{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2018-01-30T02:03:22+00:00","modifiedTime":"2018-01-30T02:03:22+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 Geometry","strippedTitle":"gmat quantitative problem solving: practice with geometry","slug":"gmat-quantitative-problem-solving-practice-geometry","canonicalUrl":"","seo":{"metaDescription":"Some Problem Solving questions in the Quantitative section of the GMAT will involve geometry. You should know how to work with angles, lines, two-dimensional sh","noIndex":0,"noFollow":0},"content":"Some Problem Solving questions in the Quantitative section of the GMAT will involve geometry. You should know how to work with angles, lines, two-dimensional shapes, three-dimensional solids, perimeter, area, surface area, volume, the Pythagorean theorem, and coordinate geometry.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<em>The figure shows a triangle inscribed in a semicircle. </em>\r\n\r\n<img class=\"alignnone size-full wp-image-249290\" src=\"https://www.dummies.com/wp-content/uploads/9781119363125-fg0301.jpg\" alt=\"gmat-triangle-semi\" width=\"400\" height=\"211\" />\r\n<ol>\r\n \t<li>If <em>PQ</em> = 16 and <em>QR</em> = 12, what is the length of arc <em>PQR</em>?\r\n\r\n<img class=\"alignnone size-full wp-image-249368\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0901.jpg\" alt=\"GMAT_0901\" width=\"69\" height=\"159\" />\r\n\r\n<em>The figure shown is a rhombus in which the measure of angle A is 120 degrees.\r\n</em>\r\n<img class=\"alignnone size-full wp-image-249291\" src=\"https://www.dummies.com/wp-content/uploads/9781119363125-fg0302-NEW.jpg\" alt=\"gmat-rhombus\" width=\"500\" height=\"374\" /></li>\r\n \t<li>What is the ratio of the length of line <em>AC</em> to the length of line <em>DB</em>?\r\n\r\n<img class=\"alignnone size-full wp-image-249301\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0902.jpg\" alt=\"GMAT_0902\" width=\"88\" height=\"177\" /></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li>The correct answer is A.\r\n\r\nAn angle inscribed in a semicircle is a right angle. Thus, triangle <em>PQR</em> is a right triangle with legs of lengths 16 and 12. The length, <em>PR,</em> of the hypotenuse is\r\n\r\n<img class=\"alignnone size-full wp-image-249369\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0903.jpg\" alt=\"GMAT_0903\" width=\"288\" height=\"31\" />\r\n\r\nThus, the diameter of the semicircle is 20. The length of the arc <em>PQR</em> is half the circumference of the circle that contains the semicircle. This length is\r\n\r\n<img class=\"alignnone size-full wp-image-249302\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0904.jpg\" alt=\"GMAT_0904\" width=\"164\" height=\"45\" /></li>\r\n \t<li>The correct answer is D.\r\n\r\nConsecutive interior angles of a rhombus are supplementary, so the measure of\r\n\r\n<img class=\"alignnone size-full wp-image-249370\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0905.jpg\" alt=\"GMAT_0905\" width=\"176\" height=\"19\" />\r\n\r\nThe diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus. Construct the diagonals of the rhombus. Label the intersection <em>E.</em>\r\n\r\n<img class=\"alignnone size-full wp-image-249293\" src=\"https://www.dummies.com/wp-content/uploads/9781119363125-fg0803-NEW.jpg\" alt=\"gmat-bisector\" width=\"500\" height=\"374\" />\r\n\r\nThus, triangle <em>AED</em> is a\r\n\r\n<img class=\"alignnone size-full wp-image-249371\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0906.jpg\" alt=\"GMAT_0906\" width=\"113\" height=\"19\" />\r\n\r\nright triangle, with hypotenuse\r\n\r\n<img class=\"alignnone size-full wp-image-249372\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0907.jpg\" alt=\"GMAT_0907\" width=\"196\" height=\"28\" />\r\n\r\nGiven that the diagonals bisect each other, the length of line <em>AC</em> is twice the length of line <em>AE</em>, and the length of line <em>DB</em> is twice the length of line <em>DE</em>. Hence, the ratio of the length of line <em>AC</em> to the length of line <em>DB</em> is the same as the ratio of the length of line <em>AE</em> to the length of line <em>DE</em>. The lengths of the sides of a 30 – 60 – 90 right triangle are in the ratio\r\n\r\n<img class=\"alignnone size-full wp-image-249373\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0908.jpg\" alt=\"GMAT_0908\" width=\"69\" height=\"49\" />\r\n\r\nTherefore, the ratio of the length of line <em>AC</em> to line <em>DB</em> equals the ratio of the length of line <em>AE</em> to line <em>DE</em> equals\r\n\r\n<img class=\"alignnone size-full wp-image-249374\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0909.jpg\" alt=\"GMAT_0909\" width=\"53\" height=\"49\" />\r\n\r\nwhich is\r\n\r\n<img class=\"alignnone size-full wp-image-249375\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0910.jpg\" alt=\"GMAT_0910\" width=\"44\" height=\"28\" />\r\n\r\nin simplified form.</li>\r\n</ol>","description":"Some Problem Solving questions in the Quantitative section of the GMAT will involve geometry. You should know how to work with angles, lines, two-dimensional shapes, three-dimensional solids, perimeter, area, surface area, volume, the Pythagorean theorem, and coordinate geometry.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<em>The figure shows a triangle inscribed in a semicircle. </em>\r\n\r\n<img class=\"alignnone size-full wp-image-249290\" src=\"https://www.dummies.com/wp-content/uploads/9781119363125-fg0301.jpg\" alt=\"gmat-triangle-semi\" width=\"400\" height=\"211\" />\r\n<ol>\r\n \t<li>If <em>PQ</em> = 16 and <em>QR</em> = 12, what is the length of arc <em>PQR</em>?\r\n\r\n<img class=\"alignnone size-full wp-image-249368\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0901.jpg\" alt=\"GMAT_0901\" width=\"69\" height=\"159\" />\r\n\r\n<em>The figure shown is a rhombus in which the measure of angle A is 120 degrees.\r\n</em>\r\n<img class=\"alignnone size-full wp-image-249291\" src=\"https://www.dummies.com/wp-content/uploads/9781119363125-fg0302-NEW.jpg\" alt=\"gmat-rhombus\" width=\"500\" height=\"374\" /></li>\r\n \t<li>What is the ratio of the length of line <em>AC</em> to the length of line <em>DB</em>?\r\n\r\n<img class=\"alignnone size-full wp-image-249301\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0902.jpg\" alt=\"GMAT_0902\" width=\"88\" height=\"177\" /></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li>The correct answer is A.\r\n\r\nAn angle inscribed in a semicircle is a right angle. Thus, triangle <em>PQR</em> is a right triangle with legs of lengths 16 and 12. The length, <em>PR,</em> of the hypotenuse is\r\n\r\n<img class=\"alignnone size-full wp-image-249369\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0903.jpg\" alt=\"GMAT_0903\" width=\"288\" height=\"31\" />\r\n\r\nThus, the diameter of the semicircle is 20. The length of the arc <em>PQR</em> is half the circumference of the circle that contains the semicircle. This length is\r\n\r\n<img class=\"alignnone size-full wp-image-249302\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0904.jpg\" alt=\"GMAT_0904\" width=\"164\" height=\"45\" /></li>\r\n \t<li>The correct answer is D.\r\n\r\nConsecutive interior angles of a rhombus are supplementary, so the measure of\r\n\r\n<img class=\"alignnone size-full wp-image-249370\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0905.jpg\" alt=\"GMAT_0905\" width=\"176\" height=\"19\" />\r\n\r\nThe diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus. Construct the diagonals of the rhombus. Label the intersection <em>E.</em>\r\n\r\n<img class=\"alignnone size-full wp-image-249293\" src=\"https://www.dummies.com/wp-content/uploads/9781119363125-fg0803-NEW.jpg\" alt=\"gmat-bisector\" width=\"500\" height=\"374\" />\r\n\r\nThus, triangle <em>AED</em> is a\r\n\r\n<img class=\"alignnone size-full wp-image-249371\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0906.jpg\" alt=\"GMAT_0906\" width=\"113\" height=\"19\" />\r\n\r\nright triangle, with hypotenuse\r\n\r\n<img class=\"alignnone size-full wp-image-249372\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0907.jpg\" alt=\"GMAT_0907\" width=\"196\" height=\"28\" />\r\n\r\nGiven that the diagonals bisect each other, the length of line <em>AC</em> is twice the length of line <em>AE</em>, and the length of line <em>DB</em> is twice the length of line <em>DE</em>. Hence, the ratio of the length of line <em>AC</em> to the length of line <em>DB</em> is the same as the ratio of the length of line <em>AE</em> to the length of line <em>DE</em>. The lengths of the sides of a 30 – 60 – 90 right triangle are in the ratio\r\n\r\n<img class=\"alignnone size-full wp-image-249373\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0908.jpg\" alt=\"GMAT_0908\" width=\"69\" height=\"49\" />\r\n\r\nTherefore, the ratio of the length of line <em>AC</em> to line <em>DB</em> equals the ratio of the length of line <em>AE</em> to line <em>DE</em> equals\r\n\r\n<img class=\"alignnone size-full wp-image-249374\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0909.jpg\" alt=\"GMAT_0909\" width=\"53\" height=\"49\" />\r\n\r\nwhich is\r\n\r\n<img class=\"alignnone size-full wp-image-249375\" src=\"https://www.dummies.com/wp-content/uploads/GMAT_0910.jpg\" alt=\"GMAT_0910\" width=\"44\" height=\"28\" />\r\n\r\nin simplified form.</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. 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","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":[{"articleId":175788,"title":"Trig Identities for Pre-Calculus","slug":"trig-identities-for-pre-calculus","categoryList":["academics-the-arts","math","pre-calculus"],"_links":{"self":"/articles/175788"}},{"articleId":147241,"title":"How to Use the Z-Table","slug":"how-to-use-the-z-table","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"/articles/147241"}},{"articleId":192609,"title":"How to Pray the Rosary: A Comprehensive 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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 Geometry

By: Sandra Luna McCune and Shannon Reed and

Updated: 01-30-2018

From The Book: GMAT

GMAT

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Some Problem Solving questions in the Quantitative section of the GMAT will involve geometry. You should know how to work with angles, lines, two-dimensional shapes, three-dimensional solids, perimeter, area, surface area, volume, the Pythagorean theorem, and coordinate geometry.

Practice questions

The figure shows a triangle inscribed in a semicircle.

gmat-triangle-semi

If PQ = 16 and QR = 12, what is the length of arc PQR?
The figure shown is a rhombus in which the measure of angle A is 120 degrees.
What is the ratio of the length of line AC to the length of line DB?

Answers and explanations

The correct answer is A.
An angle inscribed in a semicircle is a right angle. Thus, triangle PQR is a right triangle with legs of lengths 16 and 12. The length, PR, of the hypotenuse is
Thus, the diameter of the semicircle is 20. The length of the arc PQR is half the circumference of the circle that contains the semicircle. This length is
The correct answer is D.
Consecutive interior angles of a rhombus are supplementary, so the measure of
The diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus. Construct the diagonals of the rhombus. Label the intersection E.
Thus, triangle AED is a
right triangle, with hypotenuse
Given that the diagonals bisect each other, the length of line AC is twice the length of line AE, and the length of line DB is twice the length of line DE. Hence, the ratio of the length of line AC to the length of line DB is the same as the ratio of the length of line AE to the length of line DE. The lengths of the sides of a 30 – 60 – 90 right triangle are in the ratio
Therefore, the ratio of the length of line AC to line DB equals the ratio of the length of line AE to line DE equals
which is
in simplified form.

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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