{"id":21151,"date":"2022-05-01T15:25:00","date_gmt":"2022-05-01T09:55:00","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21151"},"modified":"2022-11-16T22:59:54","modified_gmt":"2022-11-16T17:29:54","slug":"in-the-figure-above-what-is-the-area-of-region-pqrst-og-2020-question-332-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/in-the-figure-above-what-is-the-area-of-region-pqrst-og-2020-question-332-with-solution\/","title":{"rendered":"In the figure above, what is the area of region PQRST? &#8211; OG 2020 Question #332 with Solution"},"content":{"rendered":"<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\"> 2<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<h2 class=\"wp-block-heading\" id=\"h-og-2020-question-no-332\">OG 2020: Question No. 332<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/OG_DS_332.png\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In the figure above, what is the area of region PQRST?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>PQ = RS<\/li><li>PT = QT<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class='one_third et_column_last'>\n\t\t\t\t\t<table>\n<tbody>\n<tr>\n<td width=\"301\">Source<\/td>\n<td width=\"301\">OG 2020<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Type<\/td>\n<td width=\"301\">Data Sufficiency<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Topic<\/td>\n<td width=\"301\">Geometry<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Sub-Topic<\/td>\n<td width=\"301\">Quadrilateral\/Triangle<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Difficulty<\/td>\n<td width=\"301\">Medium &#8211; Hard.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\t\t\t\t<\/div><div class='clear'><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-solution\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><u>Steps 1 &amp; 2: Understand Question and Draw Inferences<\/u><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this question, we are given<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>A diagram, consisting of \u0394PQT and quadrilateral QRST.<\/li><li>PQ = 6<\/li><li>RT = 10<\/li><li>Also, each angle in the quadrilateral QRST is 90\u00b0.<ul><li>Hence, QRST is a rectangle.<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We need to determine<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The area of the region PQRST.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">To determine the area, we need to know the individual area of \u0394PQT and quadrilateral QRST.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">With this understanding, let us now analyse the individual statements.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><u>Step 3: Analyse Statement 1<\/u><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As per the information given in statement 1, PQ = RS.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, PQ = RS = 6.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, \u0394RST is a right-angled triangle, where RS = 6 and RT = 10<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Therefore, TS = \u221a(10<sup>2<\/sup> \u2013 6<sup>2<\/sup>) = 8<\/li><li>So, the area of the rectangle QRST = 6 * 8 = 48<\/li><li>However, we have no information about the side PT of the triangle.<ul><li>Thus, we cannot determine the area of \u0394PQT<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, statement 1 is not sufficient to answer the question.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><u>Step 4: Analyse Statement 2<\/u><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As per the information given in statement 2, PT = QT.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>However, we do not know the exact value of PT or QT.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, statement 2 is not sufficient to answer the question.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><u>Step 5: Combine Both Statements Together (If Needed)<\/u><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Combining all the information present in both statements, we get<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Area of rectangle QRST = 48<\/li><li>PQ = QT (= RS) = PT = 6<\/li><li>Therefore, \u0394PQT is an equilateral triangle with side length 6.<ul><li>Hence, area of \u0394PQT = (\u221a3\/4) * 6<sup>2<\/sup><\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">As we can determine the area of both the triangles and quadrilaterals, we can determine the area of the given region.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the correct answer is option C.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p><strong>If you are planning to take the GMAT, we can help you with a personalized study plan and give you access to quality online content to prepare.<\/strong>&nbsp;<strong>Write to us at&nbsp;<a href=\"mailto:acethegmat@e-gmat.com\" target=\"_blank\" rel=\"noreferrer noopener\">acethegmat@e-gmat.com<\/a>. 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PQ = RS PT = QT Solution Steps 1 &amp; 2: Understand Question and Draw Inferences In this question, we are given A diagram, consisting of \u0394PQT and quadrilateral QRST. PQ = 6 RT = 10 Also, each angle [&hellip;]<\/p>\n","protected":false},"author":79663,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[104,44,94,60,100],"tags":[],"class_list":["post-21151","post","type-post","status-publish","format-standard","hentry","category-geometry","category-gmat-official-guide-solutions","category-gmat-prep","category-gmat-quant","category-quant-official-guide-solutions","et-doesnt-have-format-content","et_post_format-et-post-format-standard"],"featured_image_src":null,"author_info":{"display_name":"Juhi Gupta","author_link":"https:\/\/e-gmat.com\/blogs\/author\/juhie-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>In the figure above, what is the area of region PQRST? - OG 2020 Question #332 with Solution<\/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:\/\/e-gmat.com\/blogs\/in-the-figure-above-what-is-the-area-of-region-pqrst-og-2020-question-332-with-solution\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In the figure above, what is the area of region PQRST? - OG 2020 Question #332 with Solution\" \/>\n<meta property=\"og:description\" content=\"OG 2020: Question No. 332 In the figure above, what is the area of region PQRST? PQ = RS PT = QT Solution Steps 1 &amp; 2: Understand Question and Draw Inferences In this question, we are given A diagram, consisting of \u0394PQT and quadrilateral QRST. 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PQ = RS PT = QT Solution Steps 1 &amp; 2: Understand Question and Draw Inferences In this question, we are given A diagram, consisting of \u0394PQT and quadrilateral QRST. 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