ôô

# How to Use Venn Diagrams to Solve Problems

Learn how to solve SAT math problems using Venn diagrams.

By
Jason Marshall, PhD,
August 12, 2011
Episode #073

Page 1 of 2

Now that we know how to make and interpret the meaning of Venn diagrams, it’s time to put our knowledge to the test and use them to solve problems that you might encounter in the real world. And when I say put our knowledge to the test, I mean that literally since problems like the one we’ll look at today frequently show up on standardized tests like the SAT…and lots of other places too.

SPONSOR: This podcast is brought to you by St. Martin’s Griffin—the publisher of The Insider’s Guide to the Colleges of California, compiled and edited by the staff of the Yale Daily News. Download it to your computer or e-reader for just \$1.99 from Amazon, B&N, or the iBookstore.

## Today’s SAT-Inspired Question

Imagine you’re at a local city council meeting at which an important vote about where to build a new dog park is taking place. The options are to build the dog park at either Washington Park or Waterfront Park, or to build a new dog park at each location. When people who support building at Washington Park are asked to raise their hands, 47 votes are registered. When people who support building at Waterfront Park are asked to raise their hands, 36 votes are registered. As you’re watching the votes come in, you notice that 24 of the voters have raised their hands in support of building parks in both locations.

So the question is: How many people voted? In other words, how can you use the knowledge that 47 people raised their hands for Washington Park and 36 raised their hands for Waterfront Park, while also knowing that 24 people raised their hands for both parks, to figure out how many people cast votes?