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GMAT Overlapping Sets

by ejkiv


July 19, 2015


Since the theme of this content is to do things as simple as possible, as quickly as possible, and make as few mistakes as possible, I am going to leave out many of the ways that other books may describe this section. Quite frankly, the equations are easy to mess up and venn diagrams (except in one case) do not represent the information in an easy to read manner.

But first, what are GMAT overlapping sets? It is a way to describe two pieces of independent information relating to a singular group of people. The important thing to note is that when you are defining a characteristic, you want to be able to incorporate every single person. Let’s look at an example:

Of 40 people who took Calculus in a college class, 24 of them took calculus in  high school. If 13 members of the class were females who had taken  calculus in high school and there are 24 females in the class, how many males  had not taken calculus in high school?

The groups you want to break the class into are 1) took a high school calculus course or did not take and high school calculus course and 2) male or female.

To analyze a problem like this we are going to put all of the information in the figure below:

GMAT Overlapping Sets

While this may seem a bit complicated, it is actually quite simple. Any of the cells that are a total can be calculated by adding the corresponding row or column from inside the dark square. The grand total is the sum of both the column above it and the row to the left.

For a more hands on approach, let’s look at how this relates to the problem we started with:

Of 40 people who took Calculus in a college class, 24 of them took calculus in  high school. If 13 members of the class were females who had taken  calculus in high school and there are 24 females in the class, how many males had not taken calculus in high school?

When you are going through a problem like this, put the information in the square as soon as you have identified the 2 groups, which we already did, and item by item.

1) There are 40 people in a calculus course

GMAT Overlapping Sets

2) 24 of them took a HS Calc Class. Once you know this, you can also calculate how many did not take HS calc like this 40-24 = 16, because the row must sum to 40.

GMAT Overlapping Sets

3) 13 members of the class were females who had taken calculus in high school (you can also calculate males who took high school calc: 24-13=11).

GMAT Overlapping Sets

4) 24 females in the class, then calculate males (40-24=16).

GMAT Overlapping Sets

Finally, we can answer the question, which was, “how many males had not taken calculus in high school?” To do this just identify the square that represents the data we are looking for and do the calculation. In this case, as seen on the next page, the answer is 16-11 = 5.

GMAT Overlapping Sets

Obviously this is a basic example, but really these steps will help you in even the most difficult problems. This square can be used with fractions, percents, and whole numbers. Make sure the grand total is 1 when using fractions, 100% when using percents, and whatever the total value is when using whole numbers.

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