{"id":802,"date":"2012-02-06T16:01:52","date_gmt":"2012-02-07T00:01:52","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=802"},"modified":"2014-07-18T10:11:36","modified_gmt":"2014-07-18T17:11:36","slug":"gmat-math-understanding-absolute-values","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/","title":{"rendered":"GMAT Math: Understanding Absolute Values"},"content":{"rendered":"

GMAT Math will ask you about absolute values.\u00a0 Mastering the GMAT algebra<\/a> skills to answer them requires sophisticated understanding.<\/p>\n

Somewhere along the line, perhaps in middle school, you probably learned:<\/p>\n

 <\/p>\n

|positive| = positive and |negative| = positive<\/p>\n

 <\/p>\n

In other words, the equation |x| = 5 has the solution: x = 5 or<\/strong> x = \u22125.\u00a0 (Notice: the word “or” is not a garnish there; it’s actually an essential piece of mathematical equipment.)<\/p>\n

 <\/p>\n

Expanding the Pattern<\/h2>\n

That’s great, but the GMAT is simply not going to ask you to solve the equation |x| = 5.\u00a0 When the GMAT asks about absolute value, it’s going to be something more in the vein of |3x \u2013 7| = 5.\u00a0 The basic idea is (as is often the case in more advanced algebra) is to replace “x” in the simpler equation above with whatever “thing” is between the absolute value.\u00a0 If q is a positive constant, then<\/p>\n

|thing| = q<\/p>\n

has the solution:<\/p>\n

thing = q or<\/strong> thing = -q<\/p>\n

In the given example,<\/p>\n

|3x \u2013 7| = 5<\/p>\n

3x \u2013 7 = 5\u00a0or\u00a0<\/strong>3x \u2013 7 = -5<\/p>\n

3x = 12 or<\/strong> 3x = 2<\/p>\n

x = 4 or<\/strong> x =\u00a02\/3<\/p>\n

That’s an example of an absolute value equation<\/span>, which the GMAT could ask.\u00a0 The GMAT is even more likely to ask about an absolute value inequality.<\/p>\n

 <\/p>\n

Rethinking Absolute Value<\/h2>\n

OK, let’s face it.\u00a0 The definition of absolute value that says “keeps a positive positive, and makes a negative positive” \u2013 the utility of that definition peaks in middle school.\u00a0 We need to have a more sophisticated understanding of absolute value to handle everything the GMAT will ask of it.<\/p>\n

Here is the more sophisticated definition of absolute value.\u00a0 The absolute value of x, |x| is the distance<\/span> of x from zero on the number line<\/strong>.\u00a0 Of course, it’s always positive, because distance is away positive.<\/p>\n

To extend that further: |x \u2013 4| is the distance of x from 4; |x \u2013 7| is the distance of x from 7;|x + 3| is the distance of x from -3 (this is because x + 3 = x \u2013 (-3) when written as subtraction).<\/p>\n

That is profoundly important in solving the absolute value inequalities that the GMAT will ask of you.\u00a0 Suppose a GMAT Math question asks you: represent the region -1 < x < 9 as an absolute value inequality.<\/p>\n

The first step is to find the midpoint of the region: 4 is exactly halfway between -1 and 9.\u00a0 Now the distances: 9 is a distance of 5 from 4, and so is -1.\u00a0 So the distance from 4 (viz. |x \u2013 4|) can’t equal 5, but it can be anything up to 5.\u00a0 Thus<\/p>\n

|x \u2013 4|< 5<\/p>\n

is the absolute value inequality representation of the region -1 < x < 9.\u00a0 Integrate this understanding, and you will be able to handle anything the GMAT asks you about absolute value.<\/p>\n

 <\/p>\n

Here’s a free Magoosh practice problem, a challenging absolute value practice question<\/a>, with a video explanation of the answer.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

GMAT Math will ask you about absolute values.\u00a0 Mastering the GMAT algebra skills to answer them requires sophisticated understanding. Somewhere along the line, perhaps in middle school, you probably learned:   |positive| = positive and |negative| = positive   In other words, the equation |x| = 5 has the solution: x = 5 or x […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[138],"tags":[],"ppma_author":[13209],"class_list":["post-802","post","type-post","status-publish","format-standard","hentry","category-algebra"],"acf":[],"yoast_head":"\nGMAT Math: Understanding Absolute Values - 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\/gmat-math-understanding-absolute-values\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Math: Understanding Absolute Values\" \/>\n<meta property=\"og:description\" content=\"GMAT Math will ask you about absolute values.\u00a0 Mastering the GMAT algebra skills to answer them requires sophisticated understanding. Somewhere along the line, perhaps in middle school, you probably learned:   |positive| = positive and |negative| = positive   In other words, the equation |x| = 5 has the solution: x = 5 or x […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GMAT\u00ae Exam\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MagooshGMAT\/\" \/>\n<meta property=\"article:published_time\" content=\"2012-02-07T00:01:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2014-07-18T17:11:36+00:00\" \/>\n<meta name=\"author\" content=\"Mike M\u1d9cGarry\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mike M\u1d9cGarry\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"GMAT Math: Understanding Absolute Values\",\"datePublished\":\"2012-02-07T00:01:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/\"},\"wordCount\":466,\"commentCount\":21,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Algebra\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/\",\"name\":\"GMAT Math: Understanding Absolute Values - Magoosh Blog \u2014 GMAT\u00ae Exam\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\"},\"datePublished\":\"2012-02-07T00:01:52+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/gmat\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"GMAT Math: Understanding Absolute Values\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"name\":\"Magoosh Blog \u2014 GMAT\u00ae Exam\",\"description\":\"Everything you need to know about the GMAT\",\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/gmat\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\",\"name\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"contentUrl\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"width\":265,\"height\":60,\"caption\":\"Magoosh\"},\"image\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/MagooshGMAT\/\",\"https:\/\/twitter.com\/MagooshGMAT\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\",\"name\":\"Mike M\u1d9cGarry\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/image\/15a1e36ef1c2c3940179212433de141a\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"caption\":\"Mike M\u1d9cGarry\"},\"description\":\"Mike holds an A.B. in Physics (graduating magna cum laude) 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 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\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"GMAT Math: Understanding Absolute Values - Magoosh Blog \u2014 GMAT\u00ae Exam","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/","og_locale":"en_US","og_type":"article","og_title":"GMAT Math: Understanding Absolute Values","og_description":"GMAT Math will ask you about absolute values.\u00a0 Mastering the GMAT algebra skills to answer them requires sophisticated understanding. Somewhere along the line, perhaps in middle school, you probably learned:   |positive| = positive and |negative| = positive   In other words, the equation |x| = 5 has the solution: x = 5 or x […]","og_url":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/","og_site_name":"Magoosh Blog \u2014 GMAT\u00ae Exam","article_publisher":"https:\/\/www.facebook.com\/MagooshGMAT\/","article_published_time":"2012-02-07T00:01:52+00:00","article_modified_time":"2014-07-18T17:11:36+00:00","author":"Mike M\u1d9cGarry","twitter_card":"summary_large_image","twitter_creator":"@MagooshGMAT","twitter_site":"@MagooshGMAT","twitter_misc":{"Written by":"Mike M\u1d9cGarry","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/#article","isPartOf":{"@id":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/"},"author":{"name":"Mike M\u1d9cGarry","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b"},"headline":"GMAT Math: Understanding Absolute Values","datePublished":"2012-02-07T00:01:52+00:00","mainEntityOfPage":{"@id":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/"},"wordCount":466,"commentCount":21,"publisher":{"@id":"https:\/\/magoosh.com\/gmat\/#organization"},"articleSection":["GMAT Algebra"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/","url":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/","name":"GMAT Math: Understanding Absolute Values - Magoosh Blog \u2014 GMAT\u00ae Exam","isPartOf":{"@id":"https:\/\/magoosh.com\/gmat\/#website"},"datePublished":"2012-02-07T00:01:52+00:00","breadcrumb":{"@id":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/magoosh.com\/gmat\/gmat-math-understanding-absolute-values\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/magoosh.com\/gmat\/"},{"@type":"ListItem","position":2,"name":"GMAT Math: Understanding Absolute Values"}]},{"@type":"WebSite","@id":"https:\/\/magoosh.com\/gmat\/#website","url":"https:\/\/magoosh.com\/gmat\/","name":"Magoosh Blog \u2014 GMAT\u00ae Exam","description":"Everything you need to know about the GMAT","publisher":{"@id":"https:\/\/magoosh.com\/gmat\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/magoosh.com\/gmat\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/magoosh.com\/gmat\/#organization","name":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/","url":"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png","contentUrl":"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png","width":265,"height":60,"caption":"Magoosh"},"image":{"@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/MagooshGMAT\/","https:\/\/twitter.com\/MagooshGMAT"]},{"@type":"Person","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b","name":"Mike M\u1d9cGarry","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/image\/15a1e36ef1c2c3940179212433de141a","url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","caption":"Mike M\u1d9cGarry"},"description":"Mike holds an A.B. in Physics (graduating magna cum laude) 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 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\/802","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=802"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/802\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=802"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=802"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=802"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}