{"id":5531,"date":"2015-01-26T09:00:23","date_gmt":"2015-01-26T17:00:23","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=5531"},"modified":"2020-01-15T10:48:20","modified_gmt":"2020-01-15T18:48:20","slug":"the-word-or-in-gmat-math","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/the-word-or-in-gmat-math\/","title":{"rendered":"The Word “Or” in GMAT Math"},"content":{"rendered":"

Consider the following scenario. Suppose you solve for all the numbers in a Venn Diagram<\/a>, in a scenario in which 200 students are taking AP Chemistry, AP Literature, both, or neither. Here are the results you find.<\/p>\n

\"TheOK, from this solved Venn diagram, there\u2019s a ton we know:<\/p>\n

total in AP Chemistry = 50 + 30 = 80<\/p>\n

total in AP Literature = 30 + 80 = 110<\/p>\n

taking both AP Chemistry and AP Literature = 30<\/p>\n

taking AP Chemistry, and not AP Literature = 50<\/p>\n

taking AP Literature, and not AP Chemistry = 80<\/p>\n

taking neither = 40<\/p>\n

All that is unambiguous, and most folks looking at this Venn Diagram would not have much trouble with all that. The problem comes with the question: \u201cHow many students are in AP Literature OR<\/strong> AP Chemistry?\u201d Do we include the folks in both or not? There seem to be two readings of this question, and for some students, both reading might make sense. What\u2019s going on?<\/p>\n

The Two Kinds of “OR”<\/h2>\n

It turns out, in mathematical logic, there are two completely different kinds of OR: the inclusive OR<\/strong> and the exclusive OR<\/strong>. The inclusive OR<\/strong> always includes the \u201cboth\u201d case. For the inclusive OR<\/strong>, the phrase \u201cA or B\u201d includes the possibilities:<\/p>\n

(a) A by itself<\/p>\n

(b) B by itself<\/p>\n

(c) A and B together<\/p>\n

By contrast, the exclusive OR<\/strong> always excludes the \u201cboth\u201d case. For the exclusive OR<\/strong>, the phrase \u201cA or B\u201d includes (a) & (b) above, but definitely NOT (c).<\/p>\n

In colloquial language, often context makes it clear which OR is intended. For example, if you imagine when you were, say, eight years old, and it was around dessert time, and your mother said emphatically, \u201cYou can have cake or<\/strong> ice cream<\/em>!!!\u201d At that moment, your mother most certainly was not expatiating on the merits of the inclusive OR. In fact, in many scenarios of ordinary life, the word OR implicitly means the exclusive OR\u2014especially when any emotional emphasis lands on the word itself!<\/p>\n

The Word “OR” in Mathematics<\/h2>\n

Things change when we look at the use within mathematics. First of all, the word OR is very important: it is part of the logical apparatus in a problem. For example, the solution of quadratic<\/a> usually yields two solutions, and these solutions are related by the word OR.<\/p>\n

In mathematics, wherever the word OR appears, it is always the inclusive OR, 100% of the time<\/strong>. If a mathematician says \u201cA or B,\u201d she always implicitly includes the case of A and B together. If the mathematician wants to specific an exclusive OR, she would have to go out of her way to say something wordier: \u201cA alone or B alone but not both<\/em>.\u201d (In Symbolic Logic and in the Computer Science world, folks sometimes use the abbreviation XOR for the exclusive OR<\/a>.)<\/p>\n

This means, on the GMAT Quant section, wherever the word OR appears, 100% of the time it will be the inclusive OR. Thus, in the Venn Diagram above, it would be absolutely clear and unambiguous: if the test asked, \u201cHow many students are in AP Literature OR AP Chemistry?\u201d, the answer would have to be 160.<\/p>\n

Summary<\/h2>\n

The GMAT Quant section presents exceptionally high quality questions, and these are always devoid of ambiguity. Even when the word OR appears, it will have a precisely defined mathematical meaning, leaving absolutely no room for ambiguity. The word OR always, 100% of the time, means the inclusive OR. If you can remember this piece of advice, it will save you trouble in counting<\/a> and probability<\/a> problems.\u00a0\u00a0 In fact, you can apply these ideas in these Practice Probability Questions<\/a>.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Consider the following scenario. Suppose you solve for all the numbers in a Venn Diagram, in a scenario in which 200 students are taking AP Chemistry, AP Literature, both, or neither. Here are the results you find. OK, from this solved Venn diagram, there\u2019s a ton we know: total in AP Chemistry = 50 + […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[112],"tags":[],"ppma_author":[13209],"class_list":["post-5531","post","type-post","status-publish","format-standard","hentry","category-math"],"acf":[],"yoast_head":"\nThe Word "Or" in GMAT Math - 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\/the-word-or-in-gmat-math\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Word "Or" in GMAT Math\" \/>\n<meta property=\"og:description\" content=\"Consider the following scenario. Suppose you solve for all the numbers in a Venn Diagram, in a scenario in which 200 students are taking AP Chemistry, AP Literature, both, or neither. Here are the results you find. 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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\/5531","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=5531"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/5531\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=5531"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=5531"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=5531"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=5531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}