{"id":3257,"date":"2013-01-18T12:03:38","date_gmt":"2013-01-18T20:03:38","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=3257"},"modified":"2020-01-15T10:50:09","modified_gmt":"2020-01-15T18:50:09","slug":"mathematical-thinking-on-the-gmat","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/mathematical-thinking-on-the-gmat\/","title":{"rendered":"Mathematical Thinking on the GMAT"},"content":{"rendered":"<p>What does the GMAT Quantitative section test?\u00a0 Math, of course.\u00a0 As tautological as that may seem, there is a very subtle point here.\u00a0 What exactly is math?<\/p>\n<p>&nbsp;<\/p>\n<h2>Mathematics<\/h2>\n<p>Strange as it may seem, there is no generally accepted formal definition of the word mathematics.\u00a0 Most of the dictionary definitions, for example, cover the more familiar branches of mathematics, but not, say, typical Ph.D. dissertation topics in math.\u00a0 One aspect of math has to do with logical relationships and logical deductions &#8212; we could call this the more left brain part of math.\u00a0 Another aspect of math has to do with identifying formal abstract patterns.\u00a0\u00a0 The words &#8220;logic&#8221; and &#8220;patterns&#8221; give two very important clues.\u00a0 For the first, you really understand a mathematic topic when you understand all the logical connections &#8212;- for example, knowing not just the rule for adding <a href=\"https:\/\/magoosh.com\/gmat\/fractions-on-the-gmat\/\">fractions<\/a>, but understanding why fractions have to be added that way.\u00a0\u00a0 The second is relevant because several <a href=\"https:\/\/magoosh.com\/gmat\/how-to-do-gmat-math-faster\/\">out-of-the-box<\/a> GMAT questions will throw some new situation at you, and you will have to identify what is the best way to parse the situation into recognizable components.\u00a0\u00a0 Perhaps even more important is understanding what math is not.<\/p>\n<p>&nbsp;<\/p>\n<h2>Mathematics and the GMAT Math Review<\/h2>\n<p>I believe if one were to ask many a GMAT test taker, &#8220;What math does one need to know for the GMAT?&#8221;, most people would indicate the content of the OG, the section entitled &#8220;Math Review.&#8221;\u00a0 This notion is simultaneously very helpful but slightly misleading.\u00a0\u00a0 Yes, those are the math facts you need to know &#8212; and if you&#8217;re rusty on them, as many folks are at the beginning of studying, it&#8217;s good to get very clear on them &#8212; but the math facts are not the same as mathematics.\u00a0 What&#8217;s the difference?<\/p>\n<p>Well, think of the difference between, say, the content of a French dictionary vs. the language of French in living dialogue.\u00a0 As helpful as a dictionary may be, no one goes from no knowledge of the language to fluency simply by relying on the dictionary.\u00a0\u00a0 In addition to knowing what each word means in isolation, one also has to know how it is used, in combination, in the context of real live communication.\u00a0 In this analogy, the &#8220;Math Review&#8221; communicates the meaning of each individual math factoid, and knowing these is essential, but the mathematics one really has to know is how to use these in problem-solving.\u00a0 If this is what\u00a0 you need to learn, you only find it by solving problem after problem, and carefully reading the solutions of each problem.<\/p>\n<p>When you read the solutions to a problem that baffled you, pay attention to (a) the logic of the argument connecting one step to the next &#8212; not just the math factoids, but the strategies employed, and (b) the patterns the solution points out and employs.\u00a0\u00a0 Any logic that is new to you or any patterns you didn&#8217;t see on your own &#8212; make a note of these, and return to them until you are confident you would be able to use these in the solution of a new problem on your own.<\/p>\n<p>&nbsp;<\/p>\n<h2>Formulas<\/h2>\n<p>Much in the same vein, a student can easily lean on formulas too much, and mistake this reliance on formulas for mathematical thinking.\u00a0\u00a0 Don&#8217;t memorize the formula for the sum of the first n integers.\u00a0 Don&#8217;t memorize the formula for <a href=\"https:\/\/magoosh.com\/gmat\/gmat-math-memory-vs-memorizing\/\">the area of an equilateral triangle<\/a>.\u00a0 Don&#8217;t memorize the formula for <a href=\"https:\/\/magoosh.com\/gmat\/gmat-coordinate-geometry-distance-between-two-points\/\">distance in the coordinate plane<\/a>.\u00a0 Yes, those are all things you may need to calculate in a GMAT question, but instead of memorizing a formula, I highly recommend understanding, step by step, the logical argument that underlies the formula.\u00a0\u00a0 Knowing the formula, by itself, is not mathematical thinking, but understanding the logic, the argument, that leads to the formula &#8212; that most certainly is mathematical thinking.<\/p>\n<p>There are very few formulas you should simply memorize.\u00a0 One that leaps to mind is <a href=\"http:\/\/en.wikipedia.org\/wiki\/Archimedes\" target=\"_blank\" rel=\"noopener noreferrer\">Archimedes<\/a>&#8216; formula for the area of a circle.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_3aedfac61b7579c075789cd245ab203c.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"A = {pi}r^2\" title=\"A = {pi}r^2\"\/><\/p>\n<p>Archimedes was one of the greatest mathematical geniuses of all time, and \u00a0he concocted a truly brilliant argument for why this formula had to be true.\u00a0 That argument, fascinating as it may be, is a bit more math than I would recommend for the average GMAT preparer.\u00a0 On this one, I would say: take a pass &#8212; just memorize this formula by rote, if you don&#8217;t already have it memorized from school.\u00a0 Having said that, I can&#8217;t think of any other GMAT formula about which I unreservedly would say the same thing.\u00a0 For every other formula, do not settle for rote memorization.\u00a0 Strive to understand the underlying logic.<\/p>\n<p>&nbsp;<\/p>\n<h2>Summary<\/h2>\n<p>St. Paul\u00a0 wrote &#8220;<em>the letter killeth but the spirit giveth life<\/em>&#8221; (2 Cor. 3:6).\u00a0 While this is arguably an over-dramatic analogy in context here, the sense of it holds.\u00a0 Mathematical thinking is a vital fluency with math, and you won&#8217;t find it printed on the page of the GMAT &#8220;Math Review.&#8221;\u00a0 What&#8217;s on those pages is necessary but not sufficient.\u00a0 Here are a few problems, for practicing mathematical thinking.<\/p>\n<p>1) <a href=\"http:\/\/gmat.magoosh.com\/questions\/880\">http:\/\/gmat.magoosh.com\/questions\/880<\/a><\/p>\n<p>2) <a href=\"http:\/\/gmat.magoosh.com\/questions\/59\">http:\/\/gmat.magoosh.com\/questions\/59<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What does the GMAT Quantitative section test?\u00a0 Math, of course.\u00a0 As tautological as that may seem, there is a very subtle point here.\u00a0 What exactly is math? &nbsp; Mathematics Strange as it may seem, there is no generally accepted formal definition of the word mathematics.\u00a0 Most of the dictionary definitions, for example, cover the more [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[150],"tags":[],"ppma_author":[13209],"class_list":["post-3257","post","type-post","status-publish","format-standard","hentry","category-basics"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mathematical Thinking on the GMAT - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gmat\/mathematical-thinking-on-the-gmat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematical Thinking on the GMAT\" \/>\n<meta property=\"og:description\" content=\"What does the GMAT Quantitative section test?\u00a0 Math, of course.\u00a0 As tautological as that may seem, there is a very subtle point here.\u00a0 What exactly is math? &nbsp; 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Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations.","sameAs":["https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured"],"award":["Magna cum laude from Harvard"],"knowsAbout":["GMAT"],"knowsLanguage":["English"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":13209,"user_id":26,"is_guest":0,"slug":"mikemcgarry","display_name":"Mike M\u1d9cGarry","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","user_url":"","last_name":"M\u1d9cGarry","first_name":"Mike","description":"Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/3257","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=3257"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/3257\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=3257"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=3257"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=3257"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=3257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}