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The concept of abstraction involves taking things from specific values to general ideas. On the GMAT, abstraction is one of the simplest ways to turn an easy problem into a difficult one. A simple example would be to ask someone what “5 times 6” would be, and then to expand that to “x times y” or “odd number times even number.” Abstraction helps by giving broad strokes to concepts, but it also requires a deeper understanding of the underlying principles. (This is the same principle as abstract art… apparently).
Last week, we looked at alphametics involving addition and subtraction. The logic becomes a little more involved when the alphametic involves multiplication. When a two digit number is multiplied by another two digit number, the process of finding the result is composed of multiple levels. Today, let’s see how to handle those multiple levels. The question involves quite a few steps and observations using number properties. Hence, you are unlikely to see such a question in actual GMAT but you might see a simpler version so it’s good to be prepared.
In the past few weeks, I’ve written a couple of posts extolling the virtues of using strategies in lieu of doing difficult algebra. But over the course of the quant section, there’s no getting around it: at times, algebra will be an effective tool that you’ll want to deploy. The key is for us to use this tool judiciously.
Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms. He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation. In this “9 for 99th” video series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.
Today, let’s learn how to solve alphametics. An alphametic is a mathematical puzzle where every letter stands for a digit from 0 – 9. The mapping of letters to numbers is one-to-one; that is, the same letter always stands for the same digit, and the same digit is always represented by the same letter.
If you’ve ever walked into a conversation that was in progress, you know how hard it can be to figure out what’s going on without starting at the beginning. People often timidly ask “What are we talking about?” or “Could you please start over?” in such situations. This is because being parachuted into an ongoing conversation can be quite disorienting.
In a previous post, I emphasized the importance of minimizing the number of variables we assign when tackling word problems in Data Sufficiency. This philosophy also works quite well when dealing with complicated geometry questions. Let’s say, for example, that you had an isosceles triangle. We know that in isosceles triangles, two sides will be equal and the angles opposite those sides will be equal to each other. Rather than call the angles ‘x,’ ‘y,’ and ‘z,’ we can designate the two equal angles as ‘x.’ Because these two angles sum to 2x, the remaining angle must be 180-2x, as the interior angles of a triangle always sum to 180. Now we have one variable to deal with, rather than three, and this greatly simplifies any future calculations we’ll have to make.
We have discussed simple and compound interest in a previous post.
We saw that simple and compound interest (compounded annually) in the first year is the same. In the second year, the only difference is that in compound interest, you earn interest on previous year’s interest too. Hence, the total two year interest in compound interest exceeds the two year interest in case of simple interest by an amount which is interest on year 1 interest.
There are certain strategies that we all know, and yet, for whatever reason, sometimes hesitate to use during the exam. Some students are unusually skilled in algebra, for example, and so when we discuss the option of picking numbers, they dutifully nod and decide that this approach isn’t for them, that picking numbers is an unsatisfying shortcut that robs them of the opportunity to display their algebraic virtuosity.
Habitually, data sufficiency questions give students cause for concern on the GMAT quantitative section. This is primarily due to the fact that data sufficiency questions are rarely seen in high school and college, and are therefore relatively unknown to most prospective test takers. If you remember the first data sufficiency question you encountered while studying for the GMAT, it may have looked like it was written in another language.
Welcome back to Hip Hop Month in the GMAT Tip of the Week space, where we’re pneumonic by nature. We’ve talked about being a Sentence Correction MVP, about using the STOP method for Reading Comprehension, about the SWIM categories for Critical Reasoning. We’ve warned you that results can be rocky when you’re trying to finish quant problems ASAP and we spent just about all of our time talking about the GMAT. But we’d have you shaking your head and saying WTF if we didn’t cover the most noteworthy and, yes, naughty acronym of all time: OPP.
Confess it – while watching Harvey Specter and Mike Ross on ‘Suits’, many of you have wondered how ‘cool’ it would be to be a lawyer. It’s surprising how they question every assumption, every reason and come up with an innovative solution which looks as if the magician just pulled a rabbit out of a hat.
Welcome back to Hip Hop Month in the GMAT Tip of the Week space, where we know precisely why you want an MBA: so you can live some of the good life. You want a better job with a higher salary and better benefits. You want to invest big chunks of that higher salary to create passive income that brings you even more money per year. And if they hate then let ‘em hate and watch the money pile up. Welcome to the Good Life.
One of the hardest things for people to get used to on the GMAT is that there is no calculator for the quantitative section. The reasoning behind this is simple: human beings will not be faster than machines at pure calculations. Human beings, however, will be better at logic, reasoning and deduction than a machine (at least until Skynet is developed).
Welcome back to Hip Hop Month in the GMAT Tip of the Week space, where 3-13 isn’t just a day to honor Eminem’s group “Three and a Third” from 8 Mile (we’ll save that for 10/3). It’s also Common’s birthday, so what better day to let one of the most intellectual rappers in the game help you take your game toward his South Side neighborhood (Chicago-Booth isn’t all that far away) or, we suppose, to the North Side and Kellogg?
Let’s discuss how to handle functions today. People usually perceive functions as an advanced topic mainly because of the notation. But actually, the function questions are very simplistic and can be solved with a simple process. If we ask you the value of 5x^3 where x = 3, would you be worried about what to do? We assume you won’t be. Then there should be no problem with “given f(x) = 5x^3, what is the value of f(3)?”
One way in which the GMAT differs from most tests is that you only need to find the correct answer to the given question. There are absolutely no points for your development, your reasoning or indeed anything you decide to write down. This is completely contrary to much of what we learned in high school and university, where you could be rewarded for having the correct algorithm or approach even if you didn’t get the correct answer. On most math problems, if you got the wrong answer but demonstrated how you got there, you could at least get partial credit, especially if your approach was perfect but the execution lacked (like passing on the 1 yard line).
In pretty much every class I teach, at some point I’ll get the algebra vs. strategy question. Which is better? How do you know? I sympathize with the students’ confusion, as we’ll use the two approaches in different scenarios, but there doesn’t seem to be any magic formula to determine which is preferable. In many instances, both approaches will work fine, and the choice will mostly be a matter of taste and comfort for the test-taker.
We know that Combinatorics and Probability are tricky topics. It is easy to misinterpret questions of these topics and get the incorrect answer – which, unfortunately, we often find in the options, giving us a false sense of accomplishment.
In many questions, we need to account for different cases one by one but we don’t really see such questions on the GMAT since we have limited time. Also, we don’t tire of repeating this again and again – GMAT questions are more reasoning based than calculation intensive. Usually, there will be an intellectual method to solve every GMAT question – a method that will help you solve it in seconds.
In my decade of teaching the GMAT, perhaps no single group has found the quant section on the test more exasperating than math nerds. Yep, math nerds. Engineers, financial analysts, Physics majors, etc.
This may seem somewhat paradoxical, but the quant section on the GMAT isn’t testing your math ability. The skills that allowed the quantitatively-inclined to ace their tests in high school and college not only have limited value on the GMAT, but actually undermine test-takers, prompting them to grind through calculations when the question is really about how to avoid those very calculations.
When preparing to take the GMAT, you often solve hundreds or even thousands of practice problems. As you solve more and more of them, you start to realize that almost every question is testing something specific. There’s a geometry question about right angle triangles that’s really all about Pythagoras’ theorem, and an algebra problem that is easy to solve if you expand the difference of squares. However, there are some questions that make you scratch your head and wonder: “What in the world?” Some questions make you think you missed a section of material that you need to review (are there triple integrals on the GMAT?), or at the very least that you don’t know the correct strategic approach. I will euphemistically call these “WTF” questions, which of course stands for “Want To Finish”.
It’s Grammy Weekend here in Los Angeles. All local sports teams have cleared out of the LA Live / Staples Center / Nokia Theater area and local citizens are humming along to the song of the year nominees. How can you (Taylor) Swiftly make your GMAT Quant score (Ariana) Grande, even without the help of an expensive GMAT (Meghan) Trainor? The process isn’t So Fancy, so take that stress and Shake It Off. When you see exponent-based questions, the #1 thing you can do:
Today, let’s look in detail at a relation between arithmetic mean and geometric mean of two numbers. It is one of those properties which make sense the moment someone explains to us but are very hard to arrive on our own.
When two positive numbers are equal, their Arithmetic Mean = Geometric Mean = The number itself
It’s Super Bowl weekend, one of the busiest gambling weekends of the year. Maybe you’ll play a squares pool and end up with the dreaded 6:5 combination, maybe you’ll parlay three prop bets and lose on the third, and maybe you’ll bet on your team to win and lose both the game and your cash. How can you turn your gambling losses into investments?
This is a problem that I have seen many times before. It leaves students bewildered because all of the signs that would lead them to expect a lower score are absent. They did not run out of time, they did not have to guess at lots of questions, and they did not feel overwhelmed. Even I have suffered from this a bit, my lowest Quant score came on the exam where I felt most comfortable – and my highest score on Quant came on the exam that felt the worst.
One of the most uncomfortable aspects of the GMAT is that you are not allowed to use a calculator for the quantitative section. This is uncomfortable because, throughout your everyday life, you are never more than about 5 feet from a calculator (yes, even in Death Valley). Almost everyone has a cell phone, a laptop, a desktop or a GMAT guru nearby to compute difficult calculations for them. Even high school students are generally allowed their calculators on test day. However, the lack of a calculator allows the GMAT to test your reasoning skills and time management skills much more easily than if you had access to electronic help.
We all know about the role of pre-thinking in Critical Reasoning and how anticipating the answer can be supremely beneficial in not just the physical aspect of saving time in analyzing options but also the psychological aspect of promoting our self-confidence – we were thinking that the answer should look like this and that is exactly what we found! Pre-thinking puts us in the driver’s seat and we feel energized without consuming any red bull!
We often tell you that if you are short on time, you can guess intelligently on a few questions and move on. Today we will discuss what we mean by “intelligent guessing”. There are many techniques – most of them involving your reasoning skills to eliminate some options and hence generating a higher probability of an accurate guess. Let’s look at one such method to get values in the ballpark.
We know that speed is important in GMAT. We have about 2 mins per question and we always have questions in which we get stuck, waste 3-4 mins and probably still answer incorrectly. So we are always trying to go faster, rush, complete the easy ones in less time! In our bid to save time, sometimes we sacrifice accuracy. We should know that accuracy is most important. No point running through questions and completing all of them before time if at the end of it all, most of our answers are incorrect – there are no bonus points for completing the test before time, after all!
The GMAT is an exam that evaluates how you think. The test is designed to measure your reasoning skills and gauge how successful you will be in business school. This means that the test is not simply trying to ascertain how much you already know. This is similar to the mantra of “Give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime”. If you happen to already know that 144 is 12^2, then any question that asks about this specific number becomes much easier. However, if the exam starts asking about 13^2 or 14^2, and you only know 12^2, then you must find some method to take your knowledge and apply it to new and unscripted problems.
Those of you who have seen the previous version of our curriculum would know that we had tips and tricks under the heading of ‘Lazy Genius’. These used to discuss innovative shortcuts for various questions – the way very smart people would solve the question – without putting in too much effort!
Studying for the GMAT can take over your life. I’m sure many of you are nodding your heads as you read this. If you’re not, you probably haven’t gotten there yet. I sincerely hope that you never do, but it is an almost unavoidable part of studying for this test. Eventually, you start correcting artists in songs (I got one less problem without you… more like one fewer problem) and wondering if your table number is a prime number (how about table 51… oops that’s divisible by 3). The first time you catch yourself using a GMAT specific term, you know you’re really deep in studying for this exam.
As promised last week, we will look at another question which involves finding the last two digits of the product of some random numbers. In this question, along with the concepts discussed last week, we will assimilate the concept of negative remainders too discussed some weeks ago.
With the winter solstice behind us here in the Northern Hemisphere, you’re probably noticing that the daylight is starting to return; this week we begin the steady climb toward summertime and you’ll see a few extra minutes of daylight after work each week from here until June. For many GMAT applicants, the darkest days of the year in December and early January match with the darkest days of their admissions journey, hustling to post a competitive GMAT while also scrambling on essays for Round 2. But this, too, shall pass.