{"id":2574,"date":"2012-08-24T17:39:30","date_gmt":"2012-08-25T00:39:30","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=2574"},"modified":"2014-09-16T17:07:05","modified_gmt":"2014-09-17T00:07:05","slug":"gmat-sets-double-matrix-method","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/","title":{"rendered":"GMAT Sets: Double Matrix Method"},"content":{"rendered":"

Learn this powerful method for unlocking devilishly complicated problems about sets.\u00a0 <\/strong><\/p>\n

 <\/p>\n

Practice questions<\/h2>\n

First, try these challenging 700-level practice questions.<\/p>\n

1) At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males.\u00a0 There are a total of 40 managers, and the rest of the employees are associates.\u00a0 If there are a total of 135 male associates, how many female managers are there?<\/p>\n

A. 15
\nB. 20
\nC. 25
\nD. 30
\nE. 35<\/p>\n

2) In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools.\u00a0 These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools.\u00a0 If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?<\/p>\n

A. 2
\nB. 3
\nC. 4
\nD. 5
\nE. 6<\/p>\n

 <\/p>\n

This kind of question<\/h2>\n

It would not be surprising if you found one or both of those questions totally bewildering.\u00a0 Without the right method, this type of question can be a nightmare.<\/p>\n

First of all, let’s be clear about what we mean by “this type of question.”\u00a0 These are set questions in which each element, each member, is classified according to two different variables, and each one of those variables has two or more categories.\u00a0 For example, in question #1, the two variables are:<\/p>\n

a) gender (male or female)
\nb) employee type (manager or associate)<\/p>\n

Every one of those 250 employees is categorized both in terms of gender and in terms of employee type.\u00a0 That’s key: every member is categorized in two different ways<\/em>.\u00a0 This type of question is screaming for a method of solution called the Double Matrix Method<\/strong>.<\/p>\n

 <\/p>\n

The Double Matrix Method: example #1<\/h2>\n

I will demonstrate the Double Matrix Method first by solving question #1, then question #2.\u00a0 In the Double Matrix Method, you make a sectioned box, a rectangle with subdivisions.\u00a0 The horizontal subdivisions will represent the categories of one variable, and the vertical subdivisions will represent the categories of the other variable.\u00a0 Here’s the set-up for question #1: I temporarily put letters in the boxes, to facilitate talking about those boxes.<\/p>\n

\"\"<\/a><\/p>\n

A is number of male managers, B is the number of female managers, and A + B = C is the total number of managers.\u00a0 Similarly, D is the number male associates, and A + D = G is the total number of males.\u00a0 In any row, you can add across the first two boxes and the sum will be the box on the right.\u00a0 In any column, you can add the top two boxes, and the sum will be the bottom box.\u00a0 The final number, I, is the “grand total”, the total number of employees in the whole problem, which obvious has to equal the sum of males + females, as well as the sum of managers + associates.<\/p>\n

Here’s that matrix again with the numbers from the problem filled in — just the numbers stated in black-and-white in the problem.<\/p>\n

\"\"<\/a><\/p>\n

Well, first let’s take care of the “totals”.\u00a0 The numbers in the “totals” row must add up.\u00a0 If 90 are females, the other 250 \u2013 90 = 160 must be males.\u00a0 Similarly, the numbers in the “totals” column must add up.\u00a0 If 40 are managers, then the other 250 \u2013 40 = 210 must be associates.<\/p>\n

\"\"<\/a><\/p>\n

Now, in the “associate” row, 135 + E = 210, which means E = 75 — the other 75 associates must be female.<\/p>\n

\"\"<\/a><\/p>\n

Now, to find B, which is what the question is asking, we need only look at the sum in the “female” column: B + 75 = 90, which means B = 15.\u00a0 There are fifteen female managers in this company.\u00a0 Thus, the answer = (A)<\/strong>.<\/p>\n

Instead of this route, once we found all the “totals” numbers, we could have used addition in the “male” column to find A = 25, then use addition across the “managers” to find B = 15 —- in fact, if you have a second route for finding the number, you should perform that too, to verify that you get the same number both ways.<\/p>\n

 <\/p>\n

The Double Matrix Method: example #2<\/h2>\n

Question #2 is very difficult: it’s debatable whether a set question this difficult even would appear on the GMAT.\u00a0 Nevertheless, the Double Matrix Method unlocks it easily.\u00a0 First of all, our matrix now has to have three categories for each variable.<\/p>\n

\"\"<\/a><\/p>\n

As before, in any row, the sum across the first three entries will equal the right-most entry in the “totals” column; and similarly, the sum down the top three entries in any column will equal the bottom entry in the “total” row; and, of course, all the totals, in either the “totals” row or the “totals” column, have to add up to the grand total in the lower right-hand box.\u00a0 Let’s start filling this in, following the information given in the question.\u00a0 “In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools<\/em>.”<\/p>\n

\"\"<\/a><\/p>\n

“District A has 18 high schools total<\/em>.”<\/p>\n

\"\"<\/a><\/p>\n

“District B has 17 high schools total, and only two of those are private independent schools.<\/em>”<\/p>\n

\"\"<\/a><\/p>\n

“District C has an equal number of each of the three kinds of schools<\/em>.”\u00a0 Hmm.\u00a0 That’s not a simple number.\u00a0 Let’s put that on hold for a moment.\u00a0 So far, from the matrix it looks like we could figure out the missing number in the “totals” row.\u00a0 That number must be 15, because 18 + 17 + 15 = 50.<\/p>\n

\"\"<\/a><\/p>\n

Now, go back to that last fact: “District C has an equal number of each of the three kinds of schools<\/em>.”\u00a0 Now that makes sense.\u00a0 District C has 15 schools, so it must have 5 of each kind:<\/p>\n

\"\"<\/a><\/p>\n

The question is asking: “how many private independent schools are there in District A?”\u00a0 Well, now that’s just a matter of adding across the “private independent” row.\u00a0 We know 2 + 2 + 5 = 9, so the missing number must be 2.<\/p>\n

\"\"<\/a><\/p>\n

There’s still a good deal of information we can’t figure out from the information given in the question, but we are able to answer the specific question asked here.\u00a0 There are 2 private independent schools in District A, so the answer = (A)<\/strong>.<\/p>\n

Notice, incidentally, if the question were framed differently, as a DS question, the Double Matrix method would allow us to see what questions we could and couldn’t answer based on the information given.\u00a0 In a DS question, one would have to write out one Double Matrix for Statement #1, and a whole new Double Matrix for Statement #2.\u00a0 Trying to save time by cramming all the information from both statements into a single matrix is an excellent way to make the classic mistake of conflating the information given in the two statements, one of the most common mistakes on Data Sufficiency.<\/p>\n

 <\/p>\n

Practice question<\/h2>\n

Here’s another very challenging question that you should be able to unlock with the help of the Double Matrix Method.<\/p>\n

3) http:\/\/gmat.magoosh.com\/questions\/11<\/a><\/p>\n

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

Learn this powerful method for unlocking devilishly complicated problems about sets.\u00a0   Practice questions First, try these challenging 700-level practice questions. 1) At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males.\u00a0 There are a total of 40 managers, and the rest of the employees are associates.\u00a0 If […]<\/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-2574","post","type-post","status-publish","format-standard","hentry","category-word-problems"],"acf":[],"yoast_head":"\nGMAT Sets: Double Matrix Method - 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-sets-double-matrix-method\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Sets: Double Matrix Method\" \/>\n<meta property=\"og:description\" content=\"Learn this powerful method for unlocking devilishly complicated problems about sets.\u00a0   Practice questions First, try these challenging 700-level practice questions. 1) At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males.\u00a0 There are a total of 40 managers, and the rest of the employees are associates.\u00a0 If […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GMAT\u00ae Exam\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MagooshGMAT\/\" \/>\n<meta property=\"article:published_time\" content=\"2012-08-25T00:39:30+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2014-09-17T00:07:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gmat\/files\/2012\/08\/s2_img1.png\" \/>\n<meta name=\"author\" content=\"Mike M\u1d9cGarry\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mike M\u1d9cGarry\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"GMAT Sets: Double Matrix Method\",\"datePublished\":\"2012-08-25T00:39:30+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/\"},\"wordCount\":1143,\"commentCount\":21,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Word Problems\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/\",\"name\":\"GMAT Sets: Double Matrix Method - Magoosh Blog \u2014 GMAT\u00ae Exam\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\"},\"datePublished\":\"2012-08-25T00:39:30+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-sets-double-matrix-method\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/gmat\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"GMAT Sets: Double Matrix Method\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"name\":\"Magoosh Blog \u2014 GMAT\u00ae Exam\",\"description\":\"Everything you need to know about the GMAT\",\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/gmat\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\",\"name\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"contentUrl\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"width\":265,\"height\":60,\"caption\":\"Magoosh\"},\"image\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/MagooshGMAT\/\",\"https:\/\/twitter.com\/MagooshGMAT\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\",\"name\":\"Mike M\u1d9cGarry\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/image\/15a1e36ef1c2c3940179212433de141a\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"caption\":\"Mike M\u1d9cGarry\"},\"description\":\"Mike holds an A.B. in Physics (graduating magna cum laude) and an M.T.S. in Religions of the World, both from Harvard. 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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\/2574","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=2574"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/2574\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=2574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=2574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=2574"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=2574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}