{"id":5140,"date":"2014-10-13T09:00:54","date_gmt":"2014-10-13T16:00:54","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=5140"},"modified":"2020-01-15T10:48:29","modified_gmt":"2020-01-15T18:48:29","slug":"gmat-practice-problems-sets","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-sets\/","title":{"rendered":"GMAT Practice Problems: Sets"},"content":{"rendered":"

Here are four reasonably challenging problems about sets.<\/p>\n

1) At a certain school of 200 students, the students can study French, Spanish, both or neither. Just as many study both as study neither.\u00a0 One quarter of those who study Spanish also study French.\u00a0 The total number who study French is 10 fewer than those who study Spanish only.\u00a0\u00a0 How many students study French only?<\/p>\n

    \n\t(A) 30
    \n\t(B) 50
    \n\t(C) 70
    \n\t(D) 90
    \n\t(E) 120\n<\/ol>\n

    2) In a company of 300 employees, 120 are females or non-binary.\u00a0 A total of 200 employees have advanced degrees, and the rest have a college degree only.\u00a0 If 80 employees are males with college degree only, how many are females or non-binary folks with advanced degrees?<\/p>\n

      \n\t(A) 60
      \n\t(B) 80
      \n\t(C) 100
      \n\t(D) 120
      \n\t(E) 160\n<\/ol>\n

      3) In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Upperclassmen, drawn from three cities: A, B, and C.\u00a0 Sixty percent of students are from A, 30% from B, the rest from C, and all these students from C are freshmen.\u00a0 Half the student from B are upperclassman, and the rest are split evenly between the other two grades.\u00a0 How many sophomores are from A?<\/p>\n

        \n\t(A) 60
        \n\t(B) 70
        \n\t(C) 80
        \n\t(D) 90
        \n\t(E) 100\n<\/ol>\n

        4) There are a total of 400 students at a school, which offers a chorus, baseball, and Italian.\u00a0 This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities.\u00a0 If 220 students are in either Italian or baseball, then how many student are in none of the three activities?<\/p>\n

          \n\t(A) 40
          \n\t(B) 60
          \n\t(C) 70
          \n\t(D) 100
          \n\t(E) 130\n<\/ol>\n

          Solutions will be given at the end of the article.<\/p>\n

           <\/p>\n

          Set problems<\/h2>\n

          For two or more overlapping categories, in scenarios in which any given member can belong to all, some, or none of the categories, Venn Diagrams<\/a> can be helpful.\u00a0 If there are two separate variables, and each member is classified according to each variable, then the Double Matrix Method<\/a> can be helpful.\u00a0\u00a0 If reading the articles at either of those links gives you insights on any of these problems, you may want to give the problems a second look before reading the solutions below.<\/p>\n

          \"gpp-se_img1\"<\/a><\/p>\n

           <\/p>\n

          Practice problem solutions<\/h2>\n

          1) Let x be the number of folks studying both, which means it is also the number of folks studying neither.<\/p>\n

          \"gpp-se_img2\"<\/a><\/p>\n

          \u201cOne quarter of those who study Spanish also study French.\u201d\u00a0 If the Spanish students studying French are x, then all Spanish students are 4x, and those who do not study French are 3x.\u00a0 Also, let y be the number of students who study French but not Spanish.<\/p>\n

          \"gpp-se_img3\"<\/a><\/p>\n

          \u201cThe total number who study French is 10 fewer than those who study Spanish only.\u201d In other words,<\/p>\n

          x + y = 3x \u2013 10<\/p>\n

          10 = 2x \u2013 y<\/p>\n

          Also, notice that the total number of students is 200:<\/p>\n

          3x + x + y + x = 200<\/p>\n

          5x + y = 200<\/p>\n

          We have two equations with two unknowns<\/a>.\u00a0 Add the equations (2x \u2013 y = 10) and (5x + y = 200), and we get<\/p>\n

          7x = 210<\/p>\n

          x = 30<\/p>\n

          y = 50<\/p>\n

          And the number who study French is x + y = 80.\u00a0 Answer = (B)<\/strong><\/p>\n

          2) This problem is handled best with a double-matrix solution.<\/p>\n

          \"gpp-se_img4\"<\/a><\/p>\n

          Because there are 120 females or non-binary folks, we know the rest are males.\u00a0 Because there are 200 with advanced degrees, we know there are 100 with college degrees only.<\/p>\n

          \"gpp-se_img5\"<\/a><\/p>\n

          At this point, we could go either way: we could figure out all the numbers in the \u201ccollege\u201d row or all the numbers in the \u201cmale\u201d column.<\/p>\n

          \"gpp-se_img6\"<\/a><\/p>\n

          Either way, it is easy to fill in the last box:<\/p>\n

          \"gpp-se_img7\"<\/a><\/p>\n

          Thus, there are 100 employees who are females with advanced degrees.\u00a0 Answer = (C)<\/strong>.<\/p>\n

          3) This problem calls for a 3×3 double matrix.\u00a0 Here are the numbers for the grade levels, with the column totaled:<\/p>\n

          \"gpp-se_img8\"<\/a><\/p>\n

          Obviously, 10% of 400 is 40, so 30% is 3*40 = 120, and 60% = 6*40 = 240.\u00a0 This allows us to complete the bottom row.<\/p>\n

          \"gpp-se_img9\"<\/a><\/p>\n

          All 40 from C are freshmen, so we can put zeros in the other two grade level slots:<\/p>\n

          \"gpp-se_img10\"<\/a><\/p>\n

          Half of the 120 from B, 60, are upperclassmen, and the other 60 are evenly split, 30 in each of the other two slots.<\/p>\n

          \"gpp-se_img11\"<\/a><\/p>\n

          Now, we can complete the sophomore row:<\/p>\n

          \"gpp-se_img12\"<\/a><\/p>\n

          There are 70 sophomores from A.\u00a0 Answer = (B)<\/strong>.<\/p>\n

          4) This problem calls for a 3-way Venn Diagram.\u00a0 Here\u2019s the diagram with no numbers filled in.<\/p>\n

          \"gpp-se_img13\"<\/a><\/p>\n

          We know that C = 15.\u00a0 If 40 students are in both chorus & Italian, B + C = 40, and because C = 15, B = 25.\u00a0 If 45 students in both chorus & baseball, C + F = 45, and F = 30.\u00a0 We know that there are 120 in chorus, and B + C + F = 70, so E = 50.<\/p>\n

          Now, we are told that 220 student are in either Italian or baseball.\u00a0 Think about that region, Italian or baseball:<\/p>\n

          \"gpp-se_img14\"<\/a><\/p>\n

          That entire purple region, A + B + C + D + F + G, is 220.\u00a0 If we add E = 50, that\u2019s a total of 270 inside all three circles, which means that the outside of the circle, H, must equal 400 \u2013 270 = 130.\u00a0 Answer = (E)<\/strong>.<\/p>\n

           <\/p>\n

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

          Here are four reasonably challenging problems about sets. 1) At a certain school of 200 students, the students can study French, Spanish, both or neither. Just as many study both as study neither.\u00a0 One quarter of those who study Spanish also study French.\u00a0 The total number who study French is 10 fewer than those who […]<\/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-5140","post","type-post","status-publish","format-standard","hentry","category-math"],"acf":[],"yoast_head":"\nGMAT Practice Problems: Sets - 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\/gmat-practice-problems-sets\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Practice Problems: Sets\" \/>\n<meta property=\"og:description\" content=\"Here are four reasonably challenging problems about sets. 1) At a certain school of 200 students, the students can study French, Spanish, both or neither. 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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\/5140","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=5140"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/5140\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=5140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=5140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=5140"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=5140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}