{"id":6699,"date":"2011-04-26T08:00:52","date_gmt":"2011-04-26T16:00:52","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=6699"},"modified":"2011-03-24T12:56:04","modified_gmt":"2011-03-24T20:56:04","slug":"kaplan-gmat-sample-problem-prime-factors","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/kaplan-gmat-sample-problem-prime-factors\/","title":{"rendered":"Kaplan GMAT Sample Problem: Prime Factors"},"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>Good luck on this Challenge Problem involving Prime Factors! Remember, there\u2019s probably a reason that the questions are written the way that they are\u2026<\/p>\n<p><strong>Problem:<\/strong><\/p>\n<p>If a = 105 and a<sup>3 <\/sup>= 21 x 25 x 45 x b, what is the value of b?<\/p>\n<p>A) 35<\/p>\n<p>B) 42<\/p>\n<p>C) 45<\/p>\n<p>D) 49<\/p>\n<p>E) 54<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>The very first step in this problem is substituting 105 for the value of a in the main equation.\u00a0 As the variable <em>a<\/em> is not serving any function in this problem, we can simply get rid of it.\u00a0<\/p>\n<p>This makes our equation 105<sup>3 <\/sup>= 21 x 25 x 45 x b.\u00a0 Whenever we see numbers such as 105<sup>3<\/sup>, which we COULD calculate, but that might become more time consuming, so we should consider it a clue that there is likely a faster way to solve the problem.\u00a0 In many cases, this one included, the faster solution involves finding the prime factors of each number.\u00a0 105 becomes 3 x 5 x 7; 105<sup>3<\/sup>, therefore, becomes 3 x 5 x 7 x 3 x 5 x 7 x 3 x 5 x 7.\u00a0 On the other side of the equation 21 becomes 3 x 7, 25 becomes 5 x 5 and 45 becomes 3 x 3 x 5.\u00a0 When we rewrite the equation with the prime factors we get:<\/p>\n<p>3 x 5 x 7 x 3 x 5 x 7 x 3 x 5 x 7<\/p>\n<p>=<\/p>\n<p>3 x 7 x 5 x 5 x 3 x 3 x 5 x b.<\/p>\n<p>Once we have this equation, we can cancel out any numbers we see on both sides of the equation.\u00a0 This process leaves us with 7 x 7 = b.\u00a0 Thus, b = 49, which is the correct answer (D).\u00a0 The challenge was not necessarily in the level of math here, but more in your ability to identify the best and fastest approach for this given problem in the midst of your exam.\u00a0 Always be on the lookout for shortcuts on a time-pressured exam like the GMAT, and for ways that you can use your knowledge of number properties to identify things like prime factors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Good luck on this Challenge Problem involving Prime Factors! Remember, there\u2019s probably a reason that the questions are written the way that they are\u2026 Problem: If a = 105 and&#8230;<\/p>\n","protected":false},"author":120,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,558,736],"tags":[],"class_list":["post-6699","post","type-post","status-publish","format-standard","hentry","category-gmat","category-kaplan-blog","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/6699","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=6699"}],"version-history":[{"count":4,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/6699\/revisions"}],"predecessor-version":[{"id":6702,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/6699\/revisions\/6702"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=6699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=6699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=6699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}