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ISEE Lower Level Quantitative : Venn Diagrams

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #42 : Data Analysis

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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 $\small A$ represents the respondents that answered "yes" to the survey question. Group $\small B$ 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?

Possible Answers:

$\small \frac{1}{4}$

$\small \frac{1}{5}$

$\small \frac{4}{10}$

$\small \frac{2}{5}$

Correct answer:

$\small \frac{1}{5}$

Explanation:

The Venn diagram shows that exactly $\small 20$ percent of the survey respondents answered "yes" to the survey question.

Thus, to find the fraction equivalent we need to rewrite

$20\% \rightarrow \frac{20}{100}$

From here we simplify the fraction.

$\frac{20}{100}=\frac{2}{10}=\frac{1}{5}$

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Example Question #1652 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

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

Category $\small L$ represents the number of players on the team that are left-handed.
Category $\small P$ 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 $\small L=6, P=9$ and that there are $\small 3$ players in the overlapping region of the diagram.

How many players are right-handed pitchers?

Possible Answers:

Correct answer:

Explanation:

Since the question provides the information that there are $\small 3$ left-handed pitchers and $\small 9$ 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:

9-3=6

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Example Question #91 : Data Analysis And Probability

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Possible Answers:

$\small \frac{1}{5}$

$\small \frac{3}{6}$

$\small \frac{4}{5}$

$\small \frac{1}{6}$

Correct answer:

$\small \frac{1}{5}$

Explanation:

Since, there are $\small 6$ left-handed players total and $\small 3$ left-handed pitchers there must be $\small 3$ players that are left-handed but do not pitch, because $\small 6-3=3$ .

To find what fraction this represents we need to do:

$\frac{\text{left handed}}{\text{total players}}=\frac{3}{15}=\frac{1}{5}$

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Example Question #101 : Data Analysis And Probability

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

If $\small \frac{2}{8}$ of Kevin's friends only play the flute and $\small \frac{2}{8}$ of his friends only play the bass, then what fraction of Kevin's friends play both instruments?

Possible Answers:

$\small \frac{2}{8}$

$\small \frac{2}{3}$

$\small \frac{1}{2}$

$\small \frac{6}{8}$

Correct answer:

$\small \frac{1}{2}$

Explanation:

To find the fraction of Kevin's friends that play both the bass and the flute, consider that the fraction $\small \frac{8}{8}$ 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:

$\small \small \frac{2}{8}+\frac{2}{8}=\frac{4}{8}$

$\frac{8}{8}-\frac{4}{8}=\frac{8-4}{8}=\frac{4}{8}=\frac{1}{2}$

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Example Question #3 : How To Use A Venn Diagram

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Possible Answers:

$15\%$

$20\%$

$25\%$

$40\%$

Correct answer:

$25\%$

Explanation:

$\small \frac{2}{8}$ of Kevin's friends only play the bass.

Thus, to find the fractional equivalent we need to multiply the fraction by 100.

The solution becomes:

$\frac{2}{8}\times100 = \frac{200}{8}=\frac{25}{1}= 25$

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Example Question #51 : Data Analysis

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

What percentage of students only like pizza?

Possible Answers:

$35\%$

$20\%$

$48\%$

$13\%$

Correct answer:

$13\%$

Explanation:

Since Category $\small A$ represents the amount of students that only like pizza--and shows an amount of $\small 13$ percent in the Venn diagram, no calculations need to be performed.

Our answer is $13\%$ .

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Venn Diagrams

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #42 : Data Analysis

Example Question #1652 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Example Question #91 : Data Analysis And Probability

Example Question #101 : Data Analysis And Probability

Example Question #3 : How To Use A Venn Diagram

Example Question #51 : Data Analysis

All ISEE Lower Level Quantitative Resources

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