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 Geography and 74 offer Mathematics and Geography. All the students offer at least one subject. Determine the number of students who offer Mathematics.
Let's start by creating a Venn diagram to represent the information given:
Economics only = 16
Economics and Mathematics = 28
Economics and Geography = 46
Economics and Mathematics and Geography = 73
Geography only = ?
Mathematics and Geography = 74
Now let's fill in the Venn diagram with the information we have:
Economics only = 16
Economics and Mathematics = 28 (16 + 28 = 44, so Mathematics only = 0)
Economics and Geography = 46
Economics and Mathematics and Geography = 73
Mathematics and Geography = 74
Geography only = ?
We know that there are a total of 140 students, and they all offer at least one subject. Let's use this to find the number of students who offer Mathematics:
Total = Economics + Mathematics + Geography - (Economics and Mathematics + Economics and Geography + Mathematics and Geography) + (Economics and Mathematics and Geography)
140 = 16 + 0 + 0 - 73 + 28 + 46 + 74 - 0
140 = 87 + 16
Mathematics = 140 - 103
Mathematics = 37
Therefore, there are 37 students who offer Mathematics.