{"id":6697,"date":"2011-04-20T19:30:09","date_gmt":"2011-04-21T03:30:09","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=6697"},"modified":"2011-03-24T12:56:56","modified_gmt":"2011-03-24T20:56:56","slug":"kaplan-gmat-sample-problem-data-sufficiency-combinations","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/kaplan-gmat-sample-problem-data-sufficiency-combinations\/","title":{"rendered":"Kaplan GMAT Sample Problem:  Data Sufficiency Combinations"},"content":{"rendered":"<p><a href=\"https:\/\/gmatclub.com\/blog\/wp-content\/uploads\/2010\/12\/kaplan_smaller.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gmatclub.com\/blog\/wp-content\/uploads\/2010\/12\/kaplan_smaller.png\" alt=\"\" title=\"kaplan_smaller\" width=\"122\" height=\"42\" class=\"alignleft size-full wp-image-5647\" \/><\/a>Sometimes the challenge of specific <a href=\"https:\/\/www.kaptest.com\/GMAT\/Home\/index.html\">GMAT<\/a> problems is that they combine a higher-level concept such as Combinations, with a <a href=\"https:\/\/www.kaptest.com\/GMAT\/About-the-GMAT\/quantitative-section.html\">Data Sufficiency<\/a> question, with some algebra thrown in as well.\u00a0 But once you know the basics of dealing with Data Sufficiency, and the formula and concepts of Combinations, you can just follow a step-by-step approach to a problem such as this:<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Sample Problem:<\/strong><\/span><\/p>\n<p>Integers <em>x<\/em> and <em>y<\/em> are both positive, and <em>x &gt; y<\/em>.\u00a0 How many different committees of <em>y<\/em> people can be chosen from a group of <em>x<\/em> people?<\/p>\n<p>(1) The number of different committees of <em>x-y<\/em> people that can be chosen from a group of <em>x<\/em> people is 3,060.<\/p>\n<p>(2) The number of different ways to arrange <em>x-y<\/em> people in a line is 24.<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Solution:<\/strong><\/span><\/p>\n<p>The first step in this problem is to determine what we are really being asked.\u00a0 If we want to select committees of <em>y<\/em> people from a group of <em>x<\/em> people, we should use the combinations formula, which is n!\/[k!\/(n-k)!].\u00a0 Remember, in this formula<em> n<\/em> is the number with which we start and <em>k<\/em> is the number we want in each group.\u00a0 Thus, we can reword the question as what does x!\/[y!(x-y)!] equal?<\/p>\n<p>Statement 1 tells us how many committees of <em>x-y<\/em> people we can make from our initial group of <em>x<\/em> people.\u00a0 If we plug this information into the combinations formula, we get x!\/[(x-y)!(x-(x-y))!] = 3,060.\u00a0 This can be simplified to x!\/[(x-y)!(x-x+y))!] = 3,060, which in turn is simplified to x!\/[(x-y)!y!] = 3,060.\u00a0 The simplified equation matches the expression in our question, and gives us a numerical solution for it.\u00a0 Therefore, statement 1 is sufficient.<\/p>\n<p>Statement 2 tells us how many ways we can arrange a number of people.\u00a0 The formula for arrangements is simply n!.\u00a0 In this case we have <em>x-y<\/em> people, thus (<em>x-y<\/em>)! = 24.\u00a0 Therefore, <em>x-y<\/em> must equal 4.\u00a0 However, we have no way of calculating what \u00a0<em>x<\/em> and <em>y<\/em> actually are.\u00a0 This means that we cannot calculate the number of combinations in our question.\u00a0 Statement 2 is insufficient.\u00a0 So our final answer choice for this <a href=\"https:\/\/216.154.212.161\/KaplanQuizzes\/showQuiz.jsp?TID=GMATDSPT1\">Data Sufficiency<\/a> question is answer choice (A) or (1), Statement 1 is sufficient on its own, but Statement 2 is not.<\/p>\n<p>~Bret Ruber<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sometimes the challenge of specific GMAT problems is that they combine a higher-level concept such as Combinations, with a Data Sufficiency question, with some algebra thrown in as well.\u00a0 But&#8230;<\/p>\n","protected":false},"author":120,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,558,718,736],"tags":[],"class_list":["post-6697","post","type-post","status-publish","format-standard","hentry","category-gmat","category-kaplan-blog","category-data-sufficiency-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/6697","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/120"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=6697"}],"version-history":[{"count":3,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/6697\/revisions"}],"predecessor-version":[{"id":6704,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/6697\/revisions\/6704"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=6697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=6697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=6697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}