Hi team,
I'm taking practice MGMAT CATs and was stumped at how the answer to this question is 10 and not 13. It seems that they say that 81 - 68 = 10, instead of 16. My answer was that 16 - 3 = 13.
Your help is greatly appreciated!
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In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
13
10
9
8
7
For an overlapping set problem with three subsets, we can use a Venn diagram to solve.
Each circle represents the number of students enrolled in the History, English and Math classes, respectively. Notice that each circle is subdivided into different groups of students. Groups a, e, and f are comprised of students taking only 1 class. Groups b, c, and d are comprised of students taking 2 classes. In addition, the diagram shows us that 3 students are taking all 3 classes. We can use the diagram and the information in the question to write several equations:
History students: a + b + c + 3 = 25
Math students: e + b + d + 3 = 25
English students: f + c + d + 3 = 34
TOTAL students: a + e + f + b + c + d + 3 = 68
The question asks for the total number of students taking exactly 2 classes. This can be represented as b + c + d.
If we sum the first 3 equations (History, Math and English) we get:
a + e + f + 2b +2c +2d + 9 = 84.
Taking this equation and subtracting the 4th equation (Total students) yields the following:
a + e + f + 2b + 2c +2d + 9 = 84
-[a + e + f + b + c + d + 3 = 68]
b + c + d = 10
The correct answer is B.
I'm taking practice MGMAT CATs and was stumped at how the answer to this question is 10 and not 13. It seems that they say that 81 - 68 = 10, instead of 16. My answer was that 16 - 3 = 13.
Your help is greatly appreciated!
--
In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
13
10
9
8
7
For an overlapping set problem with three subsets, we can use a Venn diagram to solve.
Each circle represents the number of students enrolled in the History, English and Math classes, respectively. Notice that each circle is subdivided into different groups of students. Groups a, e, and f are comprised of students taking only 1 class. Groups b, c, and d are comprised of students taking 2 classes. In addition, the diagram shows us that 3 students are taking all 3 classes. We can use the diagram and the information in the question to write several equations:
History students: a + b + c + 3 = 25
Math students: e + b + d + 3 = 25
English students: f + c + d + 3 = 34
TOTAL students: a + e + f + b + c + d + 3 = 68
The question asks for the total number of students taking exactly 2 classes. This can be represented as b + c + d.
If we sum the first 3 equations (History, Math and English) we get:
a + e + f + 2b +2c +2d + 9 = 84.
Taking this equation and subtracting the 4th equation (Total students) yields the following:
a + e + f + 2b + 2c +2d + 9 = 84
-[a + e + f + b + c + d + 3 = 68]
b + c + d = 10
The correct answer is B.
