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Solve this question.\u00a0 Allot yourself a strict 1.5 minute time limit.<\/p>\n
1) In the figure, ABCD is a square, and all the dots are evenly spaced: each vertical or horizontal distance between two adjacent dots is 3 units.\u00a0 Find the area of the shaded region.<\/p>\n An explanation will follow below.<\/p>\n <\/p>\n Some people find GRE Math<\/a> hard because they are rusty at math in general: this post is not primarily addressed at those folks, although they may pick up some GRE math tips<\/a> from reading this.\u00a0 There’s no substitute for learning the basic math content you need.<\/p>\n Other people are reasonably comfortable with the math itself, but often complain: “I could<\/em> do most GRE Quant problems if I had enough time, but I always seem to run out of time.” \u00a0“I just wish I could do GRE math faster.” Does this sound like something you have said?\u00a0 Then this is precisely the post for you.<\/p>\n <\/p>\n First, a quick overview of hemispheric differences in the brain — this will be review for some people.\u00a0 The cerebrum, the “intelligence” part of our brain, is divided into two halves: the left & right hemisphere.\u00a0 These control all the sensation & muscular movements on the opposite side of the body — if you want to move your left leg, it’s the right half of your brain that oversees this task.\u00a0 The two hemispheres also process\u00a0 information very differently.\u00a0 Here is a brief overview of hemispheric difference: notice which set of skills feels more comfortable, more natural to you.<\/p>\n The left hemisphere is about logic, organization, precision, and detail management.\u00a0 It specializes in differentiation<\/strong>, that is, telling the exact difference between closely related things. It’s very good at following clear rules, recipes, formulas, and procedures in a step-by-step logical way.\u00a0 The left brain controls the grammar and syntax of language, the formal, almost “mathematical”, side of language.\u00a0 If I were to say, “I are happy,” it would be your left brain that recognizes this as wrong.<\/p>\n The right hemisphere is intuition and pattern-matching.\u00a0 It specializes in integration<\/strong>, that is, seeing the underlying similarity or unity behind seemingly distinct things.\u00a0 We dream in the right brain.\u00a0 The right brain is responsible for myth, poetry, analogy and metaphor.\u00a0 It is often called the “artistic” side of the brain.\u00a0 It is good at information presented as symbols or images.\u00a0 It is good at facial recognition and voice recognition (notoriously hard problems for computers!)\u00a0 The left brain does grammar and syntax, but the right brain controls a very different side of language: emotional inflection, body language, innuendo and implication.\u00a0 If person A says “Today is a great day!” in a completely bright and bubbly way in all sincerity, and then person B says “Today is a great day!” in a way that is absolutely dripping with bitter sarcasm — then, according to the left brain, exactly the same thing was said twice (same grammar, same syntax, etc.); it’s only the right brain that senses the profound emotional difference between those two statements.<\/p>\n Most folks are naturally dominant in one of the two hemispheres.\u00a0 There is some association with handedness and hemispheric dominance: left-handed people are slightly more likely to be right-brain dominant.\u00a0 The extreme left-brain folks are hyper-organized and methodical, for example, an accountant.\u00a0 The extreme right-brain people are the wild artsy folks, or folks who live from one leap of intuition to the next.<\/p>\n <\/p>\n Which hemisphere is better for math?\u00a0 Well, the detail-management and organization and precision of the left-brain are a huge help in arithmetic and algebra.\u00a0 Geometry is the only branch of math in which the right-brain pattern-matching skills can play some role.\u00a0 In general, left brain folks usually feel reasonably comfortable with math, and certainly can follow the methodical procedures with ease.\u00a0 Typically, the right brain folks tend to have a difficult time keeping all the details straight, although many times they tune into the “big picture” ideas faster.<\/p>\n Those are tendencies, but success in math — and in fact, success in almost anything that challenges our intelligence — involves developing both sides of the brain.\u00a0 One of the reasons Leonardo de Vinci<\/a> is often regarded as one of the smartest people ever to walk the earth is because he demonstrated strong skills of both hemispheres.<\/p>\n What does this mean for your GRE Quant performance?\u00a0 Well, if you are a typical right brain person, you probably need to sharpen your understanding of all the rules and all the details, and learn to manage details with precision.\u00a0 That’s something that comes with practice, practice, practice<\/a>.\u00a0 You may find this GMAT blog article<\/a> useful, because it talks about learning math rules in a holistic way.<\/p>\n <\/p>\n Now, for the left-brain folks: you probably know the rules reasonably well.\u00a0 You probably were generally a “good-at-math” kind of student.\u00a0 Probably, faced with most GRE Quant questions, you could figure out the right answer, given enough time.\u00a0 The catch, of course, is that you don’t have unlimited time on the GRE: just 40 minutes for 25 questions, or a little more than 90 seconds per question.<\/p>\n An overwhelming number of GRE Quant are designed specifically to punishing someone who is overly left-brained.\u00a0 In other words, they are designed so that if you take the methodical, step-by-step plodding approach, then yes, you would eventually reach the answer, but it would take you a very long time.\u00a0 Whenever that’s the case in a question, there’s always a way to reframe the question, so that the solution becomes very quick, sometimes almost immediate.<\/p>\n Whenever you see yourself starting out on a very straightforward, step-by-step, long haul calculation, stop yourself.\u00a0 This is always the challenge for left brain folks, but you have to re-frame the question, to understand the task from a different angle.\u00a0 You are looking for the “Leonardo da Vinci” solution to the problem.<\/p>\n <\/p>\n Here, I will demonstrate with the practice problem.\u00a0 Yes, you could figure out separately the area of each triangle, each square, each trapezoid, and then add all those shapes together.\u00a0 That would take some time.\u00a0 Here’s a right brain solution to this question — rearrange the pieces!<\/p>\n First, slide the red piece up.<\/p>\n Now, slide the green piece into that blank space.<\/p>\n Now, flip the orange piece over diagonal BD.<\/p>\n Lo and behold!\u00a0 The shaded region accounts for exactly half the area of the big square.\u00a0 The big square is 12 x 12 = 144, so the shaded region is 144\/2 = 72.\u00a0 Answer = (B)<\/strong>.\u00a0 Once you see the trick, the pattern, there is only the most minimal of calculations needed.<\/p>\n BTW, another reasonably quick right-brain approach would be simply to count all the little triangles.<\/p>\n The original shaded figure can be broken into 16 equal triangles.\u00a0 The full square is 16 little squares, or 32 triangles.\u00a0 Therefore, the area of the shaded figure is exactly half the area of the square.<\/p>\n <\/p>\n Some right-brain readers might revel in such solution.\u00a0 Meanwhile, some left-brain folks might be frustrated or annoyed at this point: “Great!\u00a0 Now that it’s pointed out, yes, that’s an efficient way to solve, but how<\/em> am I supposed to see<\/em> that on my own?”<\/p>\n Mastering the strengths and skills of your non-dominant hemisphere is never an easy task, but it can be done.<\/p>\n There are a wild variety of things one can do to enhance right-brain function.\u00a0 Read poetry.\u00a0 Look at art.\u00a0 Make art.\u00a0 Read about patterns in comparative mythology.\u00a0 Free-associate.\u00a0 Imagine.\u00a0 Follow chains of word associations.\u00a0 Slow down and really look at things.\u00a0 For example, everyone in the world has seen and could recognize Leonardo’s Mona Lisa<\/em><\/a> painting, but have you ever really looked at it?\u00a0 If you stare at it for 15-20 minutes, really just sink into staring at it, you can see every possible human emotion run across that face.\u00a0 The left-brain is relatively quick: OK, Mona Lisa, I know that, done.\u00a0 The right-brain skills take more time to “warm up”, which is why you have to put your left-brain impatience on hold and really take some time with this.\u00a0 I used the Mona Lisa<\/em> as an example here, but you could use almost any classic image.\u00a0 All of these practices can help a left-brain person, over time, to get more in touch with right brain abilities.<\/p>\n 1. If the problem asks for the value of an expression involving variables, chance are good there will be some way to solve for the value of the expression directly, without solving for the individual variables.<\/p>\n 2. In “find the area of the shaded region” in which the region is particularly complicated (as in the practice question), look for a way to rearrange and simplify.<\/p>\n 3.\u00a0 If the problem is a geometry problem stated in words, always sketch a rough diagram, unless you can visualize the diagram directly.<\/p>\n 4.\u00a0 If the problem is purely numerical or algebraic, consider whether there would be a way to visualize the problem (number line, x-y plane, etc.)<\/p>\n Here is the plan I would recommend for the extreme left-brain thinker who wants to accelerate her or his learning and mastery of the right-brain skills.\u00a0 From this point forward, whenever you practice GRE Quant, first of all, always practice against a strict time limit.\u00a0 Furthermore, the criterion is no longer: did I get the correct answer?\u00a0 No.\u00a0 Even if you got the correct answer, compare your solution to the official solution: if your solution is a slow methodical approach, and the official solution shows a shortcut, then for your purposes, consider this a question you got wrong<\/strong>.\u00a0 For every such question, force yourself to write down, verbally, the nature of the shortcut, and what you should have done to “see” that shortcut.\u00a0 Force yourself to have to put it into words and explain it: that will strengthen your inter-hemispheric connections.\u00a0 As you collect more and more write-ups like this, periodically go back to re-read the collection.\u00a0 Keep doing this consistently, learning from your mistakes, and before you know it, you will start “seeing” the Leonard-da-Vinci solutions to GRE Quant problems!<\/p>\n <\/p>\n These are two questions on which elegant shortcuts are possible.<\/p>\n 1) http:\/\/gre.magoosh.com\/questions\/123<\/a><\/p>\n![\"\"](\"https:\/\/magoosh.com\/gre\/files\/2012\/09\/ldvagm_img1.jpg\")
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Introduction<\/h2>\n
The brain<\/h2>\n
Math and the brain<\/h2>\n
The magic of right brain thinking<\/h2>\n
Example: the practice problem<\/h2>\n
<\/a><\/p>\n<\/a><\/p>\n<\/a><\/p>\n<\/a><\/p>\nLearning to see<\/h2>\n
Tips for Doing GRE Math Faster<\/h2>\n
More practice<\/h2>\n