{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2018-01-29T04:11:40+00:00","modifiedTime":"2018-01-29T04:11:40+00:00","timestamp":"2022-09-14T18:16:12+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"GMAT","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33784"},"slug":"gmat","categoryId":33784}],"title":"GMAT Quantitative Problem Solving: Practice with Algebra","strippedTitle":"gmat quantitative problem solving: practice with algebra","slug":"gmat-quantitative-problem-solving-practice-algebra","canonicalUrl":"","seo":{"metaDescription":"Some Problem Solving questions in the Quantitative section of the GMAT will involve algebra. You should be prepared to deal with polynomials, linear equations a","noIndex":0,"noFollow":0},"content":"Some Problem Solving questions in the Quantitative section of the GMAT will involve algebra. You should be prepared to deal with polynomials, linear equations and inequalities, quadratic equations, basic function concepts, and systems of linear equations.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n \t<li><strong>Given the function,</strong>\r\n\r\n<img class=\"alignnone size-full wp-image-249345\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0801.jpg\" alt=\"GMAT_0801\" width=\"173\" height=\"59\" />\r\n\r\nwhich of the following expressions is equivalent to\r\n\r\n<img class=\"alignnone size-full wp-image-249297\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0802.jpg\" alt=\"GMAT_0802\" width=\"112\" height=\"381\" /></li>\r\n \t<li><strong>What is the maximum value of <em>P</em> = 2<em>x</em> + 5<em>y</em> subject to the constraints</strong>\r\n\r\n<img class=\"alignnone size-full wp-image-249346\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0803.jpg\" alt=\"GMAT_0803\" width=\"252\" height=\"23\" />\r\n\r\n<strong>A.</strong> 3.5\r\n<strong>B.</strong> 8.75\r\n<strong>C.</strong> 12\r\n<strong>D.</strong> 12.25\r\n<strong>E.</strong> 14</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li><strong>The correct answer is C.</strong>\r\n\r\nFind\r\n\r\n<img class=\"alignnone size-full wp-image-249296\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0804.jpg\" alt=\"GMAT_0804\" width=\"44\" height=\"52\" />\r\n\r\nand simplify.\r\n\r\n<img class=\"alignnone size-full wp-image-249347\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0805.jpg\" alt=\"GMAT_0805\" width=\"155\" height=\"367\" /></li>\r\n \t<li><strong>The correct answer is C.</strong>\r\n\r\nThe three constraint inequalities define a region in the <em>xy</em>-plane that represents their intersections. The region's boundary equations are <em>x</em> = <em>y</em>, 3<em>x</em> – <em>y</em> = 1, and 3<em>x</em> + <em>y</em> = 5. The maximum value of <em>P</em> will occur at one of the intersections of these three linear equations. To find the maximum value of <em>P</em>, systematically pair the three equations and solve for their intersections. Solving <em>x</em> = <em>y</em> and 3<em>x</em> – <em>y</em> = 1 by substitution yields\r\n\r\n<img class=\"alignnone size-full wp-image-249298\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0806.jpg\" alt=\"GMAT_0806\" width=\"108\" height=\"159\" />\r\n\r\nThus, the intersection of <em>x</em> = <em>y</em> and 3<em>x</em> – <em>y</em> = 1 is\r\n\r\n<img class=\"alignnone size-full wp-image-249348\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0807.jpg\" alt=\"GMAT_0807\" width=\"53\" height=\"52\" />\r\n\r\nSolving <em>x</em> = <em>y</em> and 3<em>x</em> + <em>y</em> = 5 by substitution yields\r\n\r\n<img class=\"alignnone size-full wp-image-249349\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0810.jpg\" alt=\"GMAT_0810\" width=\"108\" height=\"159\" />\r\n\r\nThus, the intersection of <em>x</em> = <em>y</em> and 3<em>x</em> + <em>y</em> = 5 is\r\n\r\n<img class=\"alignnone size-full wp-image-249299\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0811.jpg\" alt=\"GMAT_0811\" width=\"55\" height=\"52\" />\r\n\r\nSolving 3<em>x</em> – <em>y</em> = 1 and 3<em>x</em> + <em>y</em> = 5 by elimination yields\r\n\r\n<img class=\"alignnone size-full wp-image-249300\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0812.jpg\" alt=\"GMAT_0812\" width=\"232\" height=\"148\" />\r\n\r\nThus, the intersection of 3<em>x</em> – <em>y</em> = 1 and 3<em>x</em> + <em>y</em> = 5 is (1,2). Substitute the intersection points into <em>P</em> = 2<em>x</em> + 5<em>y</em> to find the maximum:\r\n\r\n<img class=\"alignnone size-full wp-image-249350\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0813.jpg\" alt=\"GMAT_0813\" width=\"352\" height=\"156\" />\r\n\r\nTherefore, subject to the given constraints, the maximum value of <em>P</em> is 12, which occurs at (1,2).</li>\r\n</ol>","description":"Some Problem Solving questions in the Quantitative section of the GMAT will involve algebra. You should be prepared to deal with polynomials, linear equations and inequalities, quadratic equations, basic function concepts, and systems of linear equations.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n \t<li><strong>Given the function,</strong>\r\n\r\n<img class=\"alignnone size-full wp-image-249345\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0801.jpg\" alt=\"GMAT_0801\" width=\"173\" height=\"59\" />\r\n\r\nwhich of the following expressions is equivalent to\r\n\r\n<img class=\"alignnone size-full wp-image-249297\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0802.jpg\" alt=\"GMAT_0802\" width=\"112\" height=\"381\" /></li>\r\n \t<li><strong>What is the maximum value of <em>P</em> = 2<em>x</em> + 5<em>y</em> subject to the constraints</strong>\r\n\r\n<img class=\"alignnone size-full wp-image-249346\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0803.jpg\" alt=\"GMAT_0803\" width=\"252\" height=\"23\" />\r\n\r\n<strong>A.</strong> 3.5\r\n<strong>B.</strong> 8.75\r\n<strong>C.</strong> 12\r\n<strong>D.</strong> 12.25\r\n<strong>E.</strong> 14</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li><strong>The correct answer is C.</strong>\r\n\r\nFind\r\n\r\n<img class=\"alignnone size-full wp-image-249296\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0804.jpg\" alt=\"GMAT_0804\" width=\"44\" height=\"52\" />\r\n\r\nand simplify.\r\n\r\n<img class=\"alignnone size-full wp-image-249347\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0805.jpg\" alt=\"GMAT_0805\" width=\"155\" height=\"367\" /></li>\r\n \t<li><strong>The correct answer is C.</strong>\r\n\r\nThe three constraint inequalities define a region in the <em>xy</em>-plane that represents their intersections. The region's boundary equations are <em>x</em> = <em>y</em>, 3<em>x</em> – <em>y</em> = 1, and 3<em>x</em> + <em>y</em> = 5. The maximum value of <em>P</em> will occur at one of the intersections of these three linear equations. To find the maximum value of <em>P</em>, systematically pair the three equations and solve for their intersections. Solving <em>x</em> = <em>y</em> and 3<em>x</em> – <em>y</em> = 1 by substitution yields\r\n\r\n<img class=\"alignnone size-full wp-image-249298\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0806.jpg\" alt=\"GMAT_0806\" width=\"108\" height=\"159\" />\r\n\r\nThus, the intersection of <em>x</em> = <em>y</em> and 3<em>x</em> – <em>y</em> = 1 is\r\n\r\n<img class=\"alignnone size-full wp-image-249348\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0807.jpg\" alt=\"GMAT_0807\" width=\"53\" height=\"52\" />\r\n\r\nSolving <em>x</em> = <em>y</em> and 3<em>x</em> + <em>y</em> = 5 by substitution yields\r\n\r\n<img class=\"alignnone size-full wp-image-249349\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0810.jpg\" alt=\"GMAT_0810\" width=\"108\" height=\"159\" />\r\n\r\nThus, the intersection of <em>x</em> = <em>y</em> and 3<em>x</em> + <em>y</em> = 5 is\r\n\r\n<img class=\"alignnone size-full wp-image-249299\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0811.jpg\" alt=\"GMAT_0811\" width=\"55\" height=\"52\" />\r\n\r\nSolving 3<em>x</em> – <em>y</em> = 1 and 3<em>x</em> + <em>y</em> = 5 by elimination yields\r\n\r\n<img class=\"alignnone size-full wp-image-249300\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0812.jpg\" alt=\"GMAT_0812\" width=\"232\" height=\"148\" />\r\n\r\nThus, the intersection of 3<em>x</em> – <em>y</em> = 1 and 3<em>x</em> + <em>y</em> = 5 is (1,2). Substitute the intersection points into <em>P</em> = 2<em>x</em> + 5<em>y</em> to find the maximum:\r\n\r\n<img class=\"alignnone size-full wp-image-249350\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0813.jpg\" alt=\"GMAT_0813\" width=\"352\" height=\"156\" />\r\n\r\nTherefore, subject to the given constraints, the maximum value of <em>P</em> is 12, which occurs at (1,2).</li>\r\n</ol>","blurb":"","authors":[{"authorId":11243,"name":"Sandra Luna McCune","slug":"sandra-luna-mccune","description":" <p><b>Sandra Luna McCune, PhD,</b> is professor emeritus and a former Regents professor at Stephen F. Austin State University. She's now a full-time author. <b>Shannon Reed, MA, MFA,</b> is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/11243"}},{"authorId":10930,"name":"Shannon Reed","slug":"shannon-reed","description":" <p><b>Sandra Luna McCune, PhD,</b> is professor emeritus and a former Regents professor at Stephen F. Austin State University. She's now a full-time author. <b>Shannon Reed, MA, MFA,</b> is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/10930"}}],"primaryCategoryTaxonomy":{"categoryId":33784,"title":"GMAT","slug":"gmat","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33784"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":249437,"title":"GMAT Verbal Section: Practice with Sentence Completion","slug":"gmat-verbal-section-practice-sentence-completion","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249437"}},{"articleId":249434,"title":"GMAT Verbal Section: Practice with Critical Reasoning","slug":"gmat-verbal-section-practice-critical-reasoning","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249434"}},{"articleId":249431,"title":"GMAT Verbal Section: Practice with Reading Comprehension","slug":"gmat-verbal-section-practice-reading-comprehension","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249431"}},{"articleId":249422,"title":"GMAT Quantitative Data Sufficiency: Practice with Word Problems","slug":"gmat-quantitative-data-sufficiency-practice-word-problems","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249422"}},{"articleId":249416,"title":"GMAT Quantitative Data Sufficiency: Practice with Geometry","slug":"gmat-quantitative-data-sufficiency-practice-geometry","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249416"}}],"fromCategory":[{"articleId":283513,"title":"The Coordinate Plane and the GMAT","slug":"the-coordinate-plane-and-the-gmat","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/283513"}},{"articleId":283506,"title":"Multi-Source Reasoning Questions on the GMAT","slug":"multi-source-reasoning-questions-on-the-gmat","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/283506"}},{"articleId":283501,"title":"Table Analysis Questions on the GMAT","slug":"table-analysis-questions-on-the-gmat","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/283501"}},{"articleId":283496,"title":"What the GMAT's Integrated Reasoning Section Is All About","slug":"what-the-gmats-integrated-reasoning-section-is-all-about","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/283496"}},{"articleId":249437,"title":"GMAT Verbal Section: Practice with Sentence Completion","slug":"gmat-verbal-section-practice-sentence-completion","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249437"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282245,"slug":"gmat-1001-practice-questions-for-dummies","isbn":"9781119363125","categoryList":["academics-the-arts","study-skills-test-prep","gmat"],"amazon":{"default":"https://www.amazon.com/gp/product/1119363128/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119363128/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119363128-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119363128/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119363128/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/gmat-1001-practice-questions-for-dummies-cover-9781119363125-204x255.jpg","width":204,"height":255},"title":"GMAT","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"11243\">Sandra Luna McCune, PhD,</b> is professor emeritus and a former Regents professor at Stephen F. 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GMAT Quantitative Problem Solving: Practice with Algebra

By: Sandra Luna McCune and Shannon Reed and

Updated: 01-29-2018

From The Book: GMAT

GMAT

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Some Problem Solving questions in the Quantitative section of the GMAT will involve algebra. You should be prepared to deal with polynomials, linear equations and inequalities, quadratic equations, basic function concepts, and systems of linear equations.

Practice questions

Given the function,
which of the following expressions is equivalent to
What is the maximum value of P = 2x + 5y subject to the constraints
A. 3.5 B. 8.75 C. 12 D. 12.25 E. 14

Answers and explanations

The correct answer is C.
Find
and simplify.
The correct answer is C.
The three constraint inequalities define a region in the xy-plane that represents their intersections. The region's boundary equations are x = y, 3x – y = 1, and 3x + y = 5. The maximum value of P will occur at one of the intersections of these three linear equations. To find the maximum value of P, systematically pair the three equations and solve for their intersections. Solving x = y and 3x – y = 1 by substitution yields
Thus, the intersection of x = y and 3x – y = 1 is
Solving x = y and 3x + y = 5 by substitution yields
Thus, the intersection of x = y and 3x + y = 5 is
Solving 3x – y = 1 and 3x + y = 5 by elimination yields
Thus, the intersection of 3x – y = 1 and 3x + y = 5 is (1,2). Substitute the intersection points into P = 2x + 5y to find the maximum:
Therefore, subject to the given constraints, the maximum value of P is 12, which occurs at (1,2).

About This Article

This article is from the book:

GMAT ,

About the book authors:

Sandra Luna McCune, PhD, is professor emeritus and a former Regents professor at Stephen F. Austin State University. She's now a full-time author. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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