{"id":18354,"date":"2020-01-08T19:39:00","date_gmt":"2020-01-08T14:09:00","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=18354"},"modified":"2022-11-18T16:19:59","modified_gmt":"2022-11-18T10:49:59","slug":"how-to-use-tree-structures-to-solve-gmat-arithmetic-problems","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/how-to-use-tree-structures-to-solve-gmat-arithmetic-problems\/","title":{"rendered":"How to use Tree Structures to solve GMAT arithmetic problems"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">8<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<h1 id=\"h-the-objective-of-this-article\">The objective of this article<\/h1>\n\n\n\n<ul><li>The primary objective of this article is to explain the use of Visualizing the information given in a question and representing it in the form of a Tree Diagram.<\/li><li>This article is helpful for those who have a basic understanding of Percent, Sets, and Elements.<\/li><li>After going through the article, one will be able to solve various questions on Sets, Probability, Percent, and many more word problems simply by representing the given information in the form of a Tree Structure.<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"1024\" height=\"511\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/GMAT-arithmetic-problems-1024x511.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-19173\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/GMAT-arithmetic-problems-1024x511.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/GMAT-arithmetic-problems-300x150.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/GMAT-arithmetic-problems-768x383.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/GMAT-arithmetic-problems-1080x539.png 1080w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h1 id=\"h-agenda-of-the-article\">Agenda of the Article:<\/h1>\n\n\n\n<ul><li>In this article, we will solve 2 examples to learn the application of solving a question using a tree structure. First, we will see how to understand the given information and then represent the given information in the form of a Tree Structure with appropriate branching.<\/li><\/ul>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>Learn how <a href=\"https:\/\/e-gmat.com\/blogs\/gmat-non-native-speaker-100-points-improvement\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Anastasiia scored a perfect Q51 on the GMAT<\/a> and received an admit from <a href=\"https:\/\/e-gmat.com\/blogs\/columbia-business-school-mba-program-strengths-class-profile-career-outcomes-and-employment-reports\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Columbia Business School.<\/a><\/strong><\/p><\/blockquote>\n\n\n\n<h1 id=\"h-question-1\">Question 1<\/h1>\n\n\n\n<p>720 people have attended a guest lecture, which was open for only students and faculty, conducted by an MBA graduate. The number of females, who attended the lecture is half the number of males, who attended the lecture. There were four times as many students as faculty at the lecture. If 2\/3&nbsp;<sup>rd<\/sup> of the faculty were males, then how many female students have attended the lecture?<\/p>\n\n\n\n<ol><li>192<\/li><li>240<\/li><li>288<\/li><li>384<\/li><li>432<\/li><\/ol>\n\n\n\n<h2 id=\"h-understanding-the-question\">Understanding the question<\/h2>\n\n\n\n<p>In this question, we are given that,<\/p>\n\n\n\n<ul><li>A guest lecture conducted by an MBA graduate was attended by a total of 720 people<\/li><li>And, only students and faculty were allowed to attend this lecture\n<ul>\n<li>We also have information that the number of students, who attended the lecture is equal to 4 times the number of faculty who attended the lecture.\n<ul>\n<li>Among the total number of faculty, who attended the lecture, 2\/3&nbsp;<sup>rd<\/sup> were males<\/li>\n<li>And, the total number of females, who attended the lecture were half the total number of males<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>This is all the information that we have, and we are asked to find out the number of female students who attended the lecture.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong><em>If you are planning to take the GMAT, we can help you with a personalized study plan and give you access to quality online content to prepare. Write to us at\u00a0<a href=\"mailto:acethegmat@e-gmat.com\" target=\"_blank\" rel=\"noopener\">acethegmat@e-gmat.com<\/a>. We are the\u00a0<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noopener external noreferrer\" data-wpel-link=\"external\">most reviewed GMAT prep company on gmatclub<\/a>\u00a0with more than 1825 reviews (as on May 25, 2019). Why don\u2019t you\u00a0<a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">take a free trial\u00a0<\/a>and judge it for yourself?<\/em><\/strong><\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-059c0120-ede9-40ab-a16a-8a4026231fde\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 512, 512\"><path fill=\"currentColor\" d=\"M256 0C114.6 0 0 114.6 0 256c0 141.4 114.6 256 256 256s256-114.6 256-256C512 114.6 397.4 0 256 0zM406.6 278.6l-103.1 103.1c-12.5 12.5-32.75 12.5-45.25 0s-12.5-32.75 0-45.25L306.8 288H128C110.3 288 96 273.7 96 256s14.31-32 32-32h178.8l-49.38-49.38c-12.5-12.5-12.5-32.75 0-45.25s32.75-12.5 45.25 0l103.1 103.1C414.6 241.3 416 251.1 416 256C416 260.9 414.6 270.7 406.6 278.6z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Start your free trial<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<h2 id=\"h-set-up-the-tree-diagram\">Set Up the Tree Diagram<\/h2>\n\n\n\n<p>Now that we have understood all the information that is given to us, let\u2019s try to set up a Tree Diagram with proper branching<\/p>\n\n\n\n<ul><li>We typically start with the main group, which in this case is the people who attended the guest lecture.\n<ul>\n<li>This group of people is sub-divided into students and faculty, since, these are only set of people who are allowed to attend the lecture.<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"316\" height=\"206\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP1.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18356\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP1.png 316w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP1-300x196.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/figure>\n\n\n\n<ul><li style=\"list-style-type: none;\">\n<ul>\n<li>Now, we need to account for one more category of division, that is male and female. So, both the groups, students and faculty, are sub-divided into male and female.<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"490\" height=\"309\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP2.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18357\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP2.png 490w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP2-300x189.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/figure>\n\n\n\n<p>Let us assume that,<\/p>\n\n\n\n<ul><li>The number of Students = S\n<ul>\n<li>The number of female students = F<sub>S<\/sub>, and the number of male students = M<sub>S<\/sub><\/li>\n<\/ul>\n<\/li><li>Similarly, the number of faculty = F\n<ul>\n<li>The number of female faculty = F<sub>F<\/sub> and the number of male faculty = M<sub>F<\/sub><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"477\" height=\"348\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP3.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18358\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP3.png 477w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP3-300x219.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/figure>\n\n\n\n<p>With this we have accounted space for all the branches listed in the question.<\/p>\n\n\n\n<h2 id=\"h-establish-relations\">Establish Relations<\/h2>\n\n\n\n<p>The next step is to establish a relation between each and every branch with its stem.<\/p>\n\n\n\n<ul><li>Let\u2019s start with the trunk, that is, people who attended the guest lecture<\/li><li>From the diagram, we can see that the total number of people(T) = the number of students(S) + the number of faculty(F), which is equal to 720\n<ul>\n<li>T = S + F = 720\u2026\u2026\u2026 (1)<\/li>\n<\/ul>\n<\/li><li>And from the given information, we know that S = 4 * F \u2026\u2026\u2026. (2)<\/li><li>Solving equations (1) and (2), we get\n<ul>\n<li>4F + F =720, which implies, F = 144<\/li>\n<li>Thus, S = 720 \u2013 144 = 576<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"478\" height=\"358\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP4.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18359\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP4.png 478w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP4-300x225.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/figure>\n\n\n\n<p>Now that we know the number of students and the number of faculty, let\u2019s find how many of them are male and how many are female.<\/p>\n\n\n\n<ul><li>From the Diagram, we can see that, the total number of females = F<sub>F<\/sub> + F<sub>S<\/sub>\n<ul>\n<li>As per the question statement, we need to find the value of F<sub>S<\/sub><\/li>\n<li>Thus, we need to know the values of F<sub>F<\/sub> and the total number of females to find F<sub>S<\/sub><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><u>To find F<sub>F<\/sub><\/u><\/p>\n\n\n\n<ul><li>From the Diagram, we can see that, F = M<sub>F<\/sub> + F<sub>F<\/sub><\/li><li>And, from the given information, we get, M<sub>F<\/sub> = (2 * F)\/3 = (2 * 144)\/3&nbsp; = 96\n<ul>\n<li>Thus, F<sub>F<\/sub> = 144 \u2013 96 = 48<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><u>To find the total number of females<\/u><\/p>\n\n\n\n<ul><li>We are told that the number of females = 1\/2 * the number of males<\/li><li>And from the diagram, we can infer that the total number of females + the total number of males = 720\n<ul>\n<li>Using the above two relations, we get,\n<ul>\n<li>Total number of females + 2 * total number of females = 720<\/li>\n<li>Which implies that the total number of females = 720\/3 = 240<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>Therefore, F<sub>S<\/sub> = total number of females &#8211; F<sub>F<\/sub> = 240 \u2013 48 = 192<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"450\" height=\"346\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP5.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18360\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP5.png 450w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP5-300x231.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/figure>\n\n\n\n<p>Now, let\u2019s apply the learnings from this question to solve one more question, where we have more branches.<\/p>\n\n\n\n<h1 id=\"h-question-2\">Question 2<\/h1>\n\n\n\n<p>In a law firm, 1\/4&nbsp;<sup>th<\/sup> of the total employees are senior employees, who have a work experience of more than 5 years and the rest are junior employees. 60 percent of the senior employees are associates and 40% of the total employees, in the firm, are junior associates. 80% of the senior employees, who are associates, are male. If the total number of male associates is equal to the total number of female associates, in the firm, then what percentage of the junior associates, in the firm, are male?<\/p>\n\n\n\n<ol><li>(31\/2)%<\/li><li>(62\/3)%<\/li><li>(49\/2)%<\/li><li>(155\/4)%<\/li><li>(245\/4)%<\/li><\/ol>\n\n\n\n<h2 id=\"h-understanding-the-question-1\">Understanding the question<\/h2>\n\n\n\n<p>In this question, we are given that,<\/p>\n\n\n\n<ul><li>In a law firm, 1\/4&nbsp;<sup>th<\/sup> of the employees are senior employees and the rest are junior employees.\n<ul>\n<li>We are also told that,\n<ul>\n<li>60% of the total number of senior employees are associates, and<\/li>\n<li>40% of the total employees, in the firm, are junior associates<\/li>\n<\/ul>\n<\/li>\n<li>Then, we have another information that 80% of the senior employees, who are associates, are male<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>This is all the information that is given to us have, and we are asked to find out the percentage of junior associates, who are male, if the total number of male associates in the firm = the total number of female associates.<\/p>\n\n\n\n<h2 id=\"h-set-up-the-tree-diagram-1\">Set Up the Tree Diagram<\/h2>\n\n\n\n<p>Now that we have understood all the information that is given to us, let\u2019s try to set up a Tree Diagram with proper branching<\/p>\n\n\n\n<ul><li>We typically start with the main group, which is the total employees in the law firm.\n<ul>\n<li>These are sub-divided into senior employees and junior employees.<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"464\" height=\"222\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP6.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18361\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP6.png 464w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP6-300x144.png 300w\" sizes=\"(max-width: 464px) 100vw, 464px\" \/><\/figure>\n\n\n\n<ul><li>Now, we have information about the percentage of senior and junior employees, who are associates, and the rest of the senior and junior employees can be grouped as others.<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"512\" height=\"322\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP7.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18362\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP7.png 512w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP7-300x189.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP7-510x322.png 510w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/figure>\n\n\n\n<p>Let us assume that,<\/p>\n\n\n\n<ul><li>The number of employees in the firm = N\n<ul>\n<li>The number of senior employees = S, and the number of junior employees = J<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"590\" height=\"367\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP8.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18363\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP8.png 590w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP8-300x187.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP8-400x250.png 400w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/figure>\n\n\n\n<p>We need to account for one more division, that is the senior and junior associates, who are male and female.<\/p>\n\n\n\n<p>Let us assume that,<\/p>\n\n\n\n<ul><li>The number of senior associates = A<sub>S<\/sub>, and the number of junior associates = A<sub>J <\/sub><\/li><li>The number of senior associates, who are male = M<sub>1<\/sub> and number of senior associates, who are female = F<sub>1<\/sub><\/li><li>Similarly, the number of junior associates, who are male = M<sub>2<\/sub> and number of junior associates, who are female = F<sub>2<\/sub><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"578\" height=\"404\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP9.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18364\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP9.png 578w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP9-300x210.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/figure>\n\n\n\n<h2 id=\"h-establish-relations-1\">Establish Relations<\/h2>\n\n\n\n<p>The next step is to establish a relation between each and every branch with its stem.<\/p>\n\n\n\n<p>Before, that let\u2019s see what we are asked to find out: \u201c<em>what percentage of the junior associates, in the firm, are male\u201d<\/em><\/p>\n\n\n\n<ul><li>From the diagram, we can see that the number of junior associates, who are male is represented by M<sub>2<\/sub>\n<ul>\n<li>Therefore, we need to find the value of (M<sub>2<\/sub>\/A<sub>J<\/sub>) * 100, where A<sub>J<\/sub> = M<sub>2<\/sub> + F<sub>2<\/sub><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>Now that we know the expression, for what to be found, let\u2019s move further.<\/p>\n\n\n\n<p>Note that we can find the value of (M<sub>2<\/sub>\/A<sub>J<\/sub>) * 100, if we know the values of M<sub>2<\/sub> and F<sub>2<\/sub> (or) M<sub>2<\/sub> and A<sub>J<\/sub>.<\/p>\n\n\n\n<ul><li>Let\u2019s start with the trunk, that is the total number of employees in the firm<\/li><li>From the diagram, we can see that the total number of employees in the firm = the number of senior employees(S) + the number of junior employees(J)\n<ul>\n<li>N = S + J \u2026\u2026\u2026 (1)<\/li>\n<\/ul>\n<\/li><li>And from the given information, we know that S = N\/4 \u2026\u2026\u2026. (2)<\/li><li>Solving equations (1) and (2), we get\n<ul>\n<li>S = N\/4 , and J = 3N\/4<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"538\" height=\"303\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP10.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18365\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP10.png 538w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP10-300x169.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/figure>\n\n\n\n<p>Now that we know the fraction of senior and junior employees in the firm, let\u2019s move further to find how many of the senior and junior employees are associates.<\/p>\n\n\n\n<ul><li>From the given information, we can infer that,\n<ul>\n<li>A<sub>S<\/sub> = 60% of S = 6S\/10 = 6\/10 * N\/4 = 3N\/20<\/li>\n<li>A<sub>J<\/sub> = 40% of N = 4N\/10 = 2N\/5<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>Now, let\u2019s use the given information to establish more relations<\/p>\n\n\n\n<ul><li>\u201c80% of the senior employees, who are associates, are male<em>,<\/em>\u201d\n<ul>\n<li>Let\u2019s translate this statement into a mathematical equation,<\/li>\n<li>From the diagram, we can see that the number of senior employees, who are associates = A<sub>S<\/sub>\n<ul>\n<li>Thus, 80% of A<sub>S<\/sub> = (8\/10) * (3N\/20) = 3N\/25 = M<sub>1<\/sub> \u2026\u2026\u2026\u2026\u2026. (3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li><li>From the diagram, we can see that, A<sub>S<\/sub> = M<sub>1<\/sub> + F<sub>1<\/sub> = 3N\/20\n<ul>\n<li>Thus, F<sub>1<\/sub> = (3N\/20) \u2013 (3N\/25) = 3N\/100<\/li>\n<\/ul>\n<\/li><li><em>\u201c<\/em>Total number of male associates is equal to the total number of female associates<em>\u201d<\/em>\n<ul>\n<li>From the diagram, we can see that,\n<ul>\n<li>Total number of male associates = M<sub>1<\/sub> + M<sub>2<\/sub><\/li>\n<li>Total number of female associates = F<sub>1<\/sub> + F<sub>2<\/sub><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li><li>This implies, M<sub>1<\/sub> + M<sub>2 <\/sub>= F<sub>1<\/sub> + F<sub>2<\/sub><\/li><li>Substituting the values of M<sub>1<\/sub> and F<sub>1<\/sub>, we get,\n<ul>\n<li>(3N\/25) + M<sub>2<\/sub> = (3N\/100) + F<sub>2<\/sub><\/li>\n<li>Thus, F<sub>2<\/sub> \u2013 M<sub>2<\/sub> = (3N\/25) \u2013 (3N\/100) = 9N\/100 \u2026\u2026\u2026\u2026. (4)<\/li>\n<li>And, we know, A<sub>J<\/sub> = F<sub>2<\/sub> + M<sub>2<\/sub> = 2N\/5 \u2026\u2026\u2026\u2026. (5)<\/li>\n<\/ul>\n<\/li><li>Solving equations (4) and (5), we get,\n<ul>\n<li>(4) + (5) gives, 2F<sub>2<\/sub> = (2N\/5) + (9N\/100) = 49N\/100<\/li>\n<li>Implies, F<sub>2<\/sub> = 49N\/200<\/li>\n<li>Thus, M<sub>2<\/sub> will be (2N\/5) &#8211; (49N\/200) = 31N\/200<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p>Therefore, M<sub>2<\/sub>\/J * 100 = (31N\/200)\/( 2N\/5) * 100 = (155\/4)%<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"654\" height=\"332\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP11.png\" alt=\"GMAT arithmetic problems\" class=\"wp-image-18366\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP11.png 654w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/01\/AP11-300x152.png 300w\" sizes=\"(max-width: 654px) 100vw, 654px\" \/><\/figure>\n\n\n\n<h1 id=\"h-important-takeaways\">Important Takeaways<\/h1>\n\n\n\n<ul><li>Tree structures help us to summarize and visualize all the information given in the question by representing all the possible cases by a set of branches, emanating from the main stem, which is labeled according to the given information.<\/li><li>The sum of values of all the branches must be equal to the sum of its stem value.<\/li><li>In questions related to percent\u2019s, we do not need the stem value to find the percentage value of any branch or sub-branch, if we have a sufficient number of relations between them<\/li><\/ul>\n\n\n\n<h1 id=\"h-want-to-read-more-articles-like-this\">Want to read more articles like this?<\/h1>\n\n\n\n<p>Now, if you liked this article, then I am sure that you want to read some more articles like this, click <a href=\"https:\/\/e-gmat.com\/gc-articles?name=quant_consolidated\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">here to read all quant articles<\/a>.<\/p>\n\n\n\n<p>You will also get a lot of practice questions to learn from.<\/p>\n\n\n\n<p>Happy learning and in case of any other GMAT related queries, please write to us at <a href=\"mailto:acethegmat@e-gmat.com\">acethegmat@e-gmat.com.<\/a><\/p>\n\n\n\n<p><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong>If you are planning to take the GMAT, we can help you with a personalized study plan and give you access to quality online content to prepare.<\/strong>&nbsp;<strong>Write to us at&nbsp;<a href=\"mailto:acethegmat@e-gmat.com\" target=\"_blank\" rel=\"noreferrer noopener\">acethegmat@e-gmat.com<\/a>. 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This article is helpful for those who have a basic understanding of Percent, Sets, and Elements. After going through the article, [&hellip;]<\/p>\n","protected":false},"author":102412,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[94,60,102],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Asif M","author_link":"https:\/\/e-gmat.com\/blogs\/author\/asife-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to use Tree Structures to solve GMAT arithmetic problems<\/title>\n<meta name=\"description\" content=\"Tree structures can be effectively used to solve many GMAT arithmetic problems. 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