{"id":21454,"date":"2019-05-21T17:31:45","date_gmt":"2019-05-21T12:01:45","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21454"},"modified":"2022-11-16T21:25:42","modified_gmt":"2022-11-16T15:55:42","slug":"the-figure-above-shows-a-portion-of-a-road-map-on-which-the-measures-of-certain-angles-are-indicated-if-all-lines-shown-are-straight-and-intersect-as-shown-is-road-pq-parallel-to-road","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/the-figure-above-shows-a-portion-of-a-road-map-on-which-the-measures-of-certain-angles-are-indicated-if-all-lines-shown-are-straight-and-intersect-as-shown-is-road-pq-parallel-to-road\/","title":{"rendered":"The figure above shows a portion of a road map on which the measures of certain angles are indicated. If all lines shown are straight and intersect as shown, is road\u00a0PQ\u00a0parallel to road\u00a0RS? &#8211; OGQR 2020 Question #222 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-ogqr-2020-question-no-222\">OGQR 2020: Question No. 222<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/OGQR_DS_222_1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>The figure above shows a portion of a road map on which the measures of certain angles are indicated. If all lines shown are straight and intersect as shown, is road&nbsp;PQ&nbsp;parallel to road&nbsp;RS?<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Source<\/td><td>OGQR 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>Lines and Angles<\/td><\/tr><tr><td>Difficulty<\/td><td>Easy &#8211; 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 portion of the roadmap<ul><li>Showing the measures of certain angles.<\/li><\/ul><\/li><li>All the lines shown in the figure are straight.<\/li><\/ul>\n\n\n\n<p>We need to find:<\/p>\n\n\n\n<ul><li>Whether road PQ is parallel to road RS.<\/li><\/ul>\n\n\n\n<p>Per our conceptual understanding, when two parallel lines are cut by a transversal line then their corresponding angles are equal.<\/p>\n\n\n\n<p>So, If PQ and RS are two parallel lines and line L<sub>1<\/sub> as shown is the transversal line then the corresponding angles are equal.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/OGQR_DS_222_2.png\" alt=\"\"\/><\/figure>\n\n\n\n<ul><li>Hence, \u22201 = \u22202<ul><li>Or, c<sup>0<\/sup> = 180<sup>0 <\/sup>\u2013 c<sup>0<\/sup><\/li><li>2c = 180<\/li><li>c = 90\u00b0<\/li><\/ul><\/li><\/ul>\n\n\n\n<p>Therefore, if we get c = 90\u00b0 then PQ and RS are parallel else PQ and RS are not parallel,<\/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><em>\u201cb&nbsp;=&nbsp;2a\u201d<\/em><\/p>\n\n\n\n<p>Per conceptual understanding, the sum of all the angles of a triangle is 180.<\/p>\n\n\n\n<ul><li>Hence, a + b + c = 180<ul><li>a + 2a + c = 180<\/li><li>3a + c = 180<\/li><\/ul><\/li><\/ul>\n\n\n\n<p>However, from the above equation, we can get many values of a and c.<\/p>\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><em>\u201cc&nbsp;=&nbsp;3a\u201d<\/em><\/p>\n\n\n\n<ul><li>a + b + c = 180<ul><li>a + b + 3a = 180<\/li><li>b + 4a = 180<\/li><\/ul><\/li><\/ul>\n\n\n\n<p>However, from the above equation, we can get many values of a and b.<\/p>\n\n\n\n<ul><li>Hence, statement 2 is not sufficient to answer the question.<\/li><\/ul>\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>From statement 1:<\/p>\n\n\n\n<ul><li>3a + c = 180<\/li><\/ul>\n\n\n\n<p>From statement 2:<\/p>\n\n\n\n<ul><li>c = 3a<\/li><\/ul>\n\n\n\n<p>Combining both the statements:<\/p>\n\n\n\n<ul><li>3a + 3a = 180.<\/li><\/ul>\n\n\n\n<p>From the above equation, we can find the value of a. Then we can find c.<\/p>\n\n\n\n<p>Since we could find the answer by combining both the statements, option C is the correct answer.<\/p>\n\n\n\n<p>A high GMAT score can set you apart from the competition and help you get an admit at your dream business school. Start your GMAT Preparation with the <a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">most reviewed online GMAT prep company<\/a>. Try out our<a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\"> FREE Trial<\/a> Today!<\/p>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-684e5fdc-76ec-46ac-be30-25ef190a8902\"><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>","protected":false},"excerpt":{"rendered":"<p>OGQR 2020: Question No. 222 The figure above shows a portion of a road map on which the measures of certain angles are indicated. If all lines shown are straight and intersect as shown, is road&nbsp;PQ&nbsp;parallel to road&nbsp;RS? Source OGQR 2020 Type Data Sufficiency Topic Geometry Sub-Topic Lines and Angles Difficulty Easy &#8211; Medium Solution [&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":"","ub_ctt_via":""},"categories":[104,44,94,60,100],"tags":[],"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 Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The figure above shows a portion of a road map on which the measures of certain angles are indicated. 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If all lines shown are straight and intersect as shown, is road&nbsp;PQ&nbsp;parallel to road&nbsp;RS? 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