In a class of 140 students, 16 offer economics only, 28 offer Economics but not Mathematics, 46 offer Economics and Geography, 73 offer Economics, 90 offer Ge- ography and 74 offer Mathematics and Geography. All the students offer at least one subject.
i. Illustrate this information on a Venn diagram
ii. Determine the number of students who offer
• Mathematics
• Mathematics and Geography but not Economics
i.
Economics only: 16
Economics and Mathematics: 28
Economics and Geography: 46
Mathematics and Geography: 74
Mathematics only: (Unknown)
Geography only: (Unknown)
Let's label the circles:
Circle A: Economics
Circle B: Mathematics
Circle C: Geography
Now we can place the numbers into the correct sections of the Venn diagram:
[Circle A} - Economics only: 16
[Circle A and B] - Economics and Mathematics: 28
[Circle A and C] - Economics and Geography: 46
[Circle B and C] - Mathematics and Geography: 74
ii.
To determine the number of students who offer Mathematics, we need to find the total number of students that are in the Mathematics circle. This includes students who offer Mathematics only and those who offer Mathematics in combination with other subjects.
Total number of Mathematics students = Mathematics only + (Mathematics and Geography) + (Mathematics and Economics) = (Unknown) + 74 + 28
To find the number of students who offer Mathematics and Geography but not Economics, we need to look at the region where Mathematics and Geography overlap and exclude Economics.
Number of students who offer Mathematics and Geography but not Economics = (Mathematics and Geography) - (Mathematics and Economics and Geography) = 74 - 28 = 46 students.