In the figure above, point O is the center of the circle and OC=AC=AB. What is the value of X?
Why is that the case?
There are a few reasons.
1) The problem relies on a little-used geometric theorem: in short, if we know that a certain line forms the diameter of the circle, any point tangent to the edge of the circle, if connected with straight lines, creates a Right Angle.
Just look at the picture and don’t read the words. It’ll be easier.
See, it was easier to look at the picture!
2) When the diagram is complete, you’ll find that there are three different variables required to solve. Cleverly—any by that I mean “annoyingly”—if you don’t head down exactly the right path when answering the question, you’ll go in circles forever, or at the very least, take five minutes to solve the question.
3) Given the answer choices, there’s no real way to backsolve or even eliminate ridiculous answer choices.
Basically, we’re screwed.
In a very un-GMAT way, it means we’re going to have to actually do the heavy lifting on this one.
Is there a simpler way to solve the question?
Look, buddy, if you got one, then show me because I haven’t seen one.
Check out the video for the process. And sign up for the mailing list if you like it. It’s up there. At the top. And the right.
The 2016 Official Guide is not a major difference from the 11th, 12th, or 2015 editions.
This is particularly true when it comes to difficult questions. However, certain things are noticeable over time.
One of these trends has been in Combinatorics (you might think of this as Permutations and Combinations, but Combinatorics is a better umbrella term as it includes all forms of counting problems.
Sometimes GMAT Combinatorics problems involve counting problems that are embedded within Probability questions, and sometimes they are as simple as applying the Combination formula.
Arguably, trying to blindly apply any formula with a Combinatorics problem is risky. It’s a lot better to build an equation based on the description of the question implies.
This video will teach you an example of doing just that.
This is a NEW question in the Official Guide for GMAT Review 2016 (OG2016 or OG 2016), Problem Solving PS 152!
“A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
(A) 144 (B) 152 (C) 160 (D) 168 (E) 176”
This question has an unusual structure, and can only be built from scratch.
No number of permutations or combinations equations will get you to identify the split here. Watch the video and enjoy!
It’s no surprise that there are a lot of overlapping sets or Venn Diagram questions on the GMAT.
For many people it’s incredibly difficult to figure out whether to use a diagram, a table, or perhaps simple algebra.
The answer to this might be best chalked up to “feel,” but there are actually good reasons to use each of them.
Two Part Venn Diagram:
If it’s a standard overlapping sets question with Set A, Set B, and the overlap BandC, there’s no reason not to draw the picture.
Only two things? It’s this easy.
It’s probably easier to organize this graphically than it would be to set up an equation, despite the admonitions of the Official Guide.
If it’s a question that involves four or more variables with binary opposition (that is, YES/NO, ON/OFF, etc.): e.g., as in A, notA, B, and not B, then I would suggest a table.
Lots of Yes/No choices? Probably a table.
Three Part Venn Diagram:
Many books only focus on the strict way to create these: in a lot of cases–especially in the Official Guide–this is an algebraic method as in Question 178 in the OG2015 or Question XXX in OG2016.
That would be this method:
However, there is a new species of Three-Part Venn Diagram question that “requires” a graphical explanation. While an algebraic explanation is possible, it’s thoroughly pointless and will take a good 5-7 minutes to solve!
This is a video on how to tackle one of these clever little monsters:
Let’s face it—a lot of the GMAT materials out there are pretty rubbish.
In fact, at least once a month, I get offers from some dodgy company or another offering me 1/3 to 1/5 my hourly rate to write something like ten questions per hour.
(Generating fully new, good quality questions takes more like one hour per question, if you were wondering).
All I can assume is that the people who end up writing most third-party (non-Official) materials are lured into doing so through guilt, child support, or a heaving meth addiction.
Or maybe they got sick of their jobs overseeing the deep-fry basin at Burger King and are looking for a lower-paying gig on their way to the gutter.
Image from www.freefoto.com
Needless to say, I don’t take these jobs.
For that matter, I almost invariably encourage my students to use as many Official Materials as possible.
This is even to the point of outlining all of the questions that are replaced every time an Official Guide is released and compiling the old ones so that we know which are fresh.
Call me nerdy.
Still, even the best non-Official GMAT questions might test relevant concepts, but they tend to be written in an entirely different voice and tend to have an remarkably different internal structure than Official questions.
HOWEVER, a recent discussion has spurred me into thinking about something.
It’s obvious to anyone who’s studied GMAT to a high standard that we can’t always rely on Official Materials, for no other reason than that there aren’t enough difficult questions.
There’s really no way to get enough Official Questions to consistently see enough 700-level questions in a row to approximate an actual GMAT situation.
Thus we have to collect killer questions anywhere possible.
The main source, for Quant, is Manhattan’s venerable Advanced GMAT Quant. Now, of course, this book isn’t going to help much in the voice of the questions.
But the wrong voice isn’t necessarily a bad thing.
If I can go through the Manhattan materials, for example, or other decent materials such as the Jeff Sackmann books, and understand the point, then what makes me different from other people?
I seem to be able to get use out of these materials, so how does one extract the useful information?
Actually, it seems to me that the useful experience here comes not from the writing of the question—if anything, the Official questions will be clearer and therefore easier—but being able to extract the idea of the question even from a situation where the writer of the question is not able to express herself clearly enough.
This teaches two things:
First, the ability to extract information from difficult presentation.
Now, the GMAT presents information in an intentionally confusing way, and many of these questions are actually unintentionally confusing, but is that necessarily a bad thing?
Second, the ability to adapt to new situations.
After all, you are looking at information presented in different formats all the time. The concepts might be the same, but you’ll have to dig it out of new presentations.
Even if the presentation is sloppier or somehow different, that doesn’t necessarily make it bad.
Put it this way: Eric Clapton might sound better–from a technical standpoint–than the Rolling Stones, but one is 100% pure Dad Music and the other is still relevant (Some Girls and before, obviously).
You don’t need to have everything presented perfectly in order for it to be useful.
What’s the point here?
Not everything is perfect. The more you can adapt to using imperfect materials, the more you can adapt to the differences between practice questions and the invariably different questions you will see on the test.
Quality non-Official practice questions are often approximately 10-15% different from whatever Official question they used as a base, with most of that difference being from different voice, phrasing, etc. in the language.
An Official question that you haven’t seen before is 20-30% different from other Official practice questions you have seen—otherwise, it wouldn’t be a new question!
If anything, using the non-Official questions have as much merit as the Official questions.
Practice as much as you can with decent materials. Don’t stand for huge errors, and if you find too many of them, quit using that book.
A little bit of difference in voice isn’t necessarily a bad thing, especially with really tricky concept-based questions.
Still, use Official materials as much as possible in the 2-3 weeks before the exam, just to get used to the voice.
You want to go in feeling as comfortable as possible with how the questions are actually presented.
As for other questions, avoid throwing out the baby with the bathwater.
Some non-Official resources that are worth your time:
Chuck Dreyer is a colleague of mine in London and provides thoughtful, effective explanations for some of the nastiest Official Guide questions out there!
Very useful companions to your OG set.
The perennial “Manhattan Advanced.” You don’t even have to say the rest of the title.
These are nice and tricky questions — GMAT Math and GMAT Verbal are both here — just click right or left!
Combinatorics problems are feared mostly because no one teaches them properly in school.
When you learn simple methods to break these questions down, you’ll find them some of the easiest questions on the GMAT!
Strangely or not, there is an underlying logic to counting properly even if it’s not really what it would seem on the surface. More often than not, you’re simply multiplying everything together.
The main problem with this is figuring out exactly what to multiply, and when. This video shows how to apply restrictions to your multiplications to be sure that you’re doing the right thing.
This is a teaser video for our upcoming course on Probability and Combinatorics, released late 2015–sign up to the mailing list (that’s on the right side of your screen:) ) on this or any page to get more information about this course or GMAT tutoring in London and worldwide via Skype!
As part of my new series on Combinatorics (counting problems) questions, I’m introducing some basic videos to YouTube over the next few weeks.
When it’s all completed, it’ll ramp up to a proper-real Online Course based on how to get you from Zero to Hero when it comes to these fear-inspiring questions.
The first thing I’d suggest is simply to make sure that you take the information apart step by step and that you have a lot of good techniques and methods at your disposal RATHER THAN blindly memorizing equations the way a lot of Fast Food GMAT companies would recommend.
Remember, the GMAT expects you to know the basic equations AND why they work, but it will punish you relentlessly for knowing them and not knowing why they work.
How does that work?
Like this: the test suggests a particular equation or knows that you’ll be expected to use a particular type of equation to answer a question.
However, those equations tend to be “universalized,” implying that they start from a set point e.g., counting from 1, assuming consecutive integers rather than “only evens,” etc. The GMAT will then suggest that you count from 100 or count only the evens.
If you don’t know WHY and HOW the equation works, then you’ll find yourself neck deep in guano.
What’s the best way around this?
Quite simply to learn to build the equations from scratch, as I teach you to do in this new video series.
It was making me shrink into my seat. Just to breathe, I began to hyperventilate.
This wasn’t the first time that I took a practical exam, and it certainly wasn’t the last.
The first was when I was probably 11 years old and was given an ACT exam as part of a program for “gifted youth.” Yeah, one of those—don’t worry; in the Midwestern US, the term “gifted” actually applies to anyone who managed to graduate high school.
So anyway, in that case I didn’t particularly care and had no idea how the grading system worked.
This time, I did care.
Not that I should have, particularly. It was just another arbitrary SAT exam—actually an SAT II, in Physics–a subject that I was ostensibly taking but had never truly studied. Ironically, it would be my major at University.
Entering the room, I had no idea that other people were taking Physics courses in high school that actually taught them practical things instead of having abstract discussions with the teacher ranging from the moral benefits of Chaucer’s “Chanticleer” to how gravity is God’s work.
In short, I locked up. I was screwed. There were questions about things I’d never even heard of, let alone studied.
It was a wash—horrible.
Yes, this was my test.
In short, I didn’t know what I was getting into. I went in totally unprepared. Not just in terms of not understanding the material on the test, but not understanding the testing procedure. In fact, I had even brought a calculator, which we weren’t allowed to use!
Unfortunately the worst thing was that, looking back on the SAT II Physics exam—even teaching it several times after University—many of the questions made sense. I could have solved them, even with limited knowledge. They could have been worked out if only I had had the confidence.
So where was that confidence?
It’s the confidence of being able to let go.
Perhaps illogically, I couldn’t let go because I thought that doing so would make me perform less well. However, realistically, I needed to study and repeat questions. Study and repeat questions.
I needed to drill. I needed to figure out the things I was good at and do them until they were reflex actions.
I needed to figure out the things that I was bad at and do them until I was competent at them. Most importantly, I needed to assume that my conscious mind would be totally off-line due to simple terror.
It’s the same reason that musicians practice scales: when you’re on stage and ready to crap yourselves because the audience terrifies you, you need to know how to play in key. Even if it’s not the exact right note, it won’t sound wrong!
It’s the same reason that basketball players practice free throws until they can make 99/100. Because they don’t have a choice—under pressure, we revert to habit, which we develop through practice.
In fact, it’s usually the most boring practice that is the most valuable. Things need to become natural, which means you need to be able to do them without thinking about them.
The more that you intellectualize what you’re trying to do—that is, to keep it in your conscious awareness—the more brainpower you are using simply to think. Ideally, you can get rid of this excess stress by repeating the task so often that you don’t have to think about it.
And that is why Masters–in any subject–are so obsessed with practice.
A master is someone who has learned to love practice. Jerry Seinfeld is worth hundreds of millions of dollars, but he still gigs regularly because he loves the work.
He’s reached a point where—no matter how difficult stand-up might have been for him when he began—he has learned to love the craft of preparation.
Miles Davis practiced ten hours a day. John Coltrane used to sneak away at dinner parties to practice his arpeggios.
Professional athletes obviously spend all day practicing, but often do other complementary athletic work such as ballet or yoga in order to augment the skill set that is directly related to their work.
How Can You Become Obsessed with Practice?
The process might seem illogical, but bear with me:
1) Start with easy wins that don’t offer much resistance: e.g., start by basic grammar exercises such as memorizing GMAT idioms; practice algebra mindlessly. This mindless practice will shift your brain into the right gear for beneficial study. It is totally necessary: this is more important than anything. For 10-15 minutes. ALWAYS DO THIS STEP.
2) Work through hard problems with a goal of 1% improvement per day. It doesn’t matter as long as you’ve learned something. Write down what you have taken away from today’s exercises. 30min-1hr.
3) Work as quickly as you can while still getting 80% of questions correct in the section you’re working through. They don’t have to be Official questions at this point—whatever exercises you’re working through will do. 30min-1hr.
1) This assumes a two-hour study session.
2) Ramping up speed DOES NOT mean going so fast as to be demoralizing. Rather, it means doing WELL until you are comfortable doing well a little bit faster.
It’s All About Winning.
The most important thing about studying is to be making progress.
There’s no point in spending the time getting better at anything you’re already excellent at, after all!
Progress has to be realistic, though. Learn what you can reasonably accomplish in a day and set your sights to that. How long to you have to study and what can you expect to get done in that time?
Come to terms with the fact that you’ll probably get 50-70% of that actually done. That’s not a bad thing—it’s just life.
Realize that this may postpone your GMAT exam. Come to terms with that. A lot of people start studying far too late, thinking that the test will not in fact require 3-6 months of solid preparation (hint: the GMAT requires 3-6 months of solid preparation).
Learn to love studying by giving yourself small wins. Learn to break your progress into increments that make sense–increments that are achievable.
Those who love what they do are the people who do the best.
Learn to love GMAT study and you will be the best. Simple.
One of the worst bugbears of GMAT preparation is “garden variety” anxiety.
It might seem as if the test is insurmountable, that it is some kind of obstacle that cannot be avoided. In a sense this is true. You will have to take the test. It will be a pain in the ass.
However, it is a lot simpler to work with the test and go through the steps necessary to crack its code than it is to try to figure out a way not to take it or to “game the system.”
In a very Zen sense, the ultimate goal for the GMAT is to get more questions correct and fewer questions incorrect.
Thanks, That was Really Helpful.
Nevertheless, in my 10 years of experience as a GMAT tutor, I have seen any number of people—all very well prepared for the exam—fail in the moment because they have built the exam up psychologically to a point where it is insurmountable.
In fact, many of these people feel that when they are in the exam situation that they experience heaviness in their chest, trembling hands, shallow breathing, and more symptoms.
Look at it this way: the GMAT is not the same as being faced with a firing squad, so there is no realistic reason to treat it in such a way. The next time you have nine guns pointed at you at the same time, you are welcome to tremble and breathe shallowly.
Let’s take an example from performance: stage fright. It’s a very real thing and I have suffered from severe stage fright for most of my adult life. A lot of this has to do with a few very ill-considered performance situations during high school where I cracked under pressure and made a complete fool out of myself.
For this very reason, despite becoming a much better musician than I ever was during high school, I have felt unable to perform. It is totally irrational, of course, and I realize that. Nevertheless, until the past three years or so, I would lock up if playing music in front of another person.
This starts a negative feedback loop: when the person for whom you perform senses your discomfort, they judge you or zone out. This discomfort—even if they don’t say anything—is perfectly clear and adds to the stress of the situation.
Analogously, the GMAT is expert at determining when you’re having trouble with particular types of questions and will give you lower-grade questions as a response, thereby lowering your possibility of scoring highly.
Nevertheless, I have slowly but surely built up my ability to perform in front of others. How?
Two ways: the first is to do the psychological “heavy lifting.” Primarily, this means realizing that my fear is irrational and learning to work through this. Not to gloss this over—I’ll explain the technique in a moment.
The next step is to take baby steps toward the goal: performing for music teachers as well as working to find groups who play at my relative level so that no one needs to be embarrassed. Just getting used to the stage performance: for that matter, taking public speaking and comedy courses.
Exercise: the “Heavy Lifting.”
Remember a situation where you failed spectacularly. Sit down and really think about it. Close your eyes. Imagine it as if it were happening right now.
See it all as if through your own eyes, feeling the feelings throughout your body, and note any sounds that you might associate with the same situation: any noises you hear, or anything that might have been said during the original situation, including anything that you might be saying to yourself.
Now step out of the situation—that is, remove yourself so that you can see your self in the situation. Imagine the image of the situation as if it were projected on a movie screen, then push the screen farther and farther into the distance.
Notice how your perception of the events has changed. Push it as far as you need—into infinity if you have to–to completely eradicate any emotions associated with the situation.
You can apply this to any unfortunate situation you would like to. Pick a situation you dislike in your life–GMAT or otherwise—and try the above exercise again.
Repeat the exercise with each situation daily—it should take less than two minutes—until you no longer experience any emotional tug with the situation.
Do you simply find yourself meaning to do it but never getting it done?
It is easy to find the time for GMAT preparation. In fact, it is so easy that people tend to make excuses about how they don’t have time to study.
Sure—we’re all busy, and it is easy to let life get in the way. Years of working as a GMAT tutor in London and Paris has shown me every imaginable excuse. Is yours be the next one? It doesn’t have to be.
However, the people who get their study done have figured out a way, somehow, to get into the mode of studying despite the fact that it definitely takes a chunk out of the day.
There are several reasons for this, but one of the most important things to do is to analyze your motivations for doing the test in the first place.
Ask yourself why you want to take the exam. Go ahead, I’m waiting.
Think about where resistance comes in—usually this is some sort of generalized anxiety, such as “What if I don’t get accepted at Harvard?”
This is a valid concern. Of course if you don’t take the GMAT in the first place, you certainly won’t get accepted!
So let’s look at a little analogy.
Nevertheless, when you wake up in the middle of the night and have to go to the bathroom, do you consider how many steps it will take to get there?
If you consciously think of the 40 or 60 steps you would have to make to get there and back, you might as well just stay in bed, right?
I didn’t think so.
Make that drive to get into business school like having to pee so bad you wake up in the middle of the night. Let’s take that first step and develop some momentum.
Just as lifting a boulder starts with getting it loose even by a small degree, we have to start small.
It’s all psychological! To begin studying, you must become a “studier.”
One of my favorite business authors, Ramit Sethi, suggests developing the habit of flossing not by forcing yourself to do it each day.
Rather, he suggests flossing one tooth per day until you internalize the fact that you are “a flosser.”
Then it becomes easier and easier to build up the habit of studying.
Of course moving time down into units that are digestible works perfectly with the concept of “chunking” data. Break it down into a small enough task that you can do it today. Can you?
What task is small enough that you can complete it today? Is it learning the multiplication table for 2? Is it learning one grammar rule?
Even if something only takes five or ten minutes to do, it is better than nothing. In fact, you have read this blog post, which is five minutes of your time.
Do something for another five minutes and you will have spent ten fully focused minutes. Likely you have learned or practiced something that you didn’t know yesterday.
If you can start with 10-20 minutes per day, great! Increase your study time by a small amount every other day or so, reaching the optimal 1.5-2.5 hours per day at a comfortable rate.
Not all at once! Let GMAT study be comfortable, and the rewards will come.