{"id":2654,"date":"2012-09-05T09:00:53","date_gmt":"2012-09-05T16:00:53","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=2654"},"modified":"2014-09-16T16:57:34","modified_gmt":"2014-09-16T23:57:34","slug":"inclusive-counting-on-the-gmat","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/inclusive-counting-on-the-gmat\/","title":{"rendered":"Inclusive Counting on the GMAT"},"content":{"rendered":"<p><strong>Understand this common type of special counting on the GMAT!\u00a0<\/strong><\/p>\n<p><span style=\"text-decoration: underline\">Question #1<\/span>: On Monday, there were 29 bananas in the cafeteria.\u00a0 No new bananas were brought in after Monday.\u00a0 Two days later, on Wednesday, there were 14 bananas left.\u00a0 How many were eaten in that time?<\/p>\n<p><span style=\"text-decoration: underline\">Question #2<\/span>: In January of last year, MicroCorp start-up had 14 employees.\u00a0 All of those employees have stayed on through June.\u00a0 In June of last year, they had 29 employees.\u00a0 How many new employees did they hire?<\/p>\n<p>Clearly for both of these questions, we need simply the different: 29 \u2013 14 = 15.\u00a0 That&#8217;s the correct answer for each of them.\u00a0 Now, try a very different kind of question, with a different answer.<\/p>\n<p><span style=\"text-decoration: underline\">Question #3<\/span>: A certain workshop begins on the 14th of this month and ends on the 29th of this month.\u00a0 How many days long is this workshop?<\/p>\n<p><span style=\"text-decoration: underline\">Question #4<\/span>: How many multiples of 5 are there from 70 to 145?<\/p>\n<p>Those two have the same answer as each other, but it&#8217;s not the same as the answer for #1 and #2.<\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"text-decoration: underline\">Inclusive<\/span><\/h2>\n<p>We say the final two require &#8220;inclusive&#8221; counting, because both endpoints are included, whereas in the first two questions, both endpoints were not included.\u00a0 What do I mean?<\/p>\n<p>In Question #1, the 29th banana was eaten, the 28 banana was eaten, \u2026. the 15 banana was eaten, BUT the 14th banana was not eaten because there 14 remaining.\u00a0 The endpoint 14 is &#8220;<span style=\"text-decoration: underline\">not included<\/span>&#8221; in those eaten.<\/p>\n<p>In Question #2, employees #1 &#8211; #14 were already hired by last January.\u00a0 Employees #15 &#8211; #29 were new hires.\u00a0 The lower endpoint, employee #14, was &#8220;<span style=\"text-decoration: underline\">not included<\/span>&#8221; in the group of new hires.<\/p>\n<p>Now, by contrast, the 14th is the first day of the workshop, and the 29th is the last day of the workshop.\u00a0 Both the 14th and 29th are days when the workshop is happening.\u00a0 Both endpoints are <span style=\"text-decoration: underline\">included<\/span>.<\/p>\n<p>Similarly, in #4, the multiples of 5 from 70 to 145 include both 70 and 145.\u00a0 Again, both endpoints are <span style=\"text-decoration: underline\">included<\/span>.\u00a0 Incidentally, the connection to the other three questions: 70 = 5*14 and 145 = 5*29, so the list of multiples of 5 from 70 to 145 is really 5 times the list of consecutive integers from 14 to 29, so the underlying question is really: how many consecutive integers are there from 14 to 29?<\/p>\n<p>As may be apparent, the inclusive scenario always includes exactly one more member than the &#8220;not included&#8221; scenario.\u00a0 Therefore, the formula for inclusive counting is<\/p>\n<p>number included = (last) \u2013 (first) + 1<\/p>\n<p>Notice, this only works if the numbers are consecutive.\u00a0 If the question is like #4, you may have to notice what change you can make to match the given list with a list of consecutive integers.<\/p>\n<p>&nbsp;<\/p>\n<h2><span style=\"text-decoration: underline\">Practice questions<\/span><\/h2>\n<p>1) <a href=\"http:\/\/gmat.magoosh.com\/questions\/334\">http:\/\/gmat.magoosh.com\/questions\/334<\/a><\/p>\n<p>2) <a href=\"http:\/\/gmat.magoosh.com\/questions\/808\">http:\/\/gmat.magoosh.com\/questions\/808<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Understand this common type of special counting on the GMAT!\u00a0 Question #1: On Monday, there were 29 bananas in the cafeteria.\u00a0 No new bananas were brought in after Monday.\u00a0 Two days later, on Wednesday, there were 14 bananas left.\u00a0 How many were eaten in that time? Question #2: In January of last year, MicroCorp start-up [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[193],"tags":[],"ppma_author":[13209],"class_list":["post-2654","post","type-post","status-publish","format-standard","hentry","category-word-problems"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Inclusive Counting on the GMAT - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gmat\/inclusive-counting-on-the-gmat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Inclusive Counting on the GMAT\" \/>\n<meta property=\"og:description\" content=\"Understand this common type of special counting on the GMAT!\u00a0 Question #1: On Monday, there were 29 bananas in the cafeteria.\u00a0 No new bananas were brought in after Monday.\u00a0 Two days later, on Wednesday, there were 14 bananas left.\u00a0 How many were eaten in that time? 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Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations.","sameAs":["https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured"],"award":["Magna cum laude from Harvard"],"knowsAbout":["GMAT"],"knowsLanguage":["English"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":13209,"user_id":26,"is_guest":0,"slug":"mikemcgarry","display_name":"Mike M\u1d9cGarry","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","user_url":"","last_name":"M\u1d9cGarry","first_name":"Mike","description":"Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/2654","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=2654"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/2654\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=2654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=2654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=2654"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=2654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}