{"id":21439,"date":"2019-05-21T14:30:00","date_gmt":"2019-05-21T09:00:00","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21439"},"modified":"2019-05-21T14:30:00","modified_gmt":"2019-05-21T09:00:00","slug":"the-heart-shaped-decoration-shown-in-the-figure-above-consists-of-a-square-and-two-semicircles-what-is-the-radius-of-each-semicircle-ogqr-2020-question-219-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/the-heart-shaped-decoration-shown-in-the-figure-above-consists-of-a-square-and-two-semicircles-what-is-the-radius-of-each-semicircle-ogqr-2020-question-219-with-solution\/","title":{"rendered":"The heart-shaped decoration shown in the figure above consists of a square and two semicircles. What is the radius of each semicircle? – OGQR 2020 Question #219 with Solution"},"content":{"rendered":"A <\/span> 2<\/span> min read <\/span><\/span>
\n\t\t\t\t\t

OGQR 2020: Question No. 219<\/h2>\n

<\/p>\n

The heart-shaped decoration shown in the figure above consists of a square and two semicircles. What is the radius of each semicircle?<\/p>\n

    \n
  1. The diagonal of the square is\u00a010\u221a2\u00a0centimetres long.<\/li>\n
  2. The area of the square region minus the sum of the areas of the semi-circular regions is 100\u00a0\u2013\u00a025\u03c0\u00a0square centimetres.<\/li>\n<\/ol>\n\t\t\t\t<\/div>\n
    \n\t\t\t\t\t\n\n\n\n\n\n\n
    Source<\/td>\nOGQR 2020<\/td>\n<\/tr>\n
    Type<\/td>\nData Sufficiency<\/td>\n<\/tr>\n
    Topic<\/td>\nGeometry<\/td>\n<\/tr>\n
    Sub-Topic<\/td>\nSquares\/Circles<\/td>\n<\/tr>\n
    Difficulty<\/td>\nMedium<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\t\t\t\t<\/div>
    <\/div>\n

    Solution<\/h3>\n

    Steps 1 & 2: Understand Question and Draw Inferences<\/u><\/strong><\/h4>\n

    We are given:<\/p>\n

      \n
    • A heart shaped decoration figure.\n
        \n
      • It consists: A square and two semicircles.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

        We need to find:<\/p>\n

          \n
        • The radius of each semicircle.<\/li>\n<\/ul>\n

          Let us assume that r is radius of the semicircle.<\/p>\n

            \n
          • Hence, 2r is the side of the square as shown.<\/li>\n<\/ul>\n

            <\/p>\n

              \n
            • Therefore, if we know the side of square or any relation by which we can find r, we can find the radius of the semicircle.<\/li>\n<\/ul>\n

              With this understanding, let us now analyse the individual statements.<\/p>\n

               <\/p>\n

              Step 3: Analyse Statement 1<\/u><\/strong><\/h4>\n

              \u201cThe diagonal of the square is\u00a010\u221a2\u00a0centimetres long.\u201d<\/em><\/p>\n

              <\/p>\n

                \n
              • If 2r is the side of the square, then 2r is the length of the diagonal.\n
                  \n
                • Hence, 2r = 10<\/li>\n<\/ul>\n<\/li>\n
                • Therefore, we can find the value of r from the above equation.<\/li>\n<\/ul>\n

                  Hence, statement 1 is sufficient to find the answer.<\/p>\n

                   <\/p>\n

                  Step 4: Analyse Statement 2<\/u><\/strong><\/h4>\n

                  \u201cThe area of the square region minus the sum of the areas of the semi-circular regions is 100\u00a0\u2013\u00a025\u03c0\u00a0square centimetres.\u201d<\/em><\/p>\n

                    \n
                  • Area of square \u2013 2 * area of semicircle = (2r)2<\/sup> \u2013 2 *<\/li>\n
                  • 100 – 25\u03c0 = 4r2<\/sup> \u2013 \u03c0r2<\/sup> = r2<\/sup> (4 -\u03c0)<\/li>\n
                  • 25(4 \u2013 \u03c0) = r2<\/sup> (4 -\u03c0)<\/li>\n
                  • r2<\/sup> = 25<\/li>\n<\/ul>\n

                    From the above equation, we can find the value of r.<\/p>\n

                    Hence, statement 2 is sufficient to answer the question.<\/p>\n

                     <\/p>\n

                    Step 5: Combine Both Statements Together (If Needed)<\/u><\/strong><\/h4>\n

                    Since we could determine the answer from either of the statements individually, this step is not required.<\/p>\n

                    Hence, the correct answer is option D.<\/p>\n","protected":false},"excerpt":{"rendered":"

                    Solution Steps 1 & 2: Understand Question and Draw Inferences We are given: A heart shaped decoration figure. It consists: A square and two semicircles. We need to find: The radius of each semicircle. Let us assume that r is radius of the semicircle. Hence, 2r is the side of the square as shown. Therefore, […]<\/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":"\nThe heart-shaped decoration shown in the figure above consists of a square and two semicircles. 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