Venn Diagram v/s Double Set Matrix

CAT Exam
Venn diagrams are like Superman – all powerful. They can help you solve almost all questions involving either 2 or 3 overlapping sets. But then, there are some situations in which double set matrix method (aka Batman with his amazing weaponry) might be easier to use. It is possible to solve these questions using Venn diagrams, too, but it is more convenient to solve them using a Double Set Matrix. Today, we will look at the case in which using a Double Set Matrix is easier than using a Venn diagram – in instances where we have two sets of variables, such as English/Math and Middle School/High School, or Cake/Ice cream and Boys/Girls, etc. Eventually, we will solve our question again using a Venn diagram, for those who like to use a single method for all similar questions. First, take a look at our question: A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event? (A) 18 (B) 27 (C) 36 (D) 72 (E) 180 To solve this problem using a Double Set Matrix, first jot down one set of variables as the row headings and the other as the column headings, as well as a row and column for “totals.” Now all you need to do is add in the information line by line as you read through the question. “…male graduate students outnumber male undergraduates by a ratio of 7 to 2…QWQW graph 1       “…females constitute 70% of the group.” Female students make up 70% of the group, which implies that male students (total of 9x) make up 30% of the group. 9x = (30/100)*Total Students Total Students = 30x Since 9x is the total number of male students while 30x is the total number of all students, the total number of female students must be 30x – 9x = 21x. QWQW graph 2     “If undergraduate students make up 1/6 of the group…” Undergrad students make 1/6 of the group, i.e. (1/6)*30x = 5x If the total number of undergrad students is 5x and the number of male undergrad students is 2x, the number of female undergrad students must be 5x – 2x = 3x. This implies that the number of graduate females must be 18x, since the total number of females is 21x. QWQW graph 3       Therefore, the number of graduate females must be a multiple of 18. 27 is the only answer choice that is not a multiple of 18, so it cannot be the number of graduate females – therefore, our answer must be B. Now, here is how Superman can rescue us in this question. An analysis similar to the one above will give us a Venn diagram which looks like this: qwqw pic               Of course, we will get the same answer: the number of graduate females must be a multiple of 18. We know 27 is not a multiple of 18, so it cannot be the number of graduate females and therefore, our answer is still B.

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