While discussing Permutations and Combinations many months back, we worked through several examples of arranging people in seats. Today we bring you an interesting question based on those concepts. It brings to the fore the tricky nature of both Data Sufficiency and Combinatorics – so much so that when the two get together, it is unlimited fun!
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Over the course of your GMAT exam, you’ll read thousands of words. Each Reading Comp passage, for example, will have ~300 of them; each Sentence Correction prompt will have ~40. And while you won’t spend much time reading the words in the Data Sufficiency answer choices, having long since internalized what each letter means, you’ll spend plenty of time poring over keywords in the question stem. You’ll need to process tons of words as you take the GMAT, but on most questions one word will make all the difference:
Sentence correction questions are among the least understood questions on the GMAT. Many native English speakers feel they can get by using their ears on sentence correction. However, the questions chosen on the GMAT generally have specific logical elements that must be evaluated in order to get to the right answer. Simply put, the grammar matters, but it’s more about the meaning than about the grammar.
We are assuming you know the terms median, angle bisector and altitude but still, just to be sure, we will start our discussion today by defining them:
Median – A line segment joining a vertex of a triangle with the mid-point of the opposite side.
Angle Bisector – A line segment joining a vertex of a triangle with the opposite side such that the angle at the vertex is split into two equal parts.
On nearly every GMAT, you’ll see at least one of the “Min/Max” variety of word problems, a category that’s difficult for even the brightest quant minds largely for one major reason: these aren’t your typical word problems, and they don’t lend themselves very well to algebra. They tend to be every bit as “situational” as “mathematical” and in fact are labeled “scenario-driven Min/Max problems” in the Veritas Prep Word Problems lesson. Why? Because they’re almost entirely driven by the situation, including:
Critical reasoning on the GMAT requires you to evaluate the author’s conclusion and select the answer choice that best answers the given question. While there are four broad categories of questions, the two most common types of questions are the ones that ask the student to either strengthen or weaken the conclusion provided. In actuality, strengthen and weaken questions are two sides of the same coin (possibly Two Face’s trick coin) and together account for roughly ¾ of the critical reasoning questions on the exam. With stats like these, it’s important to be comfortable with these questions!
We firmly believe that teaching someone is a most productive learning for oneself and every now and then, something happens that strengthens this belief of ours. It’s the questions people ask – knowingly or unknowingly – that connect strings in our mind such that we feel we have gained more from the discussion than even our students!
So it’s Mother’s Day weekend, and all of us should be thanking our moms this weekend. For all kinds of things, of course, but for one that you may not have realized all these years growing up:
Your mom taught you one of the greatest Sentence Correction lessons you’ll ever learn.
The quantitative section of the GMAT is designed to test your understanding and application of concepts you learned in high school. The exam focuses on core mathematical concepts such as algebra, geometry and statistics. However some concepts are more engrained in the high school curriculum than others. Everyone’s done addition, multiplication, subtraction and division, but sometimes figuring out factorials or square roots may be a little more unusual.
Once you have covered your fundamentals, we suggest you to practice advanced questions and jot down your takeaways from them. Sometimes students wonder how to find that all important “takeaway”. Today, let’s discuss how to elicit a takeaway from a question which seems to have none.
What is a takeaway? It is a small note to yourself which you would do well to remember while going for the exam. Even if you don’t remember the exact property you jotted down, knowing that such a property exists is enough. You can always try it on a couple of numbers in the test to recall the exact content.
If you’ve studied for the GMAT for a while, you likely have a decent understanding of the answer choices:
(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 are needed
Many students feel that the GMAT is only necessary to get into business school, and otherwise serves no real purpose in their everyday lives. I, as a GMAT enthusiast (and overall math nerd), see a lot of real world applications in the concepts being tested on this exam. It’s actually somewhat surprising how often splitting the cheque at a restaurant or calculating investment returns requires me to delve into my GMAT knowledge. Such an instance just happened the other weekend, and it’s the kind of story I’d like to use to illustrate how pervasive GMAT knowledge is in daily life.
What makes the GMAT difficult? For most examinees, the time pressure is arguably the biggest factor; given unlimited time, most 700-level aspirants could get most problems right, but with that clock ticking and time of the essence we’re all vulnerable to silly mistakes, mental blocks, and the need to give up on hard questions.
When answering sentence correction problems on the GMAT, it’s very common to use your ear as a barometer of how the answer choice sounds. Particularly for native English speakers, this is often the number one way they approach any given sentence. The problem with this strategy is that sentence correction is often much more about the meaning than about the grammar. By extension, the test makers of the GMAT know they can fool many students by simply making the correct answer choice unappealing to the students’ ears (Won’t get fooled again!).
Before we get started, be sure to take a look at Part I of this article. Number properties concepts come across as pretty easy, theoretically, but they have some of the toughest questions. Today let’s take a look at some properties of prime numbers and their sum. Note that don’t try to “learn” all the takeaways you come across for number properties – it will be very stressful. Instead, try to understand why the properties are such so that if you get a question related to some such properties, you can replicate the results effortlessly.
Data Sufficiency is a game as much as it’s a “problem.” Look at the statistics in the Veritas Prep Question Bank and you’ll see that most Data Sufficiency questions are created with a particular trap answer in mind and that at least 1-2 answer choices are rarely-if-ever chosen.
When preparing for the GMAT, there are many different types of questions that you must master. You know the verbal section will force you to answer questions about tedious passages, strengthen dubious arguments and correct unclear sentences. The ability to juggle these three elements will be paramount to your success as the question types are interspersed throughout the 75 minute verbal section. You cannot break down the exam into 25-minute sections each based on one broad topic and then move on. You don’t know what type of question is coming next, so you have to constantly be ready for any of the three major topics.
Don’t worry, we are not going to discuss (Even + Even = Even) and (Odd + Odd = Even) type of basic number properties in this post. What we have in mind for today is something based on this but far more advanced. Often, people complain that they thoroughly understand the theory but have difficulties applying it and hence are stuck at a score of 600. They look for practice questions and tend to ignore concepts since they already “know” them. We often ask them to go back to concepts since we believe that a strong foundation of concepts is necessary for ‘score increase’. Mind you, when we do that, we don’t mean to ask them to review the basic concepts again, we mean to ask them to deduce and work on advanced concepts. Let’s show you with the help of a question.
The GMAT is an exam that primarily tests your use of logic. One of the most consistent methods used to evaluate your use in logic is to take away your calculator and ask you “difficult” math questions. More specifically, questions that seem really difficult, but break down to simple concepts once you understand what is actually happening.
I recently responded to a student who said that he was “not convinced” by the official answer to an official critical reasoning question. Here is my response:
“I am glad that you brought this up! This is an official question, and the answer choice is the official answer. I do not understand why you need to be “convinced.” You can trust the official answer to an official question!
I am no fan of formulas, especially the un-intuitive ones but the one we are going to discuss today has proved quite useful. It is for a concept tested on GMAT Prep so it might be worth your while to remember this little formula.
When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is an overall loss. The loss% = (x^2/100)%
One of the great benefits of the Veritas Prep Question Bank is that with its 4 million user responses to GMAT practice questions it does an excellent job of highlighting test-taker trends. These statistics can point out trap answers that examinees too readily fall for, conceptual areas that students need to address, and other valuable insights into the way the world takes the GMAT. And this week, one particular trend caught our eye in a major way:
On test day, you will see 78 different questions designed to test how you think, how you approach a given problem, and how well you manage your time in a stressful environment. Most of these questions are unknown to you. You’ve probably spent tens of hours poring over hundreds of GMAT problems and trying to dissect questions from every possible vantage point. However, there is one question you are guaranteed to see on test day, and the question is deceptively simple. At one point, in the verbal section, you will simply be asked: “What is the primary purpose of this passage”
In this series we return to classic movies (and TV shows!) to learn fundamental strategies for GMAT Success.
My friends from the television show The Big Bang Theory are fond of super heroes. Okay Sheldon and Leonard are not really my friends (unfortunately) but they are certainly fond of super heroes. They love Superman and Batman and the entire Justice League.
Recall the important property that we discussed about the relation between the areas of the two similar triangles last week – if the ratio of their sides is ‘k’, the ratio of their areas will be k^2. As mentioned last week, it’s an important property and helps you easily solve otherwise difficult questions. The question I have in mind today also brings in focus the Pythagorean triplets.
As Hip Hop Month draws to a close in the GMAT Tip of the Week space, it’s time to pass the torch to the new school; while Eminem, Tupac, the Wu Tang Clan, and other classic acts have taught you some important lessons about the GMAT, it’s time for the young bucks to impart some wisdom. So today we bring you an important message from A$AP Rocky, Drake, and Kendrick Lamar, who will show you one of the most common (f****g) problems that test-takers encounter while taking the GMAT.
There are certain numbers that will show up on every GMAT. Some of these numbers you need to be able to manipulate, and some others will just lie there like the rocks of Stonehenge: static and immovable. Numbers like π and √2, which can be converted into decimals but generally simply encumber the equation.
I recently had a student write in to ask me, “Can you explain to me the reasoning behind the Least Common Multiple? I understand that you take the prime factors from each number but I have no idea why. I think if I understood why I would be better at this technique.”
Let me see if I can make this concept more approachable for you. Think about calculating the Least Common Multiple as if you were a builder getting ready to build a house. The problem is you do not know which house you are going to build. So when you show up on the job site you need to have all of the materials for each of the possible houses. The “houses” are the numbers and the “materials” that you need are the prime factors.
Our Geometry book discusses the various rules we use to recognize similar triangles such as SSS, AA, SAS and RHS so we are assuming that we needn’t take those up here.
We are also assuming that you are comfortable with the figures that beg you to think about similar triangles such as
Welcome back to Hip Hop Month in the Tip of the Week space, where today we’ll cover Sentence Correction’s most devious wordplay with the rap god of wordplay himself, Eminem. Fans of Slim Shady and connoisseurs of Sentence Correction alike will note the similarity between the two: sometimes, when you least expect it, a word all the way at the end will tie back so beautifully to one all the way at the beginning that it’s just mindblowing. In Eminem’s case, you have to rewind the track to listen to it again – did he really carry that rhyme all the way back like that?! – but on the GMAT you can’t rewind, so it’s important to heed Marshall’s advice well before you put on those noise-reduction headphones (Beats by Dre?) at the test center and zone into the verbal section:
Two weeks ago I wrote an article about whether the GMAT was hard. It is a question I get asked regularly from many different students with many different interpretations of what “hard” actually means. On test day, you may get a question that seems impossible to solve, and yet most other students get it right. This means that the question wouldn’t be considered difficult by the GMAT (say a 500 level question), but for you it seemed exceptionally difficult. The notion of difficulty is thus subjective, and while many would argue that the GMAT is hard, I have a much simpler explanation I have been postulating for the past couple of years:
In this series we return to classic movies to learn fundamental strategies for GMAT Success.
In the Austin Powers movies the character known as “Dr. Evil” creates an exact version of himself, only smaller, that he calls “Mini-me.” The two characters have identical proportions even though one evil villain is 8 times the size of the other. The hero, Austin Powers, quickly recognizes the similarity, despite the difference in size. This is something that you will need to be able to do on the GMAT!
Today, we will discuss the question we left you with last week. It involves a lot of different concepts – remainder on division by 5, cyclicity and negative remainders. Since we did not get any replies with the solution, we are assuming that it turned out to be a little hard.
Where the Venn Diagram of “Hip Hop Month in the Veritas Prep GMAT Tip space” and “Guy who Photoshops all the preview images for these posts does so for the last time before leaving for an amazing new opportunity” intersects, you’ll find a lot of Boyz II Men, rap ballads, and other assorted slow jams playing bittersweetly in the background. And as it so happens, arguably the best of those slow jams – Tupac’s “Life Goes On” – is a perfect metaphor for GMAT test-day strategy:
In this series we return to classic movies to learn fundamental strategies for GMAT Success.
There are two facets to each quantitative problem – (1) deciding what to do and (2) then actually doing the math. I refer to these respectively as the “diagnosis” and “surgery.”
A Good Diagnosis Avoids Unnecessary Surgery
I could have sworn that I had discussed negative remainders on my blog but the other day I was looking for a post discussing it and much as I would try, I could not find one. I am a little surprised since this concept is quite useful and I should have taken it in detail while discussing divisibility. Though we did have a fleeting discussion of it here.
As Hip Hop Month rolls along in the GMAT Tip space, we’ll pass the torch from classic artists to the future, today letting Drake take the mic.
One of the main goals of the GMAT is to determine whether or not you can analyze a situation in front of you and determine the information needed to solve the question. In this way, the GMAT is testing the same skills required to solve a business case. The numbers in front of you are not important, but your method of solving the question is. Crunching numbers and measuring hypotenuses are not useful skills in business; you’ll have a calculator (or an abacus) to do that. Understanding how to approach and solve problems is the true skill being tested.