{"id":3621,"date":"2024-06-05T09:03:11","date_gmt":"2024-06-05T16:03:11","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=3621"},"modified":"2024-06-03T15:06:07","modified_gmt":"2024-06-03T22:06:07","slug":"three-algebra-formulas-essential-for-the-gmat","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/three-algebra-formulas-essential-for-the-gmat\/","title":{"rendered":"Essential GMAT Algebra Formulas and Practice Questions"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/files\/2020\/04\/image-gmat-header-algebra101.jpg\" alt=\"a graph paper with scratch work that could be on gmat algebra -image by magoosh\" width=\"1200\" height=\"600\" class=\"aligncenter size-full wp-image-9483\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2020\/04\/image-gmat-header-algebra101.jpg 1200w, https:\/\/magoosh.com\/gmat\/files\/2020\/04\/image-gmat-header-algebra101-300x150.jpg 300w, https:\/\/magoosh.com\/gmat\/files\/2020\/04\/image-gmat-header-algebra101-600x300.jpg 600w, https:\/\/magoosh.com\/gmat\/files\/2020\/04\/image-gmat-header-algebra101-768x384.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>This post was updated in 2024 for the new GMAT.<\/strong><\/p>\n<p>What are the most essential topics of algebra that you need to know to succeed in <a href=\"https:\/\/gmat.magoosh.com\/lessons\/307-intro-to-gmat-math?utm_source=gmatblog&#038;utm_medium=blog&#038;utm_campaign=algebra-formulas&#038;utm_term=inline\">GMAT math<\/a>? How many formulas and equations do you have to memorize? Why must we be tortured by all this math???<\/p>\n<p>The good news is that it doesn&#8217;t take a huge amount of time or energy to master the basics. Most likely, you already have the fundamentals down. <\/p>\n<p><img decoding=\"async\" class=\"wp-image-19356  alignleft\" src=\"https:\/\/magoosh.com\/gre\/files\/2019\/09\/teachvid_fill-e1570164158808.png\" alt=\"magoosh video lesson icon with human figure\" width=\"93\" height=\"48\" data-wp-editing=\"1\" \/> Of course, it never hurts to review, so you might want to check out these first: <a href=\"https:\/\/gmat.magoosh.com\/lessons\/230-intro-to-algebra?utm_source=gmatblog&#038;utm_medium=blog&#038;utm_campaign=algebra-formulas&#038;utm_term=inline\">Introduction to Algebra<\/a> and <a href=\"https:\/\/magoosh.com\/gmat\/foil-on-the-gmat-simplifying-and-expanding\/\">FOIL on the GMAT: Simplifying and Expanding<\/a>.<\/li>\n<\/ul>\n<p>&nbsp;<br \/>\nThis post is intended to help you gain the edge if you already have a solid foundation. By recognizing and taking advantage of some common algebraic expressions or patterns, and by <strong>remembering<\/strong> rather than <strong>memorizing.<\/strong> <\/p>\n<h2>Table of Contents<\/h2>\n<ul>\n<li><a href=\"#formula\">Three Essential Formulas for GMAT Algebra<\/a><\/li>\n<li><a href=\"#practice\">GMAT Algebra Practice Problems<\/a>\n<ul>\n<li><a href=\"#problemsolving\">Problem Solving Questions<\/a><\/li>\n<\/ul>\n<p><a name=\"formula\"><\/a><\/p>\n<h2>Three Essential Formulas for GMAT Algebra<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/files\/2012\/02\/pattern-matching.png\" alt=\"GMAT Algebra Patterns -- filling in the pieces of a puzzle\" width=\"344\" height=\"251\" class=\"aligncenter size-full wp-image-903\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2012\/02\/pattern-matching.png 688w, https:\/\/magoosh.com\/gmat\/files\/2012\/02\/pattern-matching-300x219.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><\/p>\n<p>Here are two algebraic equations and one formula that you should <strong>remember<\/strong> for the GMAT Quant section. <\/p>\n<ol>\n<li><strong><a href=\"https:\/\/magoosh.com\/gmat\/gmat-quant-difference-of-two-squares\/\">Difference of Two Squares<\/a>:<\/strong>  \\(a^2 &#8211; b^2 = (a-b)(a+b) \\)<\/li>\n<li><strong>Squaring a Binomial:<\/strong>  \\((a \\pm b)^2 = a^2 \\pm 2ab + b^2 \\)<\/li>\n<li><strong>The Discriminant:<\/strong>  \\(D = b^2 &#8211; 4ac \\)<\/li>\n<\/ol>\n<p>There is a common theme among the three items. In one way or another, they all have something to do with <strong>quadratic expressions<\/strong>. These tend to be more difficult to work with than linear equations, simply because the tools look more complicated.<\/p>\n<h3>Using the Patterns<\/h3>\n<p>The first two items in the list pertain to factoring\u2014you can check out this post for more on that topic: <a href=\"https:\/\/magoosh.com\/gmat\/algebra-on-the-gmat-how-to-factor\/\">Algebra on the GMAT: How to Factor<\/a>.<\/p>\n<p>The idea is that you can replace the expression on the left of the equals sign by the one on the right, and vice versa. This technique is often used in simplifying algebraic expressions. The practice problems below will also help you to understand when to use this strategy. The third item, the <strong>discriminant<\/strong>, is a powerful tool to help analyze the roots of quadratic equations without ever having to find the roots explicitly. <\/p>\n<p><img decoding=\"async\" class=\"wp-image-19356  alignleft\" src=\"https:\/\/magoosh.com\/gre\/files\/2019\/09\/teachvid_fill-e1570164158808.png\" alt=\"magoosh video lesson icon with purple figure\" width=\"93\" height=\"48\" data-wp-editing=\"1\" \/> To see these concepts in action, check out our lesson videos on <a href=\"https:\/\/gmat.magoosh.com\/lessons\/238-factoring-rational-expressions?utm_source=gmatblog&#038;utm_medium=blog&#038;utm_campaign=algebra-formulas&#038;utm_term=inline\">Factoring &#8211; Rational Expressions<\/a> and <a href=\"https:\/\/gmat.magoosh.com\/lessons\/241-quadratic-equations?utm_source=gmatblog&#038;utm_medium=blog&#038;utm_campaign=algebra-formulas&#038;utm_term=inline\">Quadratic Equations<\/a>. <\/p>\n<p><a name=\"practice\"><\/a><\/p>\n<h2>GMAT Algebra Practice Problem<\/h2>\n<p>Now let&#8217;s see if we can apply what we learned to the following GMAT Quant question!<\/p>\n<p><a name=\"problemsolving\"><\/a><\/p>\n<h3>Problem Solving Questions<\/h3>\n<div class=\"mox\">\n<ol start=\"1\">\n<li> What is the largest integral value of  \\(m \\) such that the quadratic equation  \\(x^2 &#8211; 10x + m \\) will have two unique solutions?<\/li>\n<\/ol>\n<p><input type=\"radio\" id=\"Q2A\" name=\"choice-q2\" value=\"A\"><label for=\"Q2A\">A. \\(23 \\)<\/label><br \/>\n<input type=\"radio\" id=\"Q2B\" name=\"choice-q2\" value=\"B\"><label for=\"Q2B\">B. \\(24 \\)<\/label><br \/>\n<input type=\"radio\" id=\"Q2C\" name=\"choice-q2\" value=\"C\"><label for=\"Q2C\">C. \\(25 \\)<\/label><br \/>\n<input type=\"radio\" id=\"Q2D\" name=\"choice-q2\" value=\"D\"><label for=\"Q2D\">D. \\(26 \\)<\/label><br \/>\n<input type=\"radio\" id=\"Q2E\" name=\"choice-q2\" value=\"E\"><label for=\"Q2E\">E. \\(27 \\)<\/label><\/p>\n<details>\n<summary><font color=#005bc2>Click here for the answer<\/font><\/summary>\n<p>&nbsp;<br \/>\n<strong>B.<\/strong><\/p>\n<p>This question is <em>made<\/em> for the <strong>discriminant<\/strong>! You won&#8217;t have to guess and check if you know how to use the formula appropriately. To find  \\(D \\), plug in the following to the formula:<\/p>\n<p><span style=\"color: #4D2079;\">\\(a = 1 \\)<\/span><br \/>\n<span style=\"color: #c5168c;\">\\(b = -10 \\)<\/span><br \/>\n<span style=\"color: #4d2079;\">\\(c = m \\)<\/span><\/p>\n<p>\\(D =\\) <span style=\"color: #c5168c;\">\\(b^2\\)<\/span>\\( &#8211; 4\\)<span style=\"color: #4D2079;\">\\(a\\)<\/span><span style=\"color: #4d2079;\">\\(c\\)<\/span><br \/>\n\\(D =\\) <span style=\"color: #c5168c;\">\\((-10)^2\\)<\/span> \\(- 4\\)<span style=\"color: #4D2079;\">\\((1)\\)<\/span><span style=\"color: #4d2079;\">\\((m)\\)<\/span> \\(= 100 &#8211; 4m \\)<\/p>\n<p>Now, we know that we&#8217;re looking for two real solutions, so we want  \\(D = 100 &#8211; 4m &gt; 0 \\). <\/p>\n<p> \\(100 &#8211; 4m &gt; 0 \\implies 100 &gt; 4m \\implies 25 &gt; m \\)<\/p>\n<p>So, we get  \\(m &lt; 25 \\). Be careful NOT to choose 25 as your answer! The largest integer that is <em>less<\/em> than 25 would be 24.<\/details>\n<\/div>\n<h3>Final Thoughts<\/h3>\n<p>GMAT algebra questions do not have to be intimidating. Linear and quadratic expressions and their close relatives make up the bulk of the material that you need to know. By mastering the three essential formulas mentioned above, you will be well on your way to Complete GMAT Domination! <\/p>\n<p>If you&#8217;re looking for more GMAT algebra practice, check out our FREE <a href=\"https:\/\/gmat.magoosh.com\/practice_tests\/free?utm_source=gmatblog&#038;utm_medium=blog&#038;utm_campaign=gmatpracticetest&#038;utm_term=inline&#038;utm_content=three-algebra-formulas-essential-for-the-gmat\">GMAT practice test<\/a> with accurate score prediction and subject-by-subject performance breakdown. You can practice a single section like Math, Data Insights, or Verbal for 45 minutes or take the whole assessment for 2 hours and 15 minutes. Give it a try!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This post was updated in 2024 for the new GMAT. What are the most essential topics of algebra that you need to know to succeed in GMAT math? How many formulas and equations do you have to memorize? Why must we be tortured by all this math??? The good news is that it doesn&#8217;t take [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[138],"tags":[],"ppma_author":[13209],"class_list":["post-3621","post","type-post","status-publish","format-standard","hentry","category-algebra"],"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>Three Algebra Formulas Essential for the GMAT<\/title>\n<meta name=\"description\" content=\"GMAT algebra is similar to what you&#039;ve seen in past math classes. 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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\/3621","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=3621"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/3621\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=3621"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=3621"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=3621"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=3621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}