A cafeteria survey shows that 125 students like steak, 60 like shrimp, and 40 students like both steak and shrimp. Assuming that all of the students surveyed liked at least one of the options, how many students were surveyed?

The answer is not 225 students. Why not?

Try using a Venn diagram to account for the overlap.

Cooking survey

A student was asked to interview at least 140 people about their cooking habits. She handed in the following results. Did she interview at least 140 people?

58 use microwave ovens

63 use electric ranges

58 use gas ranges

19 use microwave ovens and electric ranges

17 use microwave ovens and gas ranges

4 use both gas and electric ranges

1 use all three (gas, electric, microwave)

4 use only solar energy

Use a Venn diagram to keep track of overlaps.

Start with the center and move out.

Near-sighted lawyers

In a group of 37 people, 18 are neither near-sighted nor lawyers. Ten are near-sighted and 13 are lawyers. How many lawyers in the group are near-sighted?

Thingamajigs

Every doodad is a doohickey. Half of all thingamajigs are doohickeys. Half of all doohickeys are doodads. There are 30 thingamajigs and 20 doodads. No thingamajig is a doodad. How many doohickeys are neither doodads nor thingamajigs?