{"id":21298,"date":"2022-05-02T20:07:00","date_gmt":"2022-05-02T14:37:00","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21298"},"modified":"2022-11-16T22:55:25","modified_gmt":"2022-11-16T17:25:25","slug":"in-the-figure-above-the-vertices-of-%ce%b4opq-and-%ce%b4qrs-have-coordinates-as-indicated-do-%ce%b4opq-and-%ce%b4qrs-have-equal-areas-og-2020-question-325-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/in-the-figure-above-the-vertices-of-%ce%b4opq-and-%ce%b4qrs-have-coordinates-as-indicated-do-%ce%b4opq-and-%ce%b4qrs-have-equal-areas-og-2020-question-325-with-solution\/","title":{"rendered":"In the figure above, the vertices of \u0394OPQ and \u0394QRS have coordinates as indicated. Do \u0394OPQ and \u0394QRS have equal areas? &#8211; OG 2020 Question #325 with Solution"},"content":{"rendered":"<span class=\"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 id=\"h-og-2020-question-no-325\">OG 2020: Question No. 325<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"281\" height=\"165\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/325.png\" alt=\"\" class=\"wp-image-21299\"\/><\/figure>\n\n\n\n<p>In the figure above, the vertices of \u0394OPQ and \u0394QRS have coordinates as indicated. Do \u0394OPQ and \u0394QRS have equal areas?<\/p>\n\n\n\n<ol><li>b = 2a<\/li><li>d = 2c<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Source<\/td><td>OG 2020<\/td><\/tr><tr><td>Type<\/td><td>Data Sufficiency<\/td><\/tr><tr><td>Topic<\/td><td>Geometry<\/td><\/tr><tr><td>Sub-Topic<\/td><td>Triangles \/ Coordinate Geometry<\/td><\/tr><tr><td>Difficulty<\/td><td>Medium<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 id=\"h-solution\">Solution<\/h3>\n\n\n\n<h4 id=\"h-steps-1-2-understand-question-and-draw-inferences\"><strong><u>Steps 1 &amp; 2: Understand Question and Draw Inferences<\/u><\/strong><\/h4>\n\n\n\n<p>In this question, we are given<\/p>\n\n\n\n<ul><li>A diagram, comprising of \u0394OPQ and \u0394QRS, along with the coordinates of their vertices, as shown.<\/li><\/ul>\n\n\n\n<p>We need to determine<\/p>\n\n\n\n<ul><li>Whether \u0394OPQ and \u0394QRS have equal areas or not.<\/li><\/ul>\n\n\n\n<p>We know the area of a triangle is given by \u00bd * base * height.<\/p>\n\n\n\n<ul><li>Area of \u0394OPQ = \u00bd * OQ * height = \u00bd * c * 3 = 3c\/2<\/li><li>Area of \u0394QRS = \u00bd * QS * height = \u00bd * (d \u2013 c) * 3 = 3(d-c)\/2<\/li><\/ul>\n\n\n\n<p>Now, if the triangles have equal area, then<\/p>\n\n\n\n<ul><li>3c\/2 = 3(d-c)\/2<\/li><\/ul>\n\n\n\n<p>Or, c = d \u2013 c<\/p>\n\n\n\n<p>Or, d = 2c<\/p>\n\n\n\n<p>Hence, we can say that if we know whether d = 2c, we can term the statement sufficient.<\/p>\n\n\n\n<p>With this understanding, let us now analyse the individual statements.<\/p>\n\n\n\n<h4 id=\"h-step-3-analyse-statement-1\"><strong><u>Step 3: Analyse Statement 1<\/u><\/strong><\/h4>\n\n\n\n<p>As per the information given in statement 1, b = 2a.<\/p>\n\n\n\n<ul><li>However, from this statement, we cannot say whether d = 2c or not.<\/li><\/ul>\n\n\n\n<p>Hence, statement 1 is not sufficient to answer the question.<\/p>\n\n\n\n<h4 id=\"h-step-4-analyse-statement-2\"><strong><u>Step 4: Analyse Statement 2<\/u><\/strong><\/h4>\n\n\n\n<p>As per the information given in statement 2, d = 2c.<\/p>\n\n\n\n<ul><li>Since d = 2c, we can conclude that the areas of both triangles are equal.<\/li><\/ul>\n\n\n\n<p>Hence, statement 2 is sufficient to answer the question.<\/p>\n\n\n\n<h4 id=\"h-step-5-combine-both-statements-together-if-needed\"><strong><u>Step 5: Combine Both Statements Together (If Needed)<\/u><\/strong><\/h4>\n\n\n\n<p>Since we can determine the answer from statement 2 individually, this step is not required.<\/p>\n\n\n\n<p>Hence, the correct answer choice is option B.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><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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Do \u0394OPQ and \u0394QRS have equal areas? b = 2a d = 2c Source OG 2020 Type Data Sufficiency Topic Geometry Sub-Topic Triangles \/ Coordinate Geometry Difficulty Medium Solution Steps 1 &amp; 2: Understand Question and [&hellip;]<\/p>\n","protected":false},"author":102413,"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":"","ub_ctt_via":""},"categories":[104,44,94,60,100],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Ashutosh","author_link":"https:\/\/e-gmat.com\/blogs\/author\/ashutoshe-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>In the figure above, the vertices of \u0394OPQ and \u0394QRS have coordinates as indicated. 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