Yes, you can use a Venn diagram here. One very important issue to consider, though, is the space outside of the diagram: that is, those who are neither students nor employed. The problem doesn't tell us anything about that group, but we cannot assume that it doesn't exist. Thus, you need to create a bubble
outside of the diagram for that group:
We're looking for the number of people that are BOTH students and employed:
As Matt said, the easiest thing to do once you've visualized this in a diagram is to assign variables. We actually have FOUR variables here, though, not three: S for "student only," E for "employed only," B both "both employed and a student," and N for "neither employed nor a student."
So, S + B + E + N = 42
(1) tells us that B + E = 29. This is not sufficient to solve for B.
(2) tells us that S + B = 24. Again, not sufficient.
If we combine both statements, we still only have 3 equations, but we have 4 variables. Insufficient.
In cases in which there is a "neither" option, I think it's much easier to use the Double Set Matrix, which naturally contains those 4 options, and the additive relationships. Venn diagrams are helpful visual aids, but they are sometimes harder to construct equations with.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
