Today let’s work on a sets problem using Venn diagrams!
In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?
This question can be solved using a Venn diagram or a matrix to make sense of the information:
The key to understanding this question lies in the last sentence:
who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?
We have two categories to sum: the people who ONLY received a science degree but NOT from one of the 6 schools, and the people who ONLY went to the 6 schools but did NOT receive a science degree. I made up variables for these categories (x and y).
If N = 12, there are 4 applied science students, 1 of which is both. That means x = 3. If 4 students are applied science, then 12-4 = 8 are from one of the six states but NOT applied science. y = 8.
3 + 8 = 11
So we are looking for an answer choice that gives us 11 when N = 12; the answer is (A).