# ISEE Lower Level Quantitative : How to use a Venn Diagram

## Example Questions

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### Example Question #1 : How To Find The Common Part With A Venn Diagram

If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?

Explanation:

The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.

### Example Question #1 : How To Use A Venn Diagram

The following Venn diagram depicts the number of students who like soccer, football, or both. How many students like soccer but not football?

28

12

16

8

12

Explanation:

A Venn diagram is used to demonstrate the number of people (or things) in particular categories. The regions of the circle that are overlapping indicate the number of individuals that belong to multiple groups. Therefore, based on this diagram, 12 students like soccer only, 16 like football only, and 8 like both.

### Example Question #1 : Venn Diagrams

The Venn diagram above represents the results from a recent survey given to middle school students. Category  represents the amount of students that only like pizza. Category  represents the amount of students that only chicken nuggets.

What fraction of the students only like chicken nuggets?

Explanation:

Since exactly  of a total  percent of the students only like chicken nuggets, the solution is:

### Example Question #41 : Data Analysis

The Venn diagram above represents the results from a recent survey given to middle school students. Category  represents the amount of students that only like pizza. Category  represents the amount of students that only chicken nuggets.

What fraction of the students only like pizza?

Explanation:

Since category  represents the total number of students that only like pizza, the correct answer is that  percent is equivalent to .

### Example Question #1 : How To Use A Venn Diagram

Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.

Group  represents the respondents that answered "yes" to the survey question. Group  represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.

What percentage of the respondents answered "no" to Aracely's survey question?

Explanation:

The Venn diagram has three separate categories. Category  represents the respondents that answered "yes" to the survey question, category  represents the respondents that answered "no" and the overlapping portion of the diagram represents the respondents that answered "maybe" to the survey question.

Category  .

Thus,  of the respondents answered "no" to the survey question.

### Example Question #1 : How To Use A Venn Diagram

Aracely posted a  survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.

Group  represents the respondents that answered "yes" to the survey question. Group  represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.

What fraction represents the amount of respondents that answered "yes" to the survey question?

Explanation:

The Venn diagram shows that exactly  percent of the survey respondents answered "yes" to the survey question.

Thus, to find the fraction equivalent we need to rewrite

From here we simplify the fraction.

### Example Question #1 : How To Use A Venn Diagram

The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.

Category  represents the number of players on the team that are left-handed.
Category  represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.

Given that  and that there are  players in the overlapping region of the diagram.

How many players are right-handed pitchers?

Explanation:

Since the question provides the information that there are  left-handed pitchers and  total pitchers, one can infer that the number of right-handed pitchers is equal to the difference between the total number of pitchers and the number of left-handed pitchers.

Thus, the solution is:

### Example Question #1 : How To Use A Venn Diagram

The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.

Category  represents the number of players on the team that are left-handed.
Category  represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.

Given that  and that there are  players in the overlapping region of the diagram.

What fraction of the players are only left-handed?

Explanation:

Since, there are  left-handed players total and  left-handed pitchers there must be  players that are left-handed but do not pitch, because .

To find what fraction this represents we need to do:

### Example Question #1 : How To Use A Venn Diagram

In the above Venn diagram category  represents the number of Kevin's friends that play the flute, while category  represents the number of Kevin's friends that play the bass.

If  of Kevin's friends only play the flute and  of his friends only play the bass, then what fraction of Kevin's friends play both instruments?

Explanation:

To find the fraction of Kevin's friends that play both the bass and the flute, consider that the fraction  represents all of Kevin's friends in this senario.

Thus, the solution can be found by adding those that only play flute with those that only play bass and subtracting that final answer from the fraqction that represents all of Kevin's friends:

### Example Question #101 : Data Analysis And Probability

In the above Venn diagram category  represents the number of Kevin's friends that play the flute, while category  represents the number of Kevin's friends that play the bass.

If  of Kevin's friends only play the flute and  of his friends only play the bass, then what percentage of Kevin's friends only only play the bass?