GMAT Tip of the Week: How to Avoid GMAT (and Pokemon Go) Traps

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

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

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

And the GMAT can and will do the same thing.

How?

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

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

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

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

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

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

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

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

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

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

By Brian Galvin.

How to Avoid Trap Answers On GMAT Data Sufficiency Questions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Use This Tip to Avoid Critical Reasoning Traps on the GMAT

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

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

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

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

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

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

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

3 * 5 = 15

3 * 7 = 21

3 * 19 = 57

5 * 7 = 35

5 * 19 = 95

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

11!(12! + 10!)

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

11!10!(12*11 + 1)

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

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

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

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

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

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

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

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

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

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

By Brian Galvin.