{"id":21249,"date":"2019-05-20T15:04:36","date_gmt":"2019-05-20T09:34:36","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21249"},"modified":"2023-02-09T19:58:18","modified_gmt":"2023-02-09T14:28:18","slug":"quant-og-2020-q317-if-each-side-of-parallelogram","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/quant-og-2020-q317-if-each-side-of-parallelogram\/","title":{"rendered":"GMAT Quant OG 2020 Question #317 with Solution &#8211; &#8220;If each side of parallelogram P has length 1, what is the area of P?&#8221;"},"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>PQID &#8211; DS28502.01 | OG 2020: Question No. 317<\/h2>\n\n\n\n<p>If each side of parallelogram P has length 1, what is the area of P?<\/p>\n\n\n\n<ol><li>One angle of P measures 45 degrees.<\/li><li>The altitude of P is \u221a2\/2.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Source<\/td><td>OG 2020<\/td><\/tr><tr><td><u><span style=\"text-decoration: underline;\">PQID<\/span><\/u><\/td><td>DS28502.01<\/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>Quadrilateral<\/td><\/tr><tr><td>Difficulty<\/td><td>Hard<\/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>Each side of the parallelogram P has length 1.<\/li><\/ul>\n\n\n\n<p>We need to determine<\/p>\n\n\n\n<ul><li>The area of the parallelogram P.<\/li><\/ul>\n\n\n\n<p>To determine the area of the parallelogram, we need to know the base (which is given as 1), and the height of the parallelogram because area of a parallelogram = Base \u00d7 Height.<\/p>\n\n\n\n<ul><li>Hence, in this case, we need to know the height of the parallelogram to find its area.<\/li><\/ul>\n\n\n\n<p>With this understanding, let us now analyze 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, one angle of P measures 45 degrees.<\/p>\n\n\n\n<p>Hence, we can draw the parallelogram as shown:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"300\" height=\"232\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/317-300x232.png\" alt=\"\" class=\"wp-image-21255\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/317-300x232.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/317.png 386w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<ul><li>\u25b3ABC is a right-angled triangle as shown. <ul><li>By applying the property that sum of all angles in a triangle is 180<sup>0<\/sup>, we can say: <ul><li>90<sup>0<\/sup> + 45<sup>0<\/sup> + \u2220ACB = 180<sup>0<\/sup><\/li><li>\u2220ACB = 45<sup>0<\/sup> <\/li><\/ul><\/li><\/ul><\/li><\/ul>\n\n\n\n<ul><li>Hence, \u25b3ABC is a 45 &#8211; 45 &#8211; 90 triangle.<ul><li>So, AB = BC = h<\/li><\/ul><ul><li>Applying Pythagoras theorem:<ul><li>AC<sup>2<\/sup> = AB<sup>2<\/sup> + BC<sup>2<\/sup><\/li><\/ul><ul><li>1 = 2h<sup>2<\/sup><\/li><\/ul><ul><li>So, h = 1\/\u221a2<\/li><\/ul><\/li><\/ul><\/li><\/ul>\n\n\n\n<p>Hence, statement 1 is sufficient to find the answer to 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, the altitude of P is \u221a2\/2.<\/p>\n\n\n\n<ul><li>Hence, h = \u221a2\/2 =\u221a2.<\/li><li>We can find out the area of the triangles.<\/li><\/ul>\n\n\n\n<p>Hence, statement 2 is sufficient to find the answer to 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 either of the statements individually, this step is not required.<\/p>\n\n\n\n<p>Hence, the correct answer choice is option D.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2>Takeaways<\/h2>\n\n\n\n<ol type=\"1\"><li>Area of a parallelogram = Base \u00d7 Height<\/li><li>Angle-Sum property of a triangle: Sum of all the angles in a triangle is 180\u00b0.<\/li><\/ol>\n\n\n\n<p><strong>Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don\u2019t you<a href=\"https:\/\/e-gmat.com\/ft-gmat\/?channel=blogsin_article&amp;utm_source=blogs&amp;utm_medium=in_article&amp;utm_campaign=free_trial&amp;utm_term=blogs_in_article_lekhika\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">\u00a0try out our FREE Trial?<\/a>\u00a0We are the\u00a0<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">most-reviewed online GMAT Preparation company in GMATClub<\/a>\u00a0with more than 2500 reviews.<\/strong><\/p>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-c046d53e-6f96-48cf-a7db-ca8b01aeffd7\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-block-btn\">Sign up for a Free Trial<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<p><a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>PQID &#8211; DS28502.01 | OG 2020: Question No. 317 If each side of parallelogram P has length 1, what is the area of P? One angle of P measures 45 degrees. The altitude of P is \u221a2\/2. Source OG 2020 PQID DS28502.01 Type Data Sufficiency Topic Geometry Sub-Topic Quadrilateral Difficulty Hard Solution Steps 1 &amp; [&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>GMAT Quant OG 2020 Question #317 with Solution - &quot;If each side of parallelogram P has length 1, what is the area of P?&quot;<\/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\/quant-og-2020-q317-if-each-side-of-parallelogram\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Quant OG 2020 Question #317 with Solution - &quot;If each side of parallelogram P has length 1, what is the area of P?&quot;\" \/>\n<meta property=\"og:description\" content=\"PQID &#8211; DS28502.01 | OG 2020: Question No. 317 If each side of parallelogram P has length 1, what is the area of P? 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DS28502.01 | OG 2020: Question No. 317 If each side of parallelogram P has length 1, what is the area of P? One angle of P measures 45 degrees. The altitude of P is \u221a2\/2. 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&#8220;If each side of parallelogram P has length 1, what is the area of P?&#8221;"}]},{"@type":"Article","@id":"https:\/\/e-gmat.com\/blogs\/quant-og-2020-q317-if-each-side-of-parallelogram\/#article","isPartOf":{"@id":"https:\/\/e-gmat.com\/blogs\/quant-og-2020-q317-if-each-side-of-parallelogram\/#webpage"},"author":{"@id":"https:\/\/e-gmat.com\/blogs\/#\/schema\/person\/8f114f8ffaa8bec0ec851db39a23bd00"},"headline":"GMAT Quant OG 2020 Question #317 with Solution &#8211; &#8220;If each side of parallelogram P has length 1, what is the area of P?&#8221;","datePublished":"2019-05-20T09:34:36+00:00","dateModified":"2023-02-09T14:28:18+00:00","mainEntityOfPage":{"@id":"https:\/\/e-gmat.com\/blogs\/quant-og-2020-q317-if-each-side-of-parallelogram\/#webpage"},"wordCount":359,"commentCount":0,"publisher":{"@id":"https:\/\/e-gmat.com\/blogs\/#organization"},"image":{"@id":"https:\/\/e-gmat.com\/blogs\/quant-og-2020-q317-if-each-side-of-parallelogram\/#primaryimage"},"thumbnailUrl":"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/317-300x232.png","articleSection":["Geometry","GMAT OG Solutions","GMAT Preparation","GMAT Quant","Quant OG Solutions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/e-gmat.com\/blogs\/quant-og-2020-q317-if-each-side-of-parallelogram\/#respond"]}]},{"@type":"Person","@id":"https:\/\/e-gmat.com\/blogs\/#\/schema\/person\/8f114f8ffaa8bec0ec851db39a23bd00","name":"Ashutosh","image":{"@type":"ImageObject","@id":"https:\/\/e-gmat.com\/blogs\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/09a09d4db8be9a09edc3bec0b8f69d24?s=96&d=blank&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/09a09d4db8be9a09edc3bec0b8f69d24?s=96&d=blank&r=g","caption":"Ashutosh"},"url":"https:\/\/e-gmat.com\/blogs\/author\/ashutoshe-gmat-com\/"}]}},"_links":{"self":[{"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/posts\/21249"}],"collection":[{"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/users\/102413"}],"replies":[{"embeddable":true,"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/comments?post=21249"}],"version-history":[{"count":1,"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/posts\/21249\/revisions"}],"predecessor-version":[{"id":44306,"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/posts\/21249\/revisions\/44306"}],"wp:attachment":[{"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/media?parent=21249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/categories?post=21249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/e-gmat.com\/blogs\/wp-json\/wp\/v2\/tags?post=21249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}