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GRE - All you Need to Know about Quantitative Reasoning

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GRE - All you Need to Know about Quantitative Reasoning [#permalink] New post 09 Apr 2018, 14:10
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The Four Horsemen


Episode 1 - The strike of the Beast

Despite the fancy title of this first chapter of the story, I must admit that is not far away from the truth. I always hear students narrating of the GRE Math section quite like a beast. I remember very well when I was engaged most of my spare time throughout what I called, having in mind one of my favorite movie " Mad-Max - Fury Roads" in which the main character wandered in a wasteland, the "GMAT Land" when a private message knocked my inbox. The message was very kind and respectful. However, what surprised me was the fact that the student called the famous or notorious exam (it depends on which point you see it) "the beast."

As it turns out, he or she (I cannot remember precisely the gender because it was a long time ago) put me in a sort reflective state of mind: Do the GMAT and the leading competitor, the GRE, are "a beast" ?? After all, we are not talking of a test, for now on I promise I will focus on specifically on the test of our interest: the GRE :), in which few high-school concepts are tested ?? Do we have to deal with a few basic rules about exponents and roots or we have to compute strange and arcane formulas where at the core tensor calculation skills should be used ??

On one hand, we do have the "beast"; on the other hand, we do have simple concepts tested. So, where is the catch ??

The answer is pretty straightforward: we do have simple notions crafted in a tricky way under a time constraint


That's the GRE in a nutshell. We could stop here. The previous statement asserts what the GRE is all about. Fortunately, we will guide you in every aspect to tackle every question type you face off during the exam.

Before to descend into the maze, it is crucial that you know what you are going to face as a whole. I will not spend enough time to stress this point: as you go to cope with a quantitative comparison question, easy or less, is essential you get consciousness not only of the idea tested behind but also the whole picture in which the question is framed. Same might be said for instance of a Text completion: the complete sentence and its overall meaning will permit you to beat the problem, allowing to you to nail the right answer, NOT whether you do know tons of vocabulary words more or extra. What is important is the big picture because you are at serious risk to lose the grasp of what is going on, which is which.

In a more general way, the GRE quant section is specifically meditated to set most of its emphasis on your ability to reason quantitatively—to read a math problem, understand what it’s asking, and solve it. The accentuation of the section is not on your ability to memorize formulas or the prime numbers from 1 up to 100. The GRE is on your ability to reason, using your knowledge of the various topics. The goal is to make the test an accurate indicator of your ability to apply the given information, think logically and strategically, and to a sort of conclusions. These are skills you will need at the graduate level of study. These tests such as GRE, GMAT, SAT, or which one could jump at the top of your head are not made like a book you had studied attending the high-school. In that scenario, I start from the very first page until the last page, and I reach my goal. The result is a big A at the end of the semester.

If you do think this manner, then your GRE score will be an epic fail. Take into account this from the very beginning.

The GRE is NOT a zero-sum game !!


  • The paraphernalia you must have before to start.

    Although this may be a most difficult thing, if one will do it, it can be done. There is nothing that one should suppose cannot be done.” The Hagakure

    Every self-respecting soldier - ready for the battle - has a lethal weapon in his arsenal. It could be a katana blade, a rifle, or everything you can think about to accomplish the mission with clearness, persistence, effectiveness without compromise. Fortunately, you do have the most powerful, fatal weapon that a human being has ever had: your brain.
    This muscle, properly trained, will lead you to conquer a top score during the test with the will, the tenancy, the right strategy and the right study plan.
    But before to delve into the various steps, it is really important already to plan ahead what we are going to really cope.

    More often than not, the students ask me: which is the best and extensive vocabulary resource ?? how many vocabs should I study or memorize? well, the answer to questions like these, honestly, really is only one: a waste of time. I do not wanna be misunderstood or worse, uneducated to say this, but is the nude truth. You can fill a bunch of words in a flash-card, that is still one of the most effective ways to learn words when you commute or else but is a sterile way to conceive your GRE studying and is the wrong way to approach it. The test will ask you to use your vocabulary in context, so you should work out using words within a complete and grammarly correct sentence to grasp the meaning of the word at stake and at the same time sharpening your vocabulary and English skills as a whole.
    Another very important thing is to put away your phone. The key rule, since the very first moment you start to study, is to focus on. No distractions or random study. Only a state of mind completely delivered to your final goal: learning something more, useful, step by step along the way until your goal. Of course, your main target is an outstanding score at the end of your journey but your goal is also divided into small chunks, little breaks that will help you to build your concrete wall of knowledge. On a daily basis, you will learn a new formula, a new trick, a new way to see the question from an odd angle to tackle it faster and efficiently.

    Time takes time - Achieving the score you wanna needs effort, and it will definitely take some time. Each student has different needs and abilities, but a good rule of thumb is "5/90": five times a week for around 90 minutes a piece. Afterall, if you are not ready to sacrifice to achieve your GRE score, then what would you expect once you are attending your dream Business School ??

    The quant part of the test and the test itself in its entirely do not test whether you are a genius at math, neither if you re going to give birth to the formula \(E=MC^2\) version 2.0 nor if you are the new Kurt Godel. The test asks you to have in mind, clearly, simple notions to use in the right way at the right time; dissecting the question in front of you, understanding it in its intimacy I.E. what it really is asking you is to solve for, dissembling it, rearranging in a different possible way if it is not straightforward to solve, using all the information you might use, screwing what is fluff and nail it. All this in the allotted time. doesn't sound all the process fun ?? is it not amazing overcoming all this and being the winner ?? I think definitely YES :-D

    To make all this possible one last thing is crucial: a study plan. Without your playbook, your schemes how do you think to win your Superbowl ?? Actually, you are at a serious risk to get into a loop, doing huge efforts in terms of time, study, money, hopes but reaching nothing, or at most a poor score.


  • Oddly, the GRE is not a test of math but of translating math into words and inference skills.

    "We cannot think first and act afterward. From the moment of birth, we are immersed in the action and can only fitfully guide it by taking thought."

    As I mentioned more than one time in the aforementioned sentences, the GRE is not a math test in a pure sense one could think about. Rather, it is a way to manipulate something to obtain something else, reading something that can be stated or NOT be stated behind and in between the lines. Probably, what I just said might sound cryptic, is not it ?? I think no. Put it in simple terms, you have to move through the test quickly and efficiently without getting stuck, you’ll need to quickly decode complex GRE language to find the simple underlying concept.

    Read the next prompt:

    Quote:
    x is an integer and is equal to \(n^3 - n\)

    Quantity A
    Quantity B
    x
    24


    At this point, you start making the calculation and this is perfectly fine. However, you are not seeing what the question really wants from you I.E. the question, actually, is made of three consecutive numbers and they could be less, equal, or greater 24, without even touch your scratch paper and using the pencil. How this is possible ??

    I have applied my translation skills, changing the math in a more simple and understandable language.

    \(n^3 - n = n(n^2 - 1) = n(n - 1)(n + 1) = (n - 1)n(n + 1)\). That's it.

    The students struggle mainly NOT because they have poor math knowledge, otherwise, we would not have the case in which many of them have an engineering degree but score not so well during the exam. The students primarily fail because the test uses reading passages, vocabulary words, and mathematical concepts to assess reasoning and decision-making skills. In essence, it’s a four-hour strategy game.

    Let put this concept in a more simple way: whenever they have to solve a problem, then the students tend to apply complex concepts to solve to in a "sic et simpliciter". Instead, it would be enough a good evaluation of it up-front and apply a trick or a shortcut. This way, they gain precious time. You will not be rewarded whether you provide the most elegant, marvelous solution to nail a question during the test. You will be reward only and solely if you nail a question, I.E. you get it right, in the allotted time that is about one minute on average. That said, you will perform and consequently, you will obtain a good score if and ONLY if you do have: a good grasp of the concepts tested, a very strong strategy, a flexible and resilient approach to the test.

  • How Much Do I Have to Learn to strike the beast?

    "Beast Mode doesn't make excuses. It doesn't complain. Whatever you're doing, go out there and get it done. Keep pushing."

    Yes. To beat the beast you must be stronger than it. This does not mean at all you have to study all the possible math notions on earth. It is true that the GRE takes time, hard work, and a change in mindset. A lot of the learning you have to do to beat the GRE won’t look like what you’re used to. This is because at the very first stage, when you starting studying for the GRE, you do have to learn or, better I would say, re-learn concepts buried in your mind since the high-school, completely forgotten, or well presented in your knowledge luggage but rusted. As it turns out, it is like you have a savanna in front of you in term of learning. This is perfectly fine. However, the more you study for the exam the less the area of contents is unexplored to you. At this stage, most of the students take the exam and do not score very well.

    The question arises spontaneously: what went wrong ?? I knew everything, every single math notion or formula used to get a score even higher than 170, so ??

    Let put aside for a moment the several reasons why this happened to you: anxiety, silly mistake, willies, a bad day or else. All these factors are equally important, though they will object to another post in a separate moment. For now, focus on what I really wanna underline just now: the students say to themselves: ohh I should back to the books, and this turn I will study every possible GRE math-related notion. Therefore, I will not have surprises during the next test and I will beat the beast. Well, probably you are going to fail again, and again, and again. I am not utterly mad. Believe me :)

    The point is: students think that adding more concepts, more notions, even the most obscure method to solve a quadratic equation (if it exists) will lead them to the best score, falling into the trap of "overlearning".
    Doing this, the student:
    • waste valuable time and energies to learning what he/she already know very well;
    • doing what I have described in point one, he/she does not focus and stress heavily on strategy, tips, and shortcuts to solve in a faster and efficient way a question;
    • he/she/ does not focus on that much in reviewing the questions got right AND wrong during a training session or a mock test. From this, the consequence is you miss the possibility to learn from your own mistakes and go a step further for achieving your daily goal. It does not matter whether your goal is to nail as many questions as you take on a daily basis or the top-notch score during the exam session.

    Again, the GRE rewards those students who study smart, but at the same time hard. Those students who take care of their weakness, but at the same time reinforce their strengths. Those students with the willingness of not stopping, that everything is possible with a "feroce" inner-strength. Those students who have a really strong flexibility and resiliency, back on the problem or area of contents they do not master with proficiency over and over and over and over and over again.

    John Nash said "trying to demonstrate a new conjecture is kinda like to hit the wall with your clenched fists. The wall will be crumbling down"

    Here is an example of what is the gist, the real meaning of what we are saying: the GRE test is not a test in which you do apply "zero-sum" notions but rather is a holistic approach, characterized by the fact that the parts of something are intimately interconnected and explicable only by reference to the whole.

    Quote:
    A cube of cheese is 3-inches high. The cheese is sliced twice.


    Quantity A
    Quantity B
    Resulting surface area of all the slices of cheese
    90 square inches



    A. The quantity in Column A is greater
    B. The quantity in Column B is greater
    C. The two quantities are equal
    D. The relationship cannot be determined from the information given


    This is a medium-upper level question. Usually, an average student starts to calculate or jot down something on paper, trying to figure out the solution. This is great, I really do endorse always people proactive. People who move fast to find a solution, in a way or another. The perfect approach.

    However, what if we do analyze the question up-front and solve it in ten second-approach and move on. This is not even better ?? :-D

    Imagine if you cut two really thin slices and rest of the block is intact, then the area would be different from when the block is sliced from the middle. I.E. you can slice the cube right in the middle and the area is different could be less than 90 or you can cut it in a super tiny slice and the result could be different another time. Therefore, we do NOT have enough information to solve the riddle. The answer is D. The solution is here.

    The mentioned example is not only useful to show up the mindset to approach the GRE in its entirely but also address the following considerations, very important key-points:

    • which is your level of problem recognition ?? and, consequently, what is your solving pace during a mock and most importantly during the real exam ?
    • Do I really know what to do in a clear, efficient, and without hesitation manner, solving any GRE problem?

    If your answer is YES to the questions above, probably you are down the road for a top-notch score during the test. Because:

    • answering those questions means you do have a clear and perfectly calibrated strategy;
    • you do not have any such problem to keep your pace, tackling every question in the allotted time the questions need;
    • your problem recognition is very familiar to you, performed in such an economical way;
    • you do have a carbon-fiber approach: flexible, yet with a high tensile strength.

    If your answer is NO or maybe, well, you should know where is the problem, why you are not able to answer those questions consistently. As it turns out, you have to reflect on the negative side of the four aforementioned skills you still do not master.

    Image
    The image is owned by GREPrepClub ©

    Of the first one - the strategy - it is your tool-box, in which you do have all the necessary devices to unhinge the GRE. Having and implementing a thorough strategy is easier to say than do. What we do know as a rule of thumb is that we must have a strategy, a plan. On one hand, a poor strategy will lead us to fail, om the other hand a too much-complicated plan will position us in a sort of labyrinth from which the exist could be far from reach.

    I remember while ago to watch an interview with one of the most prominent fitness athlete, a person well respected far beyond the muscle and fitness world. He explained very clearly how to perform a very productive and effective workout, we should hit from different angles the target muscle to gain the most benefits. However, a too cumbersome and not well-focused strategy, even though it is a good one, is detrimental as well.
    The right approach is a so-called: balanced-approach.

    From the graph above, your plan should comprise of four main areas. As it turns out, those are made of several sub-lines of strategy which will drive you to a top score.
    Actually, your main goal is: you must be strategy-driven.

    For our purpose is enough that we take into account these four areas without descending in faultfinding ramifications.
    The first and foremost thing to notice, I bet on this all my music CDs collection (yes I still collect them, and I love to do, to be honest), is that everybody starts looking clock-wise the macro-area of study and move forward, usually. This is right and wrong at the same time because if you think so, you have already violated what the 1 macro-area teaches you: a flexible approach.

    The more your strategy is consistency and you cope every single question (both quant and verbal, is the same) using all the areas via a holistic approach, the more your learning curve is steep.

    Image

    A steep learning curve means that you make rapid progress. This is the part in the middle of above plot where things are starting to make sense and you move ahead quickly – this is where learning is easiest! Probably the term "steep" came to be because you can consider its figural meaning: if you hike on a learning curve, steep is probably associated with frustration and strenuous climbing. Instead, a steep curve is exactly contrary the common belief.

    Before to delve one hundred % into the specify parts of our interest, let's take a closer look to the same question of before

    Quote:
    A cube of cheese is 3-inches high. The cheese is sliced twice.


    Quantity A
    Quantity B
    Resulting surface area of all the slices of cheese
    90 square inches


    The solution is here.




    Now, a little digression: we are talking again and again and again that you must have a strategy but at the same time this concept could be abstract. However, the strategy is something realized in your brain in operation.

    • A flexible approach is the key mindset. In the question above, my mental stretching muscles start to work on and they suggest to me: which is the best way to approach this ?? should I use picking number or some kind of formula to find the cube's area ?? is better to start to scratch my paper something?
    • Problem recognition is very familiar, like a second skin. This is a geometry problem for sure. So far so good. However, is algebra or number properties implied in the process ?? or is there something hidden, tricky, that I should know ??
    • Principle and calculus walk hand in hand. I think is much better and faster to solve picking some good number and see where this way will bring me or is better a more powerful up-front work, theoretically ??
    • Your question-solving pace is workflowing. I should solve this question on average in a minute. How much time this question is taking to me ?? Am I going to be stuck somehow or I will come to an end with the right answer pretty fast ??

    As you can clearly see, every stage of your strategy work, in conjunction, inside your brain. Your cerebral mechanism is working at its finest. My question recognition is saying to me it is a geometry problem which is best attacked through an analytical approach, which is a very resilient process. I am going to solve the question in 20 seconds. Done. Perfect.

    If you spot immediately that the area of the resultant solids is vastly varying between them and that if you cut two really thin slices and rest of the block is intact then the area would be different from when the block is sliced from the middle, the die is cast, the answer id D. Twenty seconds approach to solving it, very flexible, my flowing is at the top, like a race car, no wasting time in calculus. My strategy worked like a charm AND my learning curve is going to be very steep. Bingo

    Episode 2 - The four Horsemen

    • Quantitative Comparison Question ---------- > Full strategies and tips. Completed.
    • Problem Solving ---------- > Full strategies and tips. Soon
    • Numeric Entry ------------ > Full strategies and tips. Soon.
    • Data Interpretation ----------- > Full strategies and tips. Soon.


In the next chapters, we are going to tackle every kind of questions you will encounter in the two sections of the test. Keep in mind that who performs well in the first quant section of the same test, then will cope with a harder quant section later on. The following image reports the verbal section but the way the GRE CAT exam works is alike for the quant counterpart.

Image
Source: 800score.com
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Re: All you Need to Know about Quantitative Reasoning [#permalink] New post 18 Aug 2018, 21:20
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Thanks a lot for this useful post....It would be really helpful if you could take the time to complete this mammoth of a task sometime soon. I have my gre exam coming up and I find your posts quite helpful. Thanks again.

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Re: All you Need to Know about Quantitative Reasoning [#permalink] New post 19 Aug 2018, 00:59
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I will.

I hope you read for now the QCQ link at the bottom.

https://greprepclub.com/forum/quantitat ... 10440.html

The other 3 sections will be soon completed.

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Re: GRE - All you Need to Know about Quantitative Reasoning [#permalink] New post 30 Oct 2018, 07:31
Thanks a lot for your help!
Re: GRE - All you Need to Know about Quantitative Reasoning   [#permalink] 30 Oct 2018, 07:31
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