{"id":21361,"date":"2019-05-21T02:16:38","date_gmt":"2019-05-20T20:46:38","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21361"},"modified":"2022-11-16T17:24:37","modified_gmt":"2022-11-16T11:54:37","slug":"each-of-27-white-1-centimeter-cubes-will-have-exactly-one-face-painted-red-if-these-27-cubes-are-joined-together-to-form-one-large-cube-as-shown-above-what-is-the-greatest-possible-fraction-of-the","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/each-of-27-white-1-centimeter-cubes-will-have-exactly-one-face-painted-red-if-these-27-cubes-are-joined-together-to-form-one-large-cube-as-shown-above-what-is-the-greatest-possible-fraction-of-the\/","title":{"rendered":"Each of 27 white 1-centimeter cubes will have exactly one face painted red. If these 27 cubes are joined together to form one large cube, as shown above, what is the greatest possible fraction of the surface area that could be red?  &#8211; OGQR 2020 Question #88 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-ogqr-2020-question-no-88\">OGQR 2020: Question No. 88<\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"183\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/88.png\" alt=\"\" class=\"wp-image-21364\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Each of 27 white 1-centimeter cubes will have exactly one face painted red. If these 27 cubes are joined together to form one large cube, as shown above, what is the greatest possible fraction of the surface area that could be red?<\/p>\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\">OGQR 2020<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Type<\/td>\n<td width=\"301\">Problem Solving<\/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\">Cube<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Difficulty<\/td>\n<td width=\"301\">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<h4 class=\"wp-block-heading\" id=\"h-given\"><strong><u>Given<\/u><\/strong><\/h4>\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>Each of 27 white 1-centimeter cubes will have exactly one face painted red.<\/li><li>These 27 cubes are joined together to form one large cube, as shown in the given diagram.<\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-to-find\"><strong><u>To Find<\/u><\/strong><\/h4>\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 greatest possible fraction of the surface area that could be red.<\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-approach-working\"><strong><u>Approach &amp; Working<\/u><\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">To maximize the surface area, count as red, except the cube which is at the centre, all the other cubes must have their red surface area exposed.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Number of cubes with red surface area exposed = 27 \u2013 1 = 26<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">However, in each surface of the bigger cube, there will be 9 smaller cube surfaces, and there will be total 6 surfaces for the bigger cube.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Hence, total number of cube surfaces exposed = 9 * 6 = 54<\/li><li>Therefore, the greatest fraction = 26\/54 = 13\/27<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the correct answer is option B.<\/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>. We are the&nbsp;<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">most reviewed GMAT prep company on gmatclub<\/a>&nbsp;with more than 2400 reviews&nbsp;<\/strong>and are the only prep company that has delivered&nbsp;<a href=\"https:\/\/e-gmat.com\/blogs\/e-gmat-review\/\" target=\"_blank\" rel=\"noreferrer noopener\" data-wpel-link=\"internal\">more than 700+ scores than any other GMAT club partner<strong>.<\/strong><\/a>&nbsp;<strong>Why don\u2019t you take a free trial and judge for yourself?<\/strong><\/p><\/blockquote>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div style=\"gap: 20px\" class=\"align-button-center ub-buttons orientation-button-row ub-flex-wrap wp-block-ub-button\" id=\"ub-button-22ee4182-2486-4165-aaf3-4ca758258a0e\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"ub-button-block-main  \" role=\"button\" style=\"--ub-button-background-color: #fcb900; --ub-button-color: #000000; --ub-button-border: none; --ub-button-hover-background-color: #cf2e2e; --ub-button-hover-color: #ffffff; --ub-button-hover-border: none; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-radius: 60px; \">\n\t\t\t\t<div class=\"ub-button-content-holder\" style=\"flex-direction: row\">\n\t\t\t\t\t<span class=\"ub-button-icon-holder\">\n\t\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" height=\"30\" width=\"30\" viewbox=\"0 0 512 512\">\n\t\t\t\t\t<path fill=\"currentColor\" d=\"M0 256a256 256 0 1 0 512 0A256 256 0 1 0 0 256zM281 385c-9.4 9.4-24.6 9.4-33.9 0s-9.4-24.6 0-33.9l71-71L136 280c-13.3 0-24-10.7-24-24s10.7-24 24-24l182.1 0-71-71c-9.4-9.4-9.4-24.6 0-33.9s24.6-9.4 33.9 0L393 239c9.4 9.4 9.4 24.6 0 33.9L281 385z\">\n\t\t\t\t<\/path><\/svg>\n\t\t\t<\/span><span class=\"ub-button-block-btn\">Start your free trial<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"ub-button-block-main  \" role=\"button\" style=\"--ub-button-background-color: #0693e3; --ub-button-color: #ffffff; --ub-button-border: none; --ub-button-hover-background-color: #ff6900; --ub-button-hover-color: #000000; --ub-button-hover-border: none; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-radius: 60px; \">\n\t\t\t\t<div class=\"ub-button-content-holder\" style=\"flex-direction: row\">\n\t\t\t\t\t<span class=\"ub-button-icon-holder\">\n\t\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" height=\"30\" width=\"30\" viewbox=\"0 0 448 512\">\n\t\t\t\t\t<path fill=\"currentColor\" d=\"M438.6 278.6c12.5-12.5 12.5-32.8 0-45.3l-160-160c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L370.7 256 233.4 393.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l160-160zm-352 160l160-160c12.5-12.5 12.5-32.8 0-45.3l-160-160c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L178.7 256 41.4 393.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0z\">\n\t\t\t\t<\/path><\/svg>\n\t\t\t<\/span><span class=\"ub-button-block-btn\">Take a free mock<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>OGQR 2020: Question No. 88 Each of 27 white 1-centimeter cubes will have exactly one face painted red. If these 27 cubes are joined together to form one large cube, as shown above, what is the greatest possible fraction of the surface area that could be red? Solution Given In this question, we are given [&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":"","footnotes":""},"categories":[104,44,94,60,100],"tags":[],"class_list":["post-21361","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":"Ashutosh","author_link":"https:\/\/e-gmat.com\/blogs\/author\/ashutoshe-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Each of 27 white 1-centimeter cubes will have exactly one face painted red. 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Solution Given In this question, we are given [&hellip;]","og_url":"https:\/\/e-gmat.com\/blogs\/each-of-27-white-1-centimeter-cubes-will-have-exactly-one-face-painted-red-if-these-27-cubes-are-joined-together-to-form-one-large-cube-as-shown-above-what-is-the-greatest-possible-fraction-of-the\/","og_site_name":"e-GMAT Blog | Best GMAT blog on the planet","article_publisher":"https:\/\/www.facebook.com\/E-Gmat-499275643430980","article_published_time":"2019-05-20T20:46:38+00:00","article_modified_time":"2022-11-16T11:54:37+00:00","og_image":[{"width":227,"height":183,"url":"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/88.png","type":"image\/png"}],"author":"Ashutosh","twitter_card":"summary_large_image","twitter_creator":"@e_GMAT","twitter_site":"@e_GMAT","twitter_misc":{"Written by":"Ashutosh","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/e-gmat.com\/blogs\/each-of-27-white-1-centimeter-cubes-will-have-exactly-one-face-painted-red-if-these-27-cubes-are-joined-together-to-form-one-large-cube-as-shown-above-what-is-the-greatest-possible-fraction-of-the\/#article","isPartOf":{"@id":"https:\/\/e-gmat.com\/blogs\/each-of-27-white-1-centimeter-cubes-will-have-exactly-one-face-painted-red-if-these-27-cubes-are-joined-together-to-form-one-large-cube-as-shown-above-what-is-the-greatest-possible-fraction-of-the\/"},"author":{"name":"Ashutosh","@id":"https:\/\/e-gmat.com\/blogs\/#\/schema\/person\/8f114f8ffaa8bec0ec851db39a23bd00"},"headline":"Each of 27 white 1-centimeter cubes will have exactly one face painted red. 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