle side should then be 3(4) so 12. And that lets me find the area since 9 and 12 are the sides next to the right angle, so it’s (1/2)(9)(12). C is the answer!”

And those students – take a look at the graphic here to see the official stats – are wrong:

So let’s run though the steps to make sure we learn from the problem:

1) Why was our wrong answer wrong?

The question never specified that 15 was the hypotenuse, the longest side of the triangle. And if it isn’t – if 9 and 15 are the short sides, sides a and b in the Pythagorean Theorem – then the long side can be found using (9)^2 + (15)^2 = c^2, and the area is instead (1/2)(9)(15). And more specifically, our wrong answer was wrong because we assumed something that wasn’t explicit in the problem.

2) Why was the right answer right?

The right answer is E, and it’s right because it takes into account multiple variations of triangle XYZ. XYZ has three sides: 9, 15, and one other side, XY. And since XY is a variable, you have to consider three places it could land with regard to 9 and 15: it could be the smallest of the three, the middle side, or the longest. Now, because it’s a right triangle you have a quick test with the Pythagorean Theorem, and since a and b perform the same function in that formula you can test for “shortest” and “middle” side at the same time (and realize that if it’s (XY)^2 + 9^2 = 15^2, XY has to be 12, so it can’t be the shortest). But XY *can* be either the middle or the long side, allowing for two different triangles with two different areas. By playing *all* the possibilities by “Playing Devil’s Advocate” (could this triangle look any different from the original way I drew it up?), you can avoid the trap.

3) Why was our wrong answer tempting?

This is the most important of the three questions and the one people do the least. If you wrote this one off as “I need to study geometry more”, you missed the point entirely. Our wrong answer was tempting precisely because it rewarded our understanding of geometry – it let us use the 3-4-5 rule; it satisfied our intellect and released some dopamine by letting us think “nailed it: 3-4-5!”. Our answer was tempting because you do have to know a thing or two about triangles to see that 3-4-5 (POTENTIAL) relationship.

In terms of the Veritas Prep “Think Like the Testmaker” approach, consider how the author of the question created the trap answer. He recognized that you’re likely in a hurry to use the information you memorized; he set up a question that would seem to reward you for using it; and he banked on the fact that once your mind had been satisfied that you “got it” you’d immediately call off the search for other answers. C is tempting because it shows you a reward for having studied – it sells you one possibility and in doing so encourages you to stop thinking of other possibilities. What you can learn from that is “if an answer seems too obvious or tempting in the first 45 seconds, I should play devil’s advocate for another 20-30 seconds to make sure I’m not getting trapped – are there any other possibilities other than a 3-4-5 triangle here?”.

As you should see, finding out why the trap answer was tempting is a crucial part to learning from your mistakes. On a standardized test like the GMAT, the mistakes are fairly standardized too – as you can see from the graph, there’s one trap answer that gets half the test-takers. This is true of most GMAT questions – 2-3 choices are there just to let you “feel smart” when you eliminate them and go for the trap. When you make mistakes, learn from them. You can learn a lot more from a few seconds of pain than from a few hours of glory – embrace your mistakes in practice and you won’t make nearly as many on test day.

Plan on taking the GMAT soon? See how you stack up with our completely new, 100% computer-adaptive GMAT practice test. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: The MVP Comparison for Sentence Correction

Ah, summertime. Perhaps you’re spending this first-weekend-of-July at the Jersey Shore, or perhaps you have plans to watch baseball. Either way, there’s a good chance you’ll run into an MVP comparison, and if you do you’re helping your GMAT verbal score more than you’ll ever know. Because the key to Sentence Correction success is the MVP comparison.

MVP, as everyone knows, stands for Most Valuable Player *or* for Mike, Vinny, and Pauly of Jersey Shore fame. But when you’re approaching GMAT Sentence Correction, it stands for:

Modifiers
Verbs
Pronouns

And you should throw Comparisons in there, too, whether you’re comparing Mike’s situation to Vinny’s or Mike Trout to Miguel Cabrera in an MVP debate. Why? Because those four categories – Modifiers, Verbs, Pronouns, and Comparisons – are the most commonly-occurring Decision Points in GMAT Sentence Correction AND they’re the easiest to notice. Which means that they’re your competitive advantages on the GMAT.

In a phrase, before you do anything else on a GMAT Sentence Correction problem, look for an MVP Comparison. Consider an example (courtesy of the Official Guide for GMAT Review):

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

It’s easy to get sidetracked by the phrases “things antique” vs. “things that are antiques” vs. “antique things”. But remember MVP – if you can find modifiers, verbs, pronouns, or comparisons attack those first! And here you have two verb decisions: the singular/plural of “has grown” vs. “have grown” and the singular/plural/tense decision in the last words of the answer choices related to “bring”. Since the subject of all these verbs is “market” and the event is ongoing, the verbs have to be “has grown” and “is bringing”, making B the correct choice. And more importantly, if you lock on to the verb decision early, you can avoid the danger of getting thrown off by the inversion of “things antique”, a common “false decision point” that leads people astray.

This is just one example, but you’ll find as you study that a few things stand out about the MVP Comparison:

1) Most SC problems include at least one of these four decisions
2) These decisions are easy to spot: if some answer choices say “it” and others say “they”, you have a clear pronoun decision; if some say “have been” and others “has been”, you have a clear verb decision. And if a sentence leads with a description – a modifier – or makes a comparison your task is clear. MVP Comparison is efficient.
3) You can make these categories your core competencies – you can get really good at them. Many folks dislike Sentence Correction because they hate studying “grammar”, when in actuality the scope of GMAT grammar is relatively narrow. If you become incredibly good – an MVP, perhaps – at these categorizes then you have pretty much all of SC beaten, and you’ll find that the game of spotting the errors you know is much more enjoyable and productive than the game of trying to figure out obscure decisions.

So as you study Sentence Correction this summer, think of the MVP Comparison as your most valuable process.

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!

GMAT Tip of the Week: Marshmallows are the Key to a High GMAT Score

GMAT Tip of the WeekIn the late 1960’s and early 1970’s, Stanford professor Walter Mischel conducted one of the most famous social experiments of all time.   Known as the “Marshmallow Test,” the experiment worked like this:

A child was brought into a room and a marshmallow was placed in front of that child.   The experimenter told the child that he would return in 15 minutes, and if the child did not eat the marshmallow before his return, then that child would be given two marshmallows.

Of the 600 children (mostly 5 year olds) involved in the experiment, only about 1/3rd waited the 15 minutes to get the two treats.   A full 2/3rd of the children ate the marshmallow before the experimenter returned.    All of this was videotaped and as you might imagine the videos are hysterical:  some children pop the marshmallow in as soon as the experimenter leaves; many handle the marshmallow, take little bites, and then finally give in completely before the 15 minutes are up; some stoically wait the 15 minutes and happily take their two marshmallows when the experimenter returns.

This experiment on delayed gratification became famous mainly because of the surprising data collected by the experimenters after following these 600 children over the course of their lives.   The 200 children who were able to delay their gratification and get two marshmallows had vastly better life outcomes:  higher SAT scores, higher educational attainment, lower body mass index, and superiority in many other life measures.

Interesting for sure, but how does this relate to the GMAT? In watching thousands of GMAT students over the years, I have noticed that those who are too eager for gratification – those who are too quick to attack and answer problems without first deliberately considering them – have very poor GMAT outcomes.   However, those who delay their gratification – those who patiently consider the problem and all answer choices first – have very good GMAT outcomes.     The writers of GMAT questions are well aware of the “Marshmallow Effect”:  they know that students will impatiently attack questions or go immediately to statements in Data Sufficiency before they really understand what the question is asking and before they have considered the best approach.

Consider this difficult data sufficiency question:

The infinite sequence a1, a2,…,an,… is such that a1 = x, a2 = y, a3 = z, a4 = 3, and an = an-4 for  n > 4.  What is the sum of the first 98 terms of the sequence?

(1)       x = 5
(2)       y + z = 2

(A)  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(B)  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(C)  Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked;
(E)  Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

If you patiently analyze the question stem and leverage all that information first, then you will realize that the answer is (E).   If you don’t do that and rush to the statements, then you will almost surely pick (C) – the sucker choice on this problem.   A sequence such as an = an-4 means that the sequence repeats every four terms.   For instance if a1 = 2, a2 = 4, a3 = 1, and a4 = -2 then the sequence would go like this:   2,4,1,-2,2,4,1,-2,2,4,1,-2……    Every four terms would sum to a total of 5 and you could use that knowledge to quickly get the sum of the first 98 terms.   In the first 98 terms there are 24 complete sets of 4 terms (4 x 24 = 96) and then you would have to add the first and second term to get to 98 terms.   The sum would then be 24 x 5 (the sum of every four terms) + 2 (first term) + 4(second term) and the sum would be 126.   In this question, they want the sum of the first 98 terms but variables are used instead of the sample numbers given in the previous explanation.   Still you should behave the same and simplify this question.   Using the same logic as above, this question is really asking for the value of 24 sets of the four terms + first term + second term or

24(x + y + z +4) + x + y.   Here is your new question after careful analysis of the question stem:

What is 24(x + y + z +4) + x + y?

(1)       x = 5
(2)       y + z = 2

Now it doesn’t seem so hard.   Each statement alone is clearly insufficient to get a value, and the choice between (C) and (E) is much easier if you have patiently simplified the question stem.   Since you never get a value of y from the two statements the answer must be (E).   The value of that expression with both statements is 24(5 + 2 + 3) + 5 + y so the value is cannot be determined.   It is hard to realize this if you don’t use most of your time on this question assessing and simplifying the question stem itself.

The bottom line:  don’t eat the marshmallow right away.    Fully digest the problem and THEN consider the best approach.   In critical reasoning, fully understand the argument and try to anticipate gaps and flaws before you pollute your mind with incorrect answer choices.   In data sufficiency, don’t go to statements before you have fully leveraged everything given to you in the question stem.   Remember that answer choices in multiple-choice format and statements in Data Sufficiency usually provide hints, but they are not always your friends.  On the GMAT there is a great reward for those who delay their gratification – you will be more likely to get the problem correct.  And – like in the Marshmallow test – this will probably lead to greater life successes, whether it’s admittance to Harvard Business School or that top job at Goldman Sachs.

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!

Chris Kane is a longtime Veritas Prep instructor and recipient of the worldwide Instructor of the Year Award. Having taught thousands of students in New York City and the tri-state area, he contributes frequently to the Veritas Prep lesson materials and is the primary instructor for the popular Immersion Course in Manhattan, where he will begin another such course next month.

GMAT Tip of the Week: Data Sufficiency the Smart(phone) Way

GMAT Tip of the WeekLet’s say you were in the market for some new technology, and let’s say your friend introduced you to a guy who sold used, refurbished gadgets at a huge discount. And let’s say he gave you this choice – you could buy:

A) An iPhone 5 for $50

or

B) A digital camera for $40

or

C) Both an iPhone 5 and a digital camera for $75

Now, you have a few tech goals in mind. You want to be able to send text messages, update Twitter, use Google maps on the go, and upload pictures to Facebook and Instagram. Which deal do you take?

You take the iPhone only deal for $50, right? Why don’t you take the camera too? That’s right – because option A already contains a digital camera! You don’t need to pay for another one. And because you know that the first option already gives you everything you need, you don’t pay for both products together. Agreed?

Well, that’s the game on many Data Sufficiency questions. Often times in a Data Sufficiency question one of the statements will already (but subtly) include the information from the other one. Which means, like in the case above, before you pick option C (both together) you’d better make sure you can’t do it with option A or option B alone. Here’s what we mean in a couple examples:

EXAMPLE 1:

Is 0 < x < 1 ? (1) x^2 < x (2) x > 0

In this case, many people pick option C, both together. But wait – you don’t want to buy a digital camera (the fact that x is positive) if your iPhone already has one. So let’s spend a little time playing with the features of that iPhone, or statement 1. Would a negative number even be possible given statement 1, or do we know already that x is positive? Try it: if x were to be -2, x^2 is 4…in that case x is not greater than x^2, so -2 wouldn’t work. And if x were -1/2, then x^2 is POSITIVE 1/4. Again, x is less than (not greater than) x^2. So neither a negative integer nor a negative fraction will work. Statement 1 already tells us that x is positive, so we don’t need to “buy” statement 2. It pays to take the time to – to continue the analogy – play with the features of the iPhone (statement 1) to see whether it already gives us the camera features we might want in statement 2.

Now let’s see a more advanced example.

EXAMPLE 2:

Julie is selling lemonades in two sizes, small and large. Small lemonades cost $0.52 and large lemonades cost $0.58. How many small lemonades did Julie sell?

(1) Julie sold a total of 9 lemonades.

(2) Julie’s total revenue from the sale of lemonades was $4.92

Now, by the time you take your GMAT you should be able to come up with formulas for these statements pretty quickly:

(1) S + L = 9

(2) .52S + .58L = 4.92

And you should really quickly recognize that with two variables and two equations, you’ll be able to solve for S with both statements together. But that’s a little too easy for a test like the GMAT – especially when there’s a hidden piece of information that you can add to those two statements. Julie can’t sell 2.75 small lemonades – the values of S and L must be integers. So that should give you pause – if you take both statements together you’re leaving important information on the table. So at this point it pays to see whether the iPhone (statement 2) already has a digital camera (statement 1) embedded in it. Remember – the GMAT is a business test…it will reward you for being efficient with resources and for maximizing your ROI. It’s foolish in business to pay $75 for two products when one would accomplish the task for $50; similarly, it’s foolish to blindly pick C in 30 seconds when there’s a decent chance that the answer could be B. And how can you tell? If it were, indeed, an iPhone, you could spend some time playing with it to see if it would do exactly what the camera would. And that’s the goal here.

You know that if you have the statement “S + L = 9” you can pair that with statement 2 to solve for S. So try to see whether statement 2 includes that information by “borrowing” it. Could S + L be anything but 9? See if it can be 10:

If she sells 10 (the hypothetical) but still only makes $4.92 (what we know from statement 2) she’d have to sell cheaper lemonades to keep the revenue down, so let’s try all 10 at the cheapest price. That’s 10(.52) = 5.20, which is already too much. There’s no way she can sell 10 or more!!!

If she sells 8 (another hypothetical) but still brings home $4.92 (what we know from statement 2) she’d have to sell more expensive lemonades to make up for the fact that she’s selling fewer items. So let’s try 8 of the most expensive. That’s 8(.58) = 4.64, which isn’t enough. She can’t sell 8 or less, so we’ve just used statement 2 to prove that it already tells us the information from statement 1. Statement 2 is sufficient alone.

Now, this step is a little tricky for many, but look at what we just did – we had a hunch that we didn’t need to “buy” both statements because one might already have all the features of the other, like the iPhone with the built-in camera. So with those features in mind (S + L = 9) we set out to prove that the second statement included them, by “borrowing” them from statement 1. On tricky Data Sufficiency problems in which a trap answer like C in this case seems far too easy, this is an effective strategy to make sure you only pay for what you need. So keep this iPhone analogy in mind to maximize your statement efficiency on the GMAT; after all, at least for now, the GMAT won’t let you ask Siri.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: The Remainder Remix

GMAT Tip of the WeekR. Kelly. Jermaine Dupri. Mariah Carey. The Graduate Management Admissions Council (GMAC). What do they all have in common?

It’s the remix.

All four artists above are masters of the remix, taking the same song and making it different and, in most cases, better by simply changing a few things around. To the casual observer the end result may be entirely different (hey R. Kelly – is there even a non-remixed version of “Ignition”? It almost doesn’t matter with the remix being that good…), but to those who seek to understand the art of either music or the GMAT, it’s extremely helpful to recognize the way that these artists ply their trade. To get a feel for it, let’s look at two almost-identical-but-beautifully-remixed problems from the Official Guide for GMAT Review:

1. If a and b are positive integers such that a/b = 97.16, which of the following cannot be the remainder when a is divided by b?

(A) 4
(B) 12
(C) 22
(D) 28
(E) 96

In this question, it’s extremely helpful to understand the concept of a remainder and how it relates to the overall process of division. This problem is one that we term at Veritas Prep “Reverse Engineering” – you know how to do division from start to finish, but you likely haven’t thought much about how the individual steps relate to each other conceptually. You just know how to run through the process. To master these concepts in a GMAT fashion, it’s helpful to do small problems to remind yourself of the process. So let’s take 11 divided by 4, a problem you should be able to do without much thought. The answers are:

2 remainder 3
2 and 3/4
2.75

And how does the remainder factor into the problem? This is the reverse-engineering step – the question is asking you which cannot be the remainder, which means you need to reverse-engineer the idea of a remainder and how it relates to the rest of the calculation. And here’s how – to get to the 2.75 decimal version of the answer, you take the remainder (3) and divide it back by the denominator (4). So you can reteach yourself the concept – Remainder / Denominator = Decimal Points, and it does so by way of taking that fraction (3/4) and turning it into a decimal (.75).

In the actual problem, you’re given the decimal (.16) and asked which answers could be the remainder. And since you know from that smaller problem (11 divided by 3) that the conversion of fraction to decimal is what relates the remainder to the decimals, when you’re given the decimals you should look to convert it to a fraction to relate back to the remainder. 0.16 = 16/100, which you can reduce (since that’s what you typically have to do when you’re dealing with fractions) to 4/25.

Now how does this relate to the problem? We know that the Remainder / Denominator must be able to reduce to 4/25, which means that the remainder has to be a multiple of 4 and the denominator (b) has to be a multiple of 25. So when you look at the answer choices, one should stick out – 22 is not a multiple of 4, so it cannot be the remainder, making the correct answer C. (And for more breakdown on this problem, you can check out this article)

But back to the “Remix” theme of this post – in order to achieve high quant scores on the GMAT you CANNOT simply memorize that one problem setup as a step-by-step structure (1) express decimal as fraction; 2) reduce fraction; 3) remainder must be multiple of numerator of new fraction). Because in order to test conceptual thinking and problem solving ability, the GMAT will find multiple ways to remix that problem. When Mariah or R. need a new hit single, they can always get Jay-Z or T-Pain to appear on the remixed version of the original and then cash their checks. When the GMAT needs to truly test your reasoning ability, it does just about the same – it remixes the problem you’ve seen so that the concepts are the same but you need to figure out a new process. Take a look at another problem, also from the Official Guide for GMAT Review…we present the remix:

2. When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Here the concept is the same but the steps are not. They give you the remainder and ask you about the denominator, and for those who simply memorized the format of the previous problem this one can look entirely different. Remember – the remainder divided by the denominator gives you the decimal points, so:

9/y = 0.12

In this case, you actually now have a linear equation to solve for, so reducing the left-hand fraction won’t do you any good (you don’t know y, so you can’t reduce any factors), and you’ll have to just solve:

9 = 0.12y
900 = 12y
300 = 4y
75 = y, so the answer is B (and you can find a more detailed version of *this* problem in this article)

The lesson in all this? One, you should get comfortable with remainders because the GMAT does test them (as the linked articles attest), but even more so it’s that the GMAT loves the remix, so you can’t get too familiar with just the problems you’ve seen. It’s not enough to memorize problem structures and hope to follow the same couple of steps over and over – it’s a matter of making sure you understand these three things:

  1. The concepts being tested (how do remainders relate to the rest of the division problem?)
  2. The process for reverse-engineering these concepts (if you need to remind yourself how a calculation process works, do a small-number problem like we did with 11/4)
  3. That no two problems are identical, but even when a problem looks like something you’ve never seen before, chances are it’s the remix of a problem you have seen. Arguably your foremost strategic goal on the GMAT is to take what looks new and unique and find what’s familiar about it so that you can leverage what you do recognize to make the unknown clearer.

So as you study, remember that your job is bigger than knowing how to do *that* problem; it’s to teach yourself the concepts that underlie it and how to make sense of those concepts even when they look abstract or unfamiliar. The key to the GMAT is conceptual knowledge and the ability to make what looks unfamiliar (the remix) look more like what is familiar. Now take that key and stick it in the (remix to) Ignition.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: Don’t Arrest Your Development

There are many memorable things happening this Memorial Day weekend, but perhaps none is as exciting as the much-anticipated return of Arrested Development, the cult classic sitcom re-premiering on Netflix on Sunday. Panned by the masses in large part because it’s humor was “too smart,” Arrested Development can provide some useful intelligence to aid in your own GMAT development. So if the GMAT has you down this beginning-of-summer weekend, there’s no need to hide in your Aztec tomb, join a blue man group for moral support, or hide your lack of GMAT confidence behind cutoff shorts. We don’t think you’re a chicken (coo-coo-ca-cha!). Arrested Development is here to teach you an important lesson – and this time it’s not J. Walter Weatherman, but instead the former President of the Bluth Company, Gob.

Gob Bluth is famous for his hatred of the word “trick,” (don’t call it that) in favor of the word “illusion.” Tricks he casts off as beneath him, whereas illusions seem more sophisticated for an elite magician. And you shouldn’t simply accept tricks, either – if you look deeper (as Tony Wonder would say, you can try to use your illusion) you’ll find that a more sophisticated, deeper understanding of tricks will help you gain acceptance from the Magicians Alliance or the business school of your choice. Here’s how:

Many a GMAT student will learn a rule from the solution to a problem and understand exactly how to apply it to *that* problem. But the GMAT – like a good magician – is a master of misdirection. You’ll seldom see that exact same problem structure again, so if all you know is how to apply that rule – that “trick” – in that one context you’ll be disappointed and frustrated when you see questions that look like nothing you’ve ever seen. But if you understand the rule and why it works – if you look deeper than the trick and see it as more than a single-use process – you’ll have fuller control of it in the future.

For example, it’s pretty common among GMAT students to memorize the “trick”: “If it’s an inclusive set you add 1”. And that’s because in a problem like:

What is the sum of all the integers between 10 and 50, inclusive?

You need to know how many terms there are. And the “inclusive” rule is that you take the difference (50 – 10 = 40) and add one to determine the number of terms. There are 41 terms, and the average of the terms is 30, so the correct answer is 41*30 = 1230.

But here’s where the trick can lead you astray. The word “inclusive” itself doesn’t always mean “add one.” There are many contexts in which a question could us the word “inclusive” and not be testing that rule/trick. Here’s why the rule works: Consider “how many integers are between 1 and 3, inclusive”. If you’re including both 1 and 3, you can just count them out: 1, 2, and 3 leads you to 3 integers. Because you’re including each of the endpoints, the range (2) will be one less than the number of integers (3). You have to add one to get from the range to the number of integers.

But here’s another “inclusive” question in which blindly adding one would lead you astray:

If m is the product of all the integers from 3 to 11, inclusive, how many different prime numbers are factors of m?

Notice – this problem is not asking you to determine how many integers are in that set!! The word “inclusive” just means that you have to include 3 and 11 in your work – 11 is a prime factor of m (whereas it wouldn’t be had the question said “exclusive”). To solve this one, you’ll want to check the primes of all the numbers that multiply to form m:

3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11

= 3 * (2*2) * 5 * (2*3) * 7 * (2*2*2) * (3*3) * (2*5) * 11

Then count up the different primes: 2, 3, 5, 7, and 11 lead you to the answer 5.

So what can you learn from this?

Simply memorizing rules as “tricks” can leave you vulnerable to GMAT misdirection. It’s not enough to simply memorize tricks – you should aim to understand them as principles so that you can determine when it’s helpful to apply them and when they may not apply. “Inclusive” doesn’t mean “add one” in all circumstances – the reason you’d add one is if you’re able to calculate the range and want to know the number of terms within it. “Inclusive” really just means “the first and last number are part of the calculation,” but since a couple of problems in the Official Guide for GMAT Review and other study resources allow you to use the “inclusive –> add one to find the number of terms” trick, many students simply memorize that trick as a knee-jerk reaction.

But like Gob Bluth protests, tricks are a little too juvenile and crude for someone with higher aspirations. Tricks can arrest your development, keeping you from being able to solve the higher-level, reasoning-based questions that higher scorers see plenty of. Don’t be satisfied simply memorizing tricks, but instead try to understand why the rules work conceptually and when they do/don’t apply. Transcend tricks and raise your score.

…and that’s why you always leave a note.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: Leveraging Answer Choices

GMAT Tip of the WeekIf GMAT tutoring sessions sometimes look like George (or Oscar) Bluth prison meetings from Arrested Development – two people across the table from each other speaking intelligently – the “no touching” recurring theme is embedded in this exchange:

Step one: Student begins to work on problem, places scratch paper directly underneath problem covering answer choices.
Step two: Instructor slaps the note paper away and yells “no touching (the answer choices)”

Why?

Particularly on Problem Solving questions, the answer choices are often the most important assets you have in solving the problem. Some problems require you to plug in answer choices (“backsolve”) in order to solve; other problems embed clues in the answer choice (if there’s a square root of 3, you should be looking for a 30-60-90 triangle somewhere; if all the denominators in the answer choices are either 3 or 5, you should be thinking about divisibility rules). A higher-than-you’d-think percentage of Problem Solving questions reward users for glancing at the answer choices before they start their work, but a higher-than-you’d-think percentage of students never look past the question mark in the problem before they diligently start calculating. Let’s see a few examples to show you how looking at answer choices can drastically increase your efficiency and accuracy:

Which of the following is equal to 124/93?

(A) 6/5
(B) 5/4
(C) 4/3
(D) 3/2
(E) 8/9

If you were to try to factor out the common term between 124 and 93, you’d have a tough time identifying it on its own. 124 = 4(31) and 93 = 3(31), but very few people will quickly see “oh, they’re both divisible by 31”. Instead, you’re much more likely to make that determination by looking at the answer choices. Choices A, B, and D are clearly wrong because the denominator – 93 – is not divisible by 5 and not even, so it cannot factor down to have a denominator of 5, 4, or 2. And choice E should be clearly wrong because in the original, 124/93, the numerator is greater than the denominator, but choice E reverses that. So C is the only plausible choice, and if you test it it gives you a clue as to what to factor out. You’d need to divide the numerator, 124, by 4 (leaving 31) and then test the denominator to make sure it’s also divisible by 31 (and it is, producing that 3).

When you need to reduce a fraction as the last step of a problem, try looking at the answer choices for clues as to which factors to break out – after all, one of the answer choices MUST BE correct, and several should be impossible to begin to factor, thereby lightening your load.

Take a look at another example:

3^8 + 3^7 – 3^6 – 3^5 =

(A) (3^5)(2^4)
(B) (3^6)(2^5)
(C) (3^5)(2^6)
(D) 6^5
(E) none of the above

If you aren’t sure how to even start the problem, look at the answer choices – none of them has addition or subtraction, and most of them involve multiplication. So what’s your next move? Make your math look like the answer choices – you have to factor away that add/subtract to form multiplication (try it and see if you can D-termine the answer).

The takeaway – answer choices are an absolutely integral part of problem solving questions, so make sure to glance at them before you begin your work, and to lean on them if you’re struggling at any point of your calculation. Answer choices are assets!

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: Critical Reasoning 911

By now you’ve seen the YouTube video, the autotunes, the reenactments… Charles Ramsey’s 911 call took the world by storm this week, hoisting him to pop culture sensation status reminiscent of our old friend Antoine Dodson.

And at the same time as he was saving three kidnap victims, Charles Ramsey may also have been saving your GMAT verbal score.

You see, Charles’s first couple sentences were, as GMAT students like to say, “out of scope”. He began the call by talking about his meal at McDonald’s:

Hey check this out, I just came from McDonalds right? And I’m on my porch eating my little food…

Now, in the grand scope of the situation – terrified women breaking out of a house, a 911 dispatcher trying to make sense of the situation and send officers to the scene – Mr. Ramsey’s Quarter Pounder and fries has nothing to do with anything. But in the next breath he tells the whole story and gives the dispatcher exactly what he needs to alert the proper authorities and rescue the women. Which is almost exactly how many Critical Reasoning answer choices are structured – where many GMAT students would eliminate a correct answer choice by thinking “McDonald’s? Why are we talking about McDonald’s? This is out of scope!” the astute test-takers and 911 dispatchers realize that “I’d better hang on the line to see if he’s going somewhere with this.”

Simply put, in Critical Reasoning and Reading Comprehension answer choices, the right answer often begins with 5-10 words that seem horribly out of scope. That’s bait – the testmaker wants you to eliminate the choice without reading further, and will reward those who are patient to see what the full answer has to say. Consider this example, from the Veritas Prep Question Bank:

Asset protection manager: This year, for the fifth consecutive fiscal year, we’ve managed to reduce the number of in-store thefts by more than 20% of the previous year’s figure, evidence that our store continues to profit from our vigilance against shoplifting.

Which of the following, if true, would most weaken the asset protection manager’s argument?

(A) Six years ago the store had the highest number of thefts of any store in the region.
(B) The store’s gross sales dropped by nearly 8% from the previous year’s figure.
(C) By utilizing motion-controlled cameras and digital imaging software, similar stores have reduced theft by more than 50% over the same time period.
(D) As the store’s clientele has become more affluent, the dollar value of items reported stolen has more than doubled over the last five years.
(E) Punishments for shoplifters in the city in which the store is located have been steadily becoming more lenient over the last five years.

The correct answer choice begins with a phrase that looks out of scope – why should it matter that the store’s clientele has become more affluent? We’re talking about shoplifting, not about the socioeconomic status of the surrounding community. But wait – that lead-in gets to the point after the comma: the affluent clientele have led the store to stock higher-priced items, meaning that while the number of thefts has gone down the dollar value of those thefts has still risen. That directly weakens the conclusion that the store is profiting from the decrease in thefts.

The correct answer is (D).

So much like the 911 dispatcher this week could have written off Mr. Ramsey’s call as “why do I care about McDonald’s… click,” the patience to let the answer choice finish even if it takes its sweet time getting there will help you make productive decisions on test day. As you learn to Think Like the Testmaker to better avoid Critical Reasoning traps and pitfalls, you may want to think like Charles Ramsey.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: It’s Hip to be Square

For GMAT instructors and number enthusiasts, yesterday was a banner day – on April 25, 4/25, both the month and the day (4 and 25) were perfect squares (2-squared and 5-squared). And with that in mind, let’s take a look at some properties of squares that can help you better solve exponent questions on the GMAT.

1) Squares mean that all prime factors are doubled

The definition of a square is that it’s the same thing times itself. Which means that you have two of everything. Take 6^2 – it’s 6 * 6, and if you broke those 6s down to their prime factors you’d have (2*3) * (2*3), meaning that you have two factors of 2 and two factors of 3. If you’re squaring an integer, that means that each of its prime factors are doubled – those factors must come in pairs.

How can this be helpful? The GMAT tends to ask questions such as: For positive integers x and y, if 75x = y^2, which of the following must be a factor of x?

And in this case, if you prime factor out the only given number, 75, you’ll see that you have: 3*5*5*x = y*y

This means that x MUST contribute a factor of 3 to the pairing, since you need to have two of each factor and right now you only have one 3. So x MUST BE divisible by 3 (but since y could be even bigger than 15, you don’t know that x is exactly 3…the setup could be 2*3*5*2*3*5 = y*y. But you do know that x must have a factor of 3).

When you’re dealing with integers squared, know that the prime factors must then come in pairs.

2) Squares have an odd number of factors.

When thinking in terms of factors of integers, you should recognize that every factor of a number x must multiply by another number to produce x. So factors come in pairs – take 42: Its factors are 1 and 42; 2 and 21; 3 and 14; and 6 and 7. Each factor has a pair with which it multiplies to 42. But squares have an interesting property in that one of their factors doesn’t have a *different* pair – it multiplies by itself to produce the square. Take 36: its factors are 1 and 36; 2 and 18; 3 and 12; 4 and 9; and 6 and…well, 6. So squares break that mold of “all factors come in pairs”, because one of the factors goes solo and multiplies by itself.

Perhaps more unique – squares of prime numbers have exactly three unique factors: Itself, one, and the square root. Take 9 – its factors are 1, 3 and 9. So if a number is designed as having exactly three factors, you know it’s the square of a prime number.

3) To get to the next square, “square it off”

This is a relatively rare property but understanding it can help you unlock many difficult number properties problems. Before you take the GMAT, you should absolutely know the squares from 1-15, and you should know that 25-squared is 625. But much past that the ROI on memorization gets pretty low. But here’s a way to think about larger squares if you do ever need to calculate them. Take 41-squared. You should quite easily know that 40*40 is 1600. How do you get from there to 41*41? Well, 41*40 is going to be 40*40 + 40 – if you already know what forty 40s looks like, forty-one 40s is just one more 40. So that takes you to 1640. And since you now have 41*40, or forty 41s, in order to get to forty-one 41s, you just add one more 41. So you go from 1640 to 1681, and that’s 41-squared.

This property – a quick way to calculate larger squares – derives directly from the term “squared”. If you think of 3*3 visually, it’s three rows of 3:

X X X
X X X
X X X

And if you want to go from 3×3 to 4×4, first you have to add a fourth row:

X X X
X X X
X X X
X X X

But now it’s a 3×4 rectangle, so you need to “square it off”. You’ve added three more already, but now you need to add a column of 4 to square it off:

X X X X
X X X X
X X X X
X X X X

So what you’ve done to get from 3×3 to 4×4 is add 3 (to get to 3×4) and then add 4 (to get to 4×4). So 3^2 (which is 9) is 7 away from 4^2 (which is 16).

Note that the GMAT likes to test exponents, factors/multiples, geometry (squares are big in the Pythagorean Theorem and in the shapes squares themselves) and unique number properties, so squares have plenty of opportunities to come into play on the exam. Better understand squares and you’ll find…it’s hip to be square.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: Tianlang Guan shows you how to Master the GMAT

GMAT Tip of the WeekThe sports news story du jour is an amazing one – 14 year old Tianlang Guan spent yesterday not doing math homework (like you presumably are) or household chores like a normal 14-year old on a Thursday.  He spent it shooting an incredibly impressive round at the Masters, arguably the world’s most prestigious golf tournament.  His score of 73 beat the defending champion by two strokes and kept him in the hunt for another day.  And it should also have taught you a lesson about the GMAT:

It’s good to be young and naive. Continue reading “GMAT Tip of the Week: Tianlang Guan shows you how to Master the GMAT”

GMAT Tip of the Week: Watch the Curveball

It’s the first week of the Major League Baseball season, a sure sign of springtime and a massive celebration in most MLB cities as fans begin the season with new hope and a spirit of outdoor community. And if you’re watching, it can provide you with valuable insight to your forthcoming GMAT appointment. Because like most elite pitchers, the GMAT has a nasty curveball.

The curveball in baseball is a pitch that looks to be heading toward one point, but that toward the last second moves dramatically to a different point, baffling the batter in one of two ways. It either looks like it’s going to be a strike, but dances away from the batter’s bat out of the strike zone as the batter swings hopelessly at thin air. Or it looks like it’s safely away from the plate for a ball, but then drops right into the strike zone leaving the batter looking. In either case, the misdirection causes the batter to make a bad decision – he either swings at a ball or doesn’t swing at a strike.

The GMAT is a master of misdirection, and particularly on the verbal section it throws a mean curveball that forces you into bad decisions – either you “swing” at a wrong answer or you “get caught looking” at a right answer.

Consider this example:

Citizen: Each year since 1970, a new record has been set for the number of murders committed in this city. This fact points to the decreasing ability of our law enforcement system to prevent violent crime.
City Official: You overlook the fact that the city’s population has risen steadily since 1970. In fact, the number of murder victims per 100 people has actually fallen slightly in the city since 1970.

Which one of the following, if true, would most strongly counter the city official’s response?

A. The incidence of fraud has greatly increased in the city since 1970.
B. The rate of murders in the city since 1970 decreased according to the age group of the victim, decreasing more for younger victims.
C. Murders and other violent crimes are more likely to be reported now than they were in 1970.
D. The number of law enforcement officials in the city has increased at a rate judged by city law enforcement experts to be sufficient to serve the city’s increased population.
E. If the health care received by assault victims last year had been of the same quality as it was in 1970, the murder rate in the city last year would have turned out to be several times what it actually was.

In this example, the City Official’s conclusion is essentially to refute the citizen’s claim that “you’re not doing an adequate job preventing violent crime”, and he bases that refutation on the fact that, actually, the murder rate has decreased. His argument is essentially:

Premise: The murder rate is down
Conclusion: We’re doing a better job preventing violent crime

So in order to weaken that conclusion, you should be looking for a choice that exploits the gap “murder is only one type of violent crime” – you want a choice that shows that another type of violent crime, or violent crime overall, is up.

And here’s where the curveball comes in:

Answer choice E gives you exactly what you’re looking for, showing that people are being violently assaulted at a high rate, they’re just not dying. The murder rate is down, but not because violent crime is down. But most examinees miss that point because they see “If the health care…” and think that this answer choice is way out of the strike zone. Health care? Why are we talking about health care? That has nothing to do with violent crime!

The answer is (E). 

And that’s the curveball. The GMAT item writers know that test takers are vulnerable to quick judgment – if an answer “looks wrong” after 3-5 words, many students will eliminate it immediately. “Caught looking” just like a batter facing a nasty curveball. How can you avoid the curveball?

  • Read more than just the first few words of CR and RC questions. Be patient, particularly if you haven’t yet seen a perfect answer choice. That perfect choice might just be hiding behind a curve.
  • If you can’t provide a commonly-tested reason (verb tense, subject-verb agreement…) for eliminating an SC answer choice based on the first few words of an answer choice, look at the last few words. Often SC questions try to curveball you with an awkward-sounding beginning of an answer choice, but the crystal-clear decision can be made on the last few words.
  • Pay attention to curveballs when you miss questions in practice. As you start to see how they’re executed you’ll develop more of a sense for them for test day.

As baseball players know, your first season in the big leagues, you struggle to hit the curveball, but as you get more experience your eye can recognize it much more quickly. The GMAT is similar – pay attention to curveballs as you practice this April and you’ll have an eagle eye as the admissions season progresses to “the Fall Classic”, round one deadlines in October.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: Ain’t Nobody Fresher Than Your Study Clique

It’s the last Friday in March, and all good things must come to an end, including Hip Hop Month in the GMAT Tip of the Week space. But if you’ve been reading along with us all month, hopefully your iPod or car stereo has become your best study partner. While you’re driving home from work and the Kanye/Good Music track “Clique” comes on, you might hear Jay Z’s verse and immediately start thinking about sequence problems:

Turn that 62* to 125, 125 to a 250
250 to a half a million, ain’t nothin’ nobody can do with me

(*clearly this is a sequence that doubles every term, so Jay’s leaving out the .5 for artistic reasons)

While you’re driving and singing along, you’re probably thinking “and the next term is a million, then two, then four, then eight”, and you may even be fixating on that line “ain’t nothing nobody can do with me” the way that GMAT item writers are. What can they do with it? They can ask a question like:

In Jay Z’s sequence, where a(1) is 62.5 and all terms a(n) are equal to a(n-1) * 2, by what percent is term a(10) greater than a(8)?

And they’d make it hard because you’d say “of course you just double a(8) to get to a(9) and then double it again to get to a(10), so it’s 4 times difference, so 400%”, when really it’s a 300% increase. (4 is 300% greater than 1 – the key is that the question is not asking “what percent OF” but rather “what percent GREATER THAN”.

…which is all just a long way of saying that as you look around they don’t do it like your GMAT study clique, a group of musicians (and friends here at Veritas Prep) to help you gear your mind toward the GMAT through song. Your study clique includes:

Notorious B.I.G., who can teach you valuable lessons about inequality problems on the GMAT.

Lil Wayne, who knows a few things about what makes the GMAT difficult, about Problem Solving strategies, and about how to score right above 700.

2Pac, who sees through the most common Data Sufficiency trap answer.

Ice Cube, who wants to make sure test day is a good day for you.

Vanilla Ice, who appreciates subtlety in Sentence Correction.

Macklemore, who shows you how to be thrifty with Data Sufficiency statements.

As you study for the GMAT, you have a big team behind you and opportunities to sharpen your mind. Ain’t nobody fresher than your GMAT study clique…until you add your colleagues from your new b-school to your Linked In clique, of course.

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

GMAT Tip of the Week: Biggie’s Juicy Secret About GMAT Inequality

As Hip Hop Month rolls on in the GMAT Tip of the Week space, we’re reminded that small nuances in the ways that GMAT questions are structured can have big consequences for test-takers. So who would be a more fitting man to teach that lesson – what’s small can have big consequences – than Biggie Smalls?

Biggie’s most timeless classic, Juicy, may tell the rags-to-riches story you’re hoping to live out once you grab that top tier MBA: “and my whole crew is lounging, celebrating every day no more public housing.” But first you need to get into b-school, and that’s where this lyric can prove helpful:

“Damn right I like the life I live, ’cause I went from negative to positive … and if you don’t know, now you know.”

What secret is Big Poppa passing along? It’s a critical message in two parts:

…went from negative to positive” is a word of caution. When you’re dealing with inequalities on the GMAT, you need to remember that when a number goes from negative to positive – when you multiply or divide by a negative number to change the sign from positive to negative or from negative to positive – you must also change the direction of the inequality:

If 10 > 5, then -10 is LESS THAN -5
If x > 10, then -x < -10

The lesson: Be careful when going from negative to positive – if you’re working with inequalities and need to multiply or divide by a negative, you MUST change the direction of the inequality.

Perhaps more useful is the next line, however:

And if you don’t know, now you know.” If you don’t know whether a variable is positive or negative, here’s what you need to know: The GMAT is baiting you into assuming that it’s positive. If you’re asked to multiply or divide by a variable in an inequality question, it’s almost always a trap, as the testmaker knows that negative numbers are our blind spots – we tend to overlook them until they’re made absolutely explicit. So as Biggie said, if you don’t know (whether a variable is positive or negative)…now you know that there’s a high likelihood that that distinction will be important. Consider this Data Sufficiency example:

Is a > 3b?

(1) a/b > 3
(2) b > 3

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
D) EACH statement ALONE is sufficient to answer the question asked
E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

The trap on this question is to select A, thinking that you can simply multiply both sides of that inequality by b:

a/b > 3 –> a > 3b

But you don’t know whether b is negative or positive. The above technique works if, say, a = 4 and b = 1 –> 4/1 is greater than 3, and 4 (a) is greater than 1 (b). So you get “yes”. But the situation also encompasses a = -4 and b = -1, as -4/-1 is 4, which is greater than 3. But in this case -4 (a) is LESS than -1 (b). So you get “no”. The trap is to get you to blindly multiply both sides by b…but as Biggie cautions: If you don’t know, now you know (to be careful). Statement 2 isn’t much value on its own, but as it guarantees that b is positive, when you take both statements together, now you know that you can multiply both sides by b. So the correct answer is C, but the takeaway is most important here:

When dealing with inequalities, if you don’t know (the + or – sign of a variable) now you know that the question probably hinges on that point. Heed Biggie’s sage advice and you’ll be on your way to one of the world’s most notorious b-schools.

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GMAT Tip of the Week: Taking Data Sufficiency to the Thrift Shop

As loyal readers of this space will know, if it’s a Friday in March that means it’s Hip Hop Month for GMAT tips, and the US government sequester will not slow us down! Although it may inspire us. As the government careens toward desperate austerity measures, frugality is in the air, both in Washington and on your radio. Which is good news – let’s pop some tags and talk about how going to the Thrift Shop, Macklemore style, can help you crush GMAT Data Sufficiency.

“Thrift Shop” may well be the first monster hip hop hit of 2013, and does so like few others have ever done – eschewing bling for savings, Thrift Shop is all about “looking for a come up”, finding a great deal that has more value than initially meets the eye. Which is absolutely crucial on Data Sufficiency – Data Sufficiency questions by their very nature are about value and efficiency, and they frequently come with massive rewards for those who find that come up.

Want proof? Try this sample question, and while you look at it pretend you only have “20 dollars in your pocket” – you don’t want to pay for more statements than you need.

Four GMAT students visited Macklemore’s thrift shop yesterday. Did any of the four purchase at least three shirts?

(1) No two students purchased the same number of shirts.

(2) Together they purchased a total of 8 shirts.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question asked;
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

How’d you do? Did you find that come up? Statistically, on this question (well, not *exactly* this question…the official question has a little less soul but the intent is exactly the same) more than 50% of examinees select C and only about 20% select A, the correct answer. Why? Most test-takers don’t see the reason to be frugal – they like having both statements together and don’t immediately see that one alone is sufficient, so they fall back on “let’s buy both statements”. And keep in mind – that’s really what you’re doing on the GMAT – you’re “buying” statements. If you don’t need both statements but you pick C, you’re wrong – you “spent” too much. This is a test for aspiring business managers – those who can control costs and maximize value will win. If you only need to buy statement 1 (A is correct) but you take both of them (you pick C), you’re wrong. When an answer like C or E comes easily, you *must* consider whether you could have approached the question more frugally.

And here you can – while there’s no single formula that you’d think to set up with statement 1, it guarantees the answer “yes”. If none of the four bought the same number of shirts, then the lowest total is 0, 1, 2, and 3 – which means that someone bought at least 3.

But most don’t see to to that immediately – they see statement 1 as “not mathematical”, then they try to set up an equation with statement 2 and realize they need a little extra information, so they pick C. Statement 1 is a classic “come up” in the Thrift Shop sense of the term – it’s sneaky valuable. And so that’s your job on many Data Sufficiency questions – like Macklemore you’re out there looking for a come up with a reminder that you have to be frugal. Much like most rappers like to make it rain and spend as much (or more) than they have, we all have a predisposition to selecting C – we love having more information, second opinions. But GMAT Data Sufficiency is written specifically so that you can’t take both pieces of information if just one alone will suffice. It pays to be frugal.

So how do you succeed on Data Sufficiency? Recognize that before you pick E or C, particularly if that answer comes to you quickly without much work, you must take a second to consider whether you’re leaving a “come up” statement on the table: Is there any value you’re not applying? The GMAT hides value in many DS statements (or in the question stems), setting up a reward for those who seek to cleverly apply it. One man’s trash – “no, this statement doesn’t say much” – is another man’s come up. Learn to see value in Data Sufficiency statements the way that Macklemore sees value in your granddad’s clothes and you’ll get to echo his famous line when you see your GMAT score report. “This is (pretty) awesome.”

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GMAT Tip of the Week: What the Academy Awards Can Teach You About Sentence Correction

It’s Oscar weekend here in Los Angeles, and that can only mean one thing:

The winner is…your GMAT verbal score.

How can this year’s Academy Awards improve your performance on GMAT Sentence Correction? Let’s look at the odds-on favorite to win Best Picture, Argo. The title alone, Argo, brings up two important points about GMAT Sentence Correction:

1) Are

The very presence of the word “are” in the answer choices should get your mind thinking about subject-verb agreement. Verbs make for great decision points – differences between verbs in the answer choices (are vs. is; are going vs. went; etc.) should lead your eye toward a major decision – is the subject singular or plural, and is there a logical timeline for the verb tenses in this question?

When you’re forced to make a distinction between “are” and “is”, you have some work to do. In order to make this type of question difficult, the GMAT will likely throw a bunch of nouns and modifying phrases in between the subject and the verb to try to get you to incorrectly identify the subject. But knowing that you have to make this decision gives you an advantage – you now know that you have to spend some time focusing on the true subject of the sentence. Consider this example:

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

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

Note the difference between A, B, and C – “are” vs. “is” – this tells you that it’s time to thin out the modifying phrases to make sure you’re using the correct subject. And if you do so, you can whittle the sentence down to:

A study finds that there are one phone.

In your own words you can make this decision pretty efficiently – you’d certainly say “there is one phone” (phone is subject, and it’s singular), so you can eliminate A and make your way toward the correct answer, C.

Most importantly, being highly attuned to differences like “are vs. is” (or “have vs. has” or “was vs. were”) can immediately direct you to a binary decision – find the subject via eliminating modifying phrases and you can determine whether you need the singular or the plural.

2) Are going

When answer choices feature multiple verb tenses, like “are going” vs. “has been going”, your job again should become clear – you need to look for signals in the sentence that determine the sequence of events. And one of the more-clever ways that the GMAT can reward shrewd examinees is to employ words like “since” or “from”. Consider this example:

The Academy of Motion Pictures has found that, since stadium-style seating became widespread in cinemas in 2002, over 80% moviegoers are going to modern theaters even when the cost is as much as twice that of the old auditorium-style theaters.

(A) are going
(B) have been going
(C) will go

First, recognize that “are going” (remember the Argo theme…) difference from the other verb tenses in the answer choices. You’re being asked to select the proper verb tense here. The key? Check out the word “since” earlier in the sentence. That word tells you that the action “going” started in the past and has yet to finish – so you must use the “have been going” tense. Signal words like “since” (which leads to the present perfect tense “have been”) or “from” (when you get two past-tense dates “from 2002 to 2006” that requires the past tense) often reside far from the underlined portion, but control the timeline of the sentence and help you to determine which tenses are allowed and which cannot be used. Your clue? The presence of multiple verb tenses in the answer choices should direct you to seek out such signals. If you glossed over the word “since” in your initial pass through the sentence, you’re not alone; but once you knew that you were being asked to determine the correct verb tense as one of the differences between answer choices, you should know to look for time signals and the word “since” should jump off the screen at you.

To summarize, we don’t know whether movies like Argo are going to sweep the Academy Awards, or whether Ben Affleck will finally win another Oscar to pair with his trophy from Good Will Hunting. But we do know this – focusing on words like “are” and phrases like “are going” is a wicked smart idea. The speeches this weekend may be verbose, but if the Oscars help you better direct your attention toward verbs in Sentence Correction answer choices, the next time you hear “the envelope please…” it may well contain that acceptance letter you’ve been hoping for.

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GMAT Tip of the Week: Brought to You by the Letter C

In a Valentine’s Day surprise yesterday, the standard Thursday Veritas Prep staff meeting was crashed by a lovable intruder. Cookie Monster – yes, the one-track-minded carnivore from Sesame Street – barreled into the meeting with a singing telegram for our Director of Admissions Consulting and Worldwide GMAT Instructor of the Year, Travis Morgan. Bearing a message of love and his standard message of “me want cookie”, he also reminded the GMAT staff of why Cookie Monster would fail miserably at the GMAT:

On the GMAT, you cannot have a one-track mind.

If you grew up watching Sesame Street you know all about Cookie Monster’s one-track mind – in his zeal to eat as many cookies as humanly possible (a pretty realistic goal for the toddlers who adore him) he’ll eat absolutely anything: chairs, tables, flowers, whatever you put in front of him. And in a way this caricature of a food-crazed lunatic looks a lot like many GMAT test-takers, who in their zeal to solve quantitative problems will calculate anything that’s put in front of them.

But just as Cookie Monster is designed to be absurd, so is the idea that you must get the right answer to every problem no matter how many calculations similarly absurd. The GMAT will punish that one-track-mindedness the same way that stomach pains will someday punish Cookie Monster’s.

GMAT problems are designed in many cases to waste your time, or rather to waste the time of those not astute enough to see that trap. Some questions are structured so that there’s an easy out for those who recognize it, like:

What is the square root of 5929?

(A) 67
(B) 72
(C) 75
(D) 77
(E) 83

Here you *could* try to square each answer choice, but that math could be pretty time consuming. This type of question is designed to reward you for recognizing that B and C cannot produce a number ending in 9 when squared, and that A is too small (70^2 would be 4900 so 67^2 will be far less than 5929) and E is too big (80^2 would be 6400, so 83^2 will be far too big), leading you to answer choice D.

Other questions may waste your time simply because you fail to see the “missing link”. This happens quite often in geometry – if you don’t see that there’s a direct relationship between supplemental angles or you fail to notice that the radii of a circle must be equal leading to an isosceles triangle in the figure, for example, you could work for several minutes to no avail. But that one-track-mindedness of “I’ll solve this problem or run out of time trying” has befallen many a would-be high-scorer. Years ago the holder of a PhD in engineering from MIT called the Veritas Prep offices in near tears, having well underperformed his expected quantitative score. The reason? He spent close to eight minutes on a problem early in the quant section and knew for certain that he had answered it correctly…but was good enough at math to realize that with an average of 2 minutes per question he had put himself in trouble by spending 4 times that amount on just one question, and he panicked from there.

Similarly, one of the chief architects of the GMAT at GMAC headquarters recounted to us recently that he – a PhD in statistics – encountered the same situation while taking the GMAT for R&D purposes last year. Seeking a perfect score to brag around the office, he encountered a geometry problem that took him several minutes to solve, and at a certain point he had to laugh that “for a living I tell people not to fall into this bottomless pit of time, yet here I am”. When he dub into the administrator account to view his test item-by-item he found this: while he did ultimately get that question right in several more minutes than he’d advise anyone to take on it, it turned out to be an unscored, experimental question that didn’t even count toward his score.

So here’s today’s GMAT lesson, brought to you by the letter C: don’t have a one-track mind on GMAT quant questions. If the calculations look to be too time-consuming or labor-intensive:

1) Try to find a more efficient way, often by considering the answer choices to see if an estimate or a number property can help you avoid the work altogether
2) Know when it’s time to make an educated guess and move on. Pacing is personal – some students can afford 3-4 minutes on one question because they’re so efficient on others, but must cannot. Take practice tests and get a feel for your own pacing and your own barometer for when it’s time to guess and move on. The GMAT is a war, and it’s easy to lose a war when your goal is to win every single battle. Nearly all of us need to retreat on a question here or there to regroup for the ones we can win. Don’t have that one-track “me want correct answer” Cookie Monster mindset – a more flexible frame of mind is your best path to be on your way to where the air is sweet, be it Cambridge, Palo Alto, or whatever campus you want to get to.

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

GMAT Tip of the Week: Don’t Fall in Love

As we’ve reached the midpoint between buzzing over Beyonce’s “Crazy In Love” intro over the weekend and Valentine’s Day next week, love is in the air. Which is a good thing in most respects, but can be a dangerous one on the GMAT. You might well say that one of the most common mistakes that test-takers make on verbal questions is “love at first sight”.

How does Cupid’s arrow attack your GMAT score?

Often on GMAT verbal problems, one of the first 2-3 answer choices starts to look pretty good to you – it repeats some words from the passage, or includes a grammatical structure that you like, and it gives you that warm, fuzzy feeling that only true love or a confidently correct answer can provide. You get twitterpated, to borrow the line from Bambi that well predates #socialmedia.

And once you’ve fallen in love with that answer, you only have eyes for it – you don’t hold it up to higher scrutiny that might reveal a flaw, and you don’t keep an open mind for future answers. Consider this sample Critical Reasoning question:

Hallmark Executive: In order to stay lean and efficient given the decreasing margins on our greeting card business, we should reduce our number of employees by 10 to 20% in each of our regional facilities. This way, each facility will be forced to work more efficiently and each remaining employee will have a greater incentive to work additional hours to keep her job. With a reduction in staffing we can not only restore our profits to what they were in previous years, we can take them higher.

Which of the following would most weaken the Hallmark executive’s strategy?

(A) Because of natural fatigue, the additional hours worked by each employee could not be as productive as their base hours.

(B) Greeting card sales tend to peak between November and February, and then remain comparatively low for the rest of the year other than a Mother’s Day spike in May.

(C) The predicted boom in e-cards has not made nearly the feared dent in sales of paper cards, at least not for Valentine’s Day and Mother’s Day.

(D) According to a report created by management consultants, even a marginal reduction in headcount would cripple most Hallmark facilities’ ability to function.

(E) Hallmark could also increase profits by making up a new romantic holiday; August seems open.

Many on this question tend to fall in love early with A. A suggests a lack of productivity and some diminishing returns of the plan, so especially when compared with B, a throwaway answer, A is easy to fall in love with. But if you fall in love too early, you’ll miss D, which hits the nail exactly on the head. D shows pretty emphatically that “you can’t reduce headcount at all without disastrous consequences”, so D quite clearly weakens the plan. And if you were to then return to A, having kept and open mind and realized that D is at worst “another right answer” (which won’t happen on the GMAT – there’s 1 right and 4 wrong), you’d then compare the two and realize that A doesn’t really weaken it. A shows that the *extra* hours won’t be as productive as the previous hours, but even getting 40 great hours and 15 lackluster hours out of an employee is better than getting just 40 great hours. So A looks good at first glance, but if you hold it up to higher levels of scrutiny it fails that test.

The key? Be more DiCaprio or Clooney than Taylor Swift – when it comes to GMAT answer choice love keep your options open and don’t fall in love too soon.

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GMAT Tip of the Week: Pairs Probability (And How You Can Use It to Win Super Bowl Bets)

GMAT Tip of the WeekIf you’re like many this weekend, you’ll do some gambling on the Super Bowl. Whether it’s a squares pool at a Super Bowl party, some prop bets in Vegas, or a mayoral contest between the chief executives of Baltimore and San Francisco (Rice-a-Roni against some DVDs of The Wire?), you’ll have opportunities to either win or lose based on probability. So here’s a tip that can help you on both football bets and the GMAT:

People are generally pretty bad at pairs probability.

Here’s an example – if you were to bet a friend on “will this year’s Super Bowl champion repeat as next year’s Super Bowl champion?”, your friend might see the *random* odds as 1/64 (since the GMAT only deals in random probability, we’ll take actual talent, coaching, contract status, draft position out of the equation!). That’s because, in order for the 49ers, say, to repeat, they’ll have to win this year’s championship (a 1/2 chance) and then next year’s championship (and they’re 1 team out of 32).

But this is wrong – your bet doesn’t ask for the probability of one *particular* team winning both Super Bowls, but rather the probability of “this year’s champion” (whichever team wins) doing it again next year. This year’s probability does not matter! Someone will win, and so you’re only concerned with that team’s (whatever it is – and there’s a 100% probability that there will be a winner) probability of repeating. Whatever that team is will have a 1/32 chance (again, just keeping it random) of repeating.

This is a concept that does get tested on the GMAT, and when it does there’s always a trap answer. Consider the question:

On three consecutive flips of a coin, what is the probability that all three produce the same result?

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

The trap answer here is 1/8 – you might look at this as a 1/2 probability on the first flip, then a 1/2 on the second, and a 1/2 on the third for a 1/8 probability, but remember – in this case the result of the first flip doesn’t have to be one or the other. Your job is just to match whatever the first result was on the next two. If the first was heads, then you need heads next (a 1/2 chance) and heads again (a 1/2 chance). And if it were tails, then you need tails (1/2) then tails (1/2). But because “any match will do” and you don’t care that it’s a specific match – the question doesn’t specify all heads or all tails, just “all of one of them” – your probability doubles because you’re not concerned about the result of the first event, you’re only concerned about matching whatever that result was.

So for probability questions that ask about pairs or matches, remember:

1) Check whether you need a *specific* pair/match or not.
2) If you don’t need a specific pair, but “any pair will do,” then the probability of the first result is 100% – something will happen.
3) If you need to guess, keep in mind that if it’s an unspecified pair/match, it’s almost certain that one of the trap answers will be a smaller number than the correct answer (in the above case, 1/8 is a trap and 1/4 is correct), so you can confidently rule out the smallest number and use number properties to try to eliminate another 1-2 answers.

Oh, and remember that your friends are probably pretty bad at pairs probability, too (nearly everyone is, especially after drinking a few of the products that will be advertised throughout the Super Bowl), so feel free to use the true pairs probabilities to your advantage on some prop bets.

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GMAT Tip of the Week: 8 Things to Know About Your 8-minute Breaks

GMAT Tip of the WeekIf you’re a regular reader of this corner of the Veritas Prep blog, you should know that we like to take Friday mornings to identify something newsworthy and relate it to the GMAT. But this week, the trivial-enough-to-blog news cycle has seemed to take a break. Manti Te’o is old news, the NFL playoffs are in their bye week before the Super Bowl… When the world takes a break, what’s a GMAT blogger to do?

Take a break. Or, rather, write about the ever-important 8-minute breaks between sections on the GMAT. Here are 8 things you should know about your 8-minute breaks:

1) Eight isn’t a lot, but Eight is Enough

In the early 2000s, GMAT breaks were 5 minutes, but in that “take a five” Hollywood style where no one was really counting. Then they became hard-cutoff 10-minute breaks, in which if you came back to your computer after 11 minutes, a minute would have already elapsed from your next section. Then, around 2010, the folks at GMAC and Pearson/VUE (the set of test centers where the GMAT is administered) proved that they’re great at business – by cutting the breaks down by 20%, from 10 to 8 minutes, they could run more people through the test center more quickly. So now your break is a hard 8 minutes, which can seem pretty short.

But if 8 minutes is good enough for an ab workout, 8 is enough…provided you use it wisely. Don’t plan to do much more than grab a quick snack, a drink of water, and restroom break, but since that’s likely all you need anyway you can get it done. But word to the wise – practice 8-minute breaks in your study sessions and practice tests so that you know what it feels like and what you can accomplish. Eight minutes is enough, but not much more than that.

2) Eight minutes includes the time it takes to check out and back in

Here’s where practicing with eight-minute breaks can be extremely helpful. At least a minute of that is already spoken-for. You need to check out and then back in with the proctor (for security reasons), so you need to be mindful that you’re not dealing with eight minutes of “free time”, but rather eight minutes to accomplish the entire break, from leaving your chair to sitting back down.

3) Your break starts immediately when you click “yes” and ends immediately after eight minutes

When you’re eligible for a break, the computer will inform you of that and ask you if you want to take it. Once you click “Yes”, your break time starts. And when 8 minutes has elapsed, the break is over and the clock will begin counting down on the next section, whether you’re ready or not. On the plus side, however, your break only begins when you’re done with the previous section (or when the clock runs out on it), so if you do have a few minutes left in a section and want to let your mind rest a moment, you can create yourself a mini-break by waiting to submit your answer to the last question. So if you’re efficient on a particular section, you can earn yourself a small break before the official 8-minute break, and many test-takers find that it’s helpful to catch your breath and let your mind rest before you dive into the slightly-rushed 8-minute respite from your computer.

4) You cannot study during your break

GMAC has cancelled the scores of students who “use study aids” during a break, so don’t plan to bring any notes or books to the test center with you. Even if a proctor sees a GMAT book or notebook in your hand as you’re shuffling items in your locker to grab a snack or stow a sweater, that can be grounds for score cancellation. You don’t have time to study, anyway, so planning to do so wouldn’t help your score. Don’t even take the risk.

5) You cannot talk to anyone during your break

Talking to anyone about the test is also grounds for score cancellation, so don’t take the risk. Smile, hold a door – be polite, but don’t ask anyone “how’s your test going?” or comment “wow, that was a rough quant section”. If the proctor has reason to believe that you’re communicating about the test, she can cancel your score, so keep your break quiet and efficient.

6) Breaks can be extremely important for your mind and body

By the end of your test, you’ll likely have been testing for about four hours (the official test administration time is 3:30, but when you incorporate breaks, tutorials, checking in for the test, filling out the demographic info, etc. it will approach 4:00). And with the combination of nerves, mental focus, intellectual challenge, etc., that time can take a toll on you. Breaks are a good chance to relax your mind and change mental gears (from math to verbal, for example); breaks are a great opportunity to take in a quick snack to provide energy and keep your blood sugar up; and breaks provide you with the opportunity to use the restroom so that you can avoid that mental anguish that comes from nature’s call. With most students needing to take just about the entire time on each section, you don’t have time to lose during the test from dealing with bodily needs, so use the break wisely. Four consecutive hours at a computer terminal solving mind puzzles isn’t entirely natural for any of us, so the breaks can be essential for taking care of your mind and body.

7) You must click “yes” to take your break

When the computer asks you if you want to take a break, make sure that you click “yes” before you leave your chair. At least one student in the recent past has reported that he walked away too early, and the default setting after that question was up for a minute was “no”, so when he returned to his seat after his 8-minute break, the clock had been ticking for 7 minutes on the next section. Make sure you click yes and get clearance from the proctor so that your break doesn’t cost you any time.

8) Breaks make for great transitions

A four hour test can seem daunting and can get exhausting, and the GMAT is structured so that mental fatigue or doubt can cost you dearly. The verbal section comes last, and so you will undoubtedly need to read a boring Reading Comprehension passage after you’ve already been at the test center for >3 hours and your mind is at its least receptive to new information. But here’s where the break can help you – if you break the GMAT up into three completely separate sections (AWA/IR; then Quant; then Verbal) and use the breaks to flush your mind from stress/doubt/frustration/concentration on the previous section and set it fresh to the next section, you can make the test much more manageable. It’s not at all uncommon for test-takers to still be thinking about a frustrating Data Sufficiency question even after ten verbal questions, but by that point that quant question is long gone and can only be detrimental to your verbal performance. Make the breaks a major dividing line between sections – use them to forget the previous section and gear up for the next section, and the GMAT becomes a much more manageable test and your mind can become significantly sharper.

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

GMAT Tip of the Week: Effectively Attacking Must Be True Questions

GMAT Tip of the WeekOne of the more-dreaded types of GMAT Problem Solving questions is the “must be true” question with three statements; these questions often look like:

If 20x = 49y, which of the following must be true?

I.      x > y
II.    x2  > y2
III.  x/7 is an integer

 

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

These problems can be daunting, mainly because:

  1. They’re multiple problems in one, as you have three relationships you have to deal with.
  2. It can be difficult to know if something is “always true” – how many possibilities do you try before you conclude that it’s always true?

But rest assured – there’s an efficient method for these types of questions that puts all the common GMAT trap answers firmly on your side by doing what human beings do best: be critical!

The opposite of “Must Be True” is “Could be False”, so instead of trying to prove that something is always true, you can use process of elimination (and your natural inclination to be critical) by trying to find one situation in which each of the statements could be false.  And the best way to do this is to go on the attack – use all the “weird” numbers that tend to trap you, as your weapons against the test.  “Weird” numbers like negatives, 0, and fractions tend to give the alternative answer, so you should keep those in mind as weapons that allow you to attack that idea that a statement must be true.

In the above question, for example, your goal should be to try to disprove each statement.  If you can find just one set of numbers x and y for which x is not greater than y but 20x = 49y, you can confidently eliminate statement I.  So try to attack, and use the GMAT’s tendencies against it.  “Equal to” is not the same thing as “greater than”, so you actually don’t have to find a case where x is less than y if you can just make them equal.   With that in mind, try using one the all time “gamechanger” numbers, 0.  If x and y each equal 0, the given statement is true (0 does equal 0), but both statements I and II are not, as x equals y and x-squared equals y-squared. So by going on the attack and using strange numbers to your advantage, you can quickly eliminate two statements at once.  And look now at the answer choices – there isn’t a choice for “none of the above”…so the answer simply must be C.

More important than this example is the set of takeaways, so for Must Be True questions, remember:

  1. Go on the attack and try to find a situation for each statement in which it is not true. It’s almost always easier to find one example of a “false” than it is to systematically prove that it’s always true.
  2. To effectively attack, consider those “weird” numbers like negatives, nonintegers, and 0.  Many fear these types of numbers as traps…but they’re also your weapons against the test.
  3. Consider the layout of the answer choices as an asset, too – with three statements and only five answer choices, the test can’t ask you about every possible combination, so sometimes you can save the “hardest” statement for last and end up not even having to deal with it because you’ve eliminated the other answer choices.

So don’t fear “Must Be True” questions – with some technique, strategy, and practice these questions that many feel must be feared can actually become those that you must get right.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: It’s Not the End of the World

So here we are. December 21, 2012. If the Mayans are right, you’re absolutely wasting your time reading this, as if this really is the end of the world then b-schools will cease to exist, too, so why are you thinking about applications and GMAT scores?

Probably because it’s not actually the end of the world. If, like most rational thinkers, you realize that today is not the end of the world, you might as well heed Fleetwood Mac’s advice and not stop thinking about tomorrow. Here’s where you have a leg up on the competition – you realize that today is not the end of the world, and that attitude will help you on the GMAT, where because of the adaptive scoring algorithm missing a question is not the end of the world. In fact, it’s far from it.

The way the scoring algorithm is structured, everyone misses questions. The algorithm’s job is to determine your ability level by showing you questions that will provide it with more information about your level. If your previous answers suggest that you’re somewhere between the 70th and 80th percentile, the test will likely ask a question for which people at the 80th percentile or above usually get it right and those at the 70th or below usually get it wrong. Based on your answer, the algorithm has a better feel for the probability that you’re nearer to the 80th percentile or the 70th. But even if you get it wrong, that only changes the probability…it doesn’t flat out tell the computer that you’re incapable of scoring above that mark. You will have opportunities to overcome that mistake by getting future questions right – the algorithm is self-correcting and focuses much more on probabilities than absolutes.

The converse is also true – a correct answer only tells the computer that your probability of a score above that mark is higher than initially thought. But many a test-taker has won the battle but lost the war so to speak – a right answer that takes you more than 3-4 minutes is often much worse for your score than a wrong answer in a minute, because it almost ensures that you’ll get another question or two wrong later on as you begin to run short on time.

So what does this all mean for you?

  • Don’t sweat a handful of questions that look impossible. Almost everyone guesses at least a couple times, and everyone misses questions. This isn’t just a self-esteem affirmation (“even though this question is hard I’m still smart…”) it’s just sound strategy.
  • Don’t let any one question become your Waterloo – if you don’t see where you’re going in 45 seconds to a minute, it’s not worth spending several minutes to probably still get it wrong. Make an educated guess and move on.
  • Whether a question seems too easy or too hard, remember that no one question is the end of the world. You get plenty of opportunities to counterbalance one mistake, and the worst thing you can do is let doubt or frustration creep into your mind.

If you’re reading this today, December 21, we promise that the sun will come out tomorrow. And whenever you take the GMAT, remember that whatever your answer to the question you’re on, the next question will come…unless you let that one question take enough time to last until the end of the test. That’s the only way that any one question will become the end of the world.

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

GMAT Tip of the Week: Flipping Sentence Correction Upside Down

GMAT Tip Upside DownFor many GMAT test-takers, one of the most challenging tasks on the exam is that of weeding through the clutter on Sentence Correction questions to arrive at an actionable decision point. So many Sentence Correction questions involve a lot of dense language and not-altogether-enjoyable subject matter, and as a result students spend a lot of time spinning their wheels trying to even get going.

To train yourself to cut through this problem, try this drill:
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GMAT Tip of the Week: Becoming a Sentence Correction Pro Through Pronouns

Many test-takers lament the very presence of Sentence Correction questions, feeling overwhelmed as they study grammar rules and still overwhelmed as they look at practice questions and cannot determine where to start. Sentence Correction can be daunting – the English language is far from binary in its usage (“I before E except after C”…and even that has a bunch of extra caveats), and the questions themselves are specifically designed to make finding your Decision Points difficult.

So how can Sentence Correction amateurs become pros?
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GMAT Tip of the Week: Warm Up

Baby, it’s cold outside. Pretty much no matter where you are while you read this, it’s cold right now (even here in Los Angeles), and whether it’s by blankets, Starbucks holiday drinks, or thermal underwear, you’re probably hoping to warm up. Which is actually good advice for the GMAT, too, just in a slightly different way.

En route to blowing his previous practice tests out of the water on the real thing last week, one of our professional athlete students remarked this about his GMAT studies: “I’d never go play a big game with cold muscles, so why would I try to attempt this big test without warming up my mind?” And so it began – before each practice test or study session, he’s grab 1-2 easy questions of each type, remind himself of the thought process and parameters from each question, and then dive into the more-challenging questions as a well-oiled machine.
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GMAT Tip of the Week: Nate Silver Projects Your GMAT Score Improvement

As Twitter has confirmed, the real winner in this week’s U.S. Elections was Nate Silver, the statistician behind fivethirtyeight.com and the prognosticator who called nearly every national race correctly, save for one senate race in North Dakota. Famously, he predicted each state’s presidential race correctly and he’s risen to prominence with a role on the New York Times and with his new book “The Signal and the Noise.” So with Nate Silver taking statistical analysis to heights that Moneyball only hoped to, it’s only fitting that we close this week by summoning our inner Silver and taking a statistical dive at GMAT questions.

Polling isn’t new, nor is statistical analysis. So why is Nate Silver so much more successful than others when it comes to using statistics to project outcomes? If we understood completely, we’d be writing a different article for a lot more money on a more-heavily-trafficked blog, but the layman’s answer is largely that he takes time to determine which statistics are most relevant to the outcome, and focuses his energy on those. And that’s what you should do when you analyze your GMAT practice tests and consume information about the GMAT – cut to the most meaningful statistics and focus your energy there.
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GMAT Tip of the Week: Jobs Report, Statistics, and Critical Reasoning

So it is upon us. The much-anticipated final Jobs Report before the 2012 Presidential Election has been released, and its results will fuel debates all weekend and can have a significant impact on your GMAT verbal score if you pay attention to the arguments that surround it.

Here’s what happened – the American economy added 171,000 new jobs, beating economists’ predictions by a healthy margin (good news?) but the unemployment rate ticked up a tenth of a point from last month’s figure (bad news?). And in full GMAT Critical Reasoning mode, pundits and political representatives immediately began using those statistics to draw unsupported conclusions. Check out these Critical Reasoning style Weaken questions you could make from today’s arguments:
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GMAT Tip of the Week: GMAT Questions in Halloween Costume

Happy Halloween Weekend, readers (and, yes, we do find it odd that for this generation Halloween now spans several days and seems to have more relevance for 20-somethings than does pretty much any other holiday, but we’re not complaining).

As you put the final touches on your Halloween costume for the weekend – our ever-on-the-pulse-of-costume-popularity coworker, Jason (2010 – Antoine Dodson; 2011- Angry Birds. Every year he’s ahead of the curve on “most popular costume”) is going as Gangam Style – it’s not a bad time to keep your eyes one one of the next hallmarks of the fall-winter calendar, Round Two Application Deadlines. And here’s where the two coincide:
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GMAT Tip of the Week: Larry Rudner is not Candy Crowley. Timing Matters!

There’s a lot you can learn about your GMAT preparation everywhere you look… even in the cutthroat world of American politics. Yes, even watching two Harvard grads snarl at each other can help you become a better GMAT student and, ultimately, a higher score on the exam.

If you watched the U.S. Presidential Debate this week, you hopefully saw a lot of similarities between you and the candidates:
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Make Your GMAT Game Complete, Like Justin Verlander

Within hours of the Detroit Tigers’ blown Game 4 lead against the Oakland A’s, ensuring a fifth and decisive game of the American League Divisional Series, devastated (and exhausted) Detroiters started watching their Facebook and Twitter feeds fill with an internet meme that would prove prophetic:

Justin Verlander the Game Five pitcher, with the slogan “Everybody Chill Out…I Got This”

And “got this” he did, pitching a complete and dominant game, shutting out the A’s and seemingly inspiring run support from what had been dead bats all series. And in doing so, Verlander showed you how to raise your game for the GMAT. He made it known loud and clear – not necessarily from his words but from his actions, demeanor, and commitment, that he was finishing the job no matter what — he wouldn’t hand the ball off to a relief pitcher if there were any way to avoid it.
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GMAT Tip of the Week: Avoid Beer Goggles on Verbal Questions

It’s Friday, so if you’re in the GMAT’s general demographic range (20-something, college grad, young professional) there’s a good chance you’ll hit a bar tonight. And there you may have a chance to witness (or experience) an age-old phenomenon that just may help you avoid a common pitfall on the GMAT:

Beer goggles.

If you’re unfamiliar, the general idea behind beer goggles is this – as the night goes on and you consume more alcohol, some options that you might not have considered early in the night begin to look a lot more alluring. And this concept doesn’t just apply to barroom romances – it’s actually a common mistake that people make on the GMAT. Here’s how that typically goes:
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