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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 #1 : Venn Diagrams

Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?

Possible Answers:

Correct answer:

Explanation:

The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.

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

Custom_vt_venn_d._lower_level_isee.gif_2

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 percentage of the respondents answered "maybe" to Aracely's survey question?

Possible Answers:

${} 45\%$

$35\%$

$25\%$

$55\%$

Correct answer:

${} 45\%$

Explanation:

The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.

Since the diagram shows that exactly $\small 55$ percent of the respondents answered "yes" or "no" to the question

20+35=55 .

The solution is the total percent population take away the percent that answered "yes" or "no":

$\small 100-55=45$

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Example Question #1651 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Custom_vt_venn_d._lower_level_isee.gif_lp

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.

What fraction of the players are left-handed pitchers?

Possible Answers:

$\frac{1}{6}$

$\frac{1}{5}$

$\frac{2}{6}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{5}$

Explanation:

Since there are $\small 3$ left-handed pitchers and $\small \small 15$ total players that are either left-handed, pitchers or both the solution is:

$\frac{3}{15}=\frac{1}{5}$

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Example Question #41 : Data Analysis

Custom_vt_venn_d._lower_level_isee.gif6

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 like both chicken nuggets and pizza?

Possible Answers:

$50\%$

$25\%$

$52\%$

$48\%$

Correct answer:

$52\%$

Explanation:

Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.

Thus we get,

$\small 13+35=48$ .

The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.

$\small 100-48=52$ .

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Example Question #2 : How To Find The Common Part With A Venn Diagram

Custom_vt_venn_d._lower_level_isee.gif6

Possible Answers:

$25\%$

$50\%$

$48\%$

$52\%$

$55\%$

Correct answer:

$52\%$

Explanation:

Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.

Thus we get,

$\small 13+35=48$ .

The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.

$\small 100-48=52$ .

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Example Question #3 : Venn Diagrams

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

Possible Answers:

Venn5

Venn2

Venn3

Venn4

Venn1

Correct answer:

Venn1

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.

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Example Question #2 : 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?

Possible Answers:

Correct answer:

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.

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Example Question #3 : How To Use A Venn Diagram

Custom_vt_venn_d._lower_level_isee.gif6

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 fraction of the students only like chicken nuggets?

Possible Answers:

$\small \frac{30}{100}$

$\small \frac{5}{100}$

$\small \frac{100}{35}$

$\small \frac{7}{20}$

Correct answer:

$\small \frac{7}{20}$

Explanation:

Since exactly $\small 35$ of a total $\small 100$ percent of the students only like chicken nuggets, the solution is:
$\small \frac{35}{100}=\frac{7}{20}$

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Example Question #2 : How To Use A Venn Diagram

Custom_vt_venn_d._lower_level_isee.gif6

Possible Answers:

$\small \frac{6}{50}$

$\small \frac{13}{100}$

$\small \frac{3}{5}$

$\small \frac{35}{100}$

Correct answer:

$\small \frac{13}{100}$

Explanation:

Since category $\small A$ represents the total number of students that only like pizza, the correct answer is that $\small 13$ percent is equivalent to $\small \frac{13}{100}$ .

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Example Question #4 : Venn Diagrams

Custom_vt_venn_d._lower_level_isee.gif_2

Possible Answers:

$20\%$

$45\%$

$35\%$

$55\%$

Correct answer:

$35\%$

Explanation:

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

Category $\small B=35\%$ .

Thus, $\small 35\%$ of the respondents answered "no" to the survey question.

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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 #1 : Venn Diagrams

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

Example Question #1651 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Example Question #41 : Data Analysis

Example Question #2 : How To Find The Common Part With A Venn Diagram

Example Question #3 : Venn Diagrams

Example Question #2 : How To Use A Venn Diagram

Example Question #3 : How To Use A Venn Diagram

Example Question #2 : How To Use A Venn Diagram

Example Question #4 : Venn Diagrams

All ISEE Lower Level Quantitative Resources

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