{"id":1410,"date":"2009-11-25T10:02:48","date_gmt":"2009-11-25T18:02:48","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/2009\/11\/interesting-gmat-questions-m25q02\/"},"modified":"2009-11-25T10:08:49","modified_gmt":"2009-11-25T18:08:49","slug":"interesting-gmat-questions-m25q02","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/interesting-gmat-questions-m25q02\/","title":{"rendered":"Interesting GMAT Questions &#8211; m25q02"},"content":{"rendered":"<p>How many integers are divisible by 3 between <img src='https:\/\/s0.wp.com\/latex.php?latex=10%21&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='10!' title='10!' class='latex' \/> and <img src='https:\/\/s0.wp.com\/latex.php?latex=10%21+%2B+20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='10! + 20' title='10! + 20' class='latex' \/> inclusive?<\/p>\n<p>(C) 2008 GMAT Club - m25#2<\/p>\n<p>    * 6<br \/>\n    * 7<br \/>\n    * 8<br \/>\n    * 9<br \/>\n    * 10<\/p>\n<p>4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 1 professor, how many ways can this committee be formed?<\/p>\n<p>(C) 2008 GMAT Club - m25#3<\/p>\n<p>    * 36<br \/>\n    * 60<br \/>\n    * 72<br \/>\n    * 80<br \/>\n    * 100<\/p>\n<p>First, consider an unconstrained version of the question: how many committees of 3 are possible? The answer is <img src='https:\/\/s0.wp.com\/latex.php?latex=C_%7B10%7D%5E3+%3D+%5Cfrac%7B10%21%7D%7B%287%213%21%29%7D+%3D+120&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='C_{10}^3 = \\frac{10!}{(7!3!)} = 120' title='C_{10}^3 = \\frac{10!}{(7!3!)} = 120' class='latex' \/> . Now subtract the number of committees that consist entirely of students i.e. <img src='https:\/\/s0.wp.com\/latex.php?latex=C_%7B6%7D%5E3+%3D+%5Cfrac%7B6%21%7D%7B%283%213%21%29%7D+%3D+20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='C_{6}^3 = \\frac{6!}{(3!3!)} = 20' title='C_{6}^3 = \\frac{6!}{(3!3!)} = 20' class='latex' \/> . The final answer is <img src='https:\/\/s0.wp.com\/latex.php?latex=C_%7B10%7D%5E3+-+C_6%5E3+%3D+120+-+20+%3D+100&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='C_{10}^3 - C_6^3 = 120 - 20 = 100' title='C_{10}^3 - C_6^3 = 120 - 20 = 100' class='latex' \/> .<\/p>\n<p>The correct answer is E.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many integers are divisible by 3 between and inclusive? (C) 2008 GMAT Club &#8211; m25#2 * 6 * 7 * 8 * 9 * 10 4 professors and 6&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1410","post","type-post","status-publish","format-standard","hentry","category-uncategorized","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/1410","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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=1410"}],"version-history":[{"count":1,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/1410\/revisions"}],"predecessor-version":[{"id":1413,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/1410\/revisions\/1413"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=1410"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=1410"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=1410"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}