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SSAT Middle Level Math : How to find the common part with a Venn Diagram

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Example Questions

Example Question #1 : Venn Diagrams

Vt_custome_venn_diagram_series_

Using the Venn diagram shown above, what fraction represents the amount of students that enjoy both reading and playing video games?

Possible Answers:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{6}{25}$ $\displaystyle \frac{6}{25}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\frac{12}{25}$ $\displaystyle \frac{12}{25}$

Correct answer:

$\frac{6}{25}$ $\displaystyle \frac{6}{25}$

Explanation:

The total number of survey respondents is equal to 100 $\displaystyle 100$ percent. Since the common part of the Venn diagram represents the respondents that enjoy both video games and reading, the solution is:

$\displaystyle 100-(64+12)=$

$\displaystyle 100-76=24$

Thus, $\displaystyle 24$ percent is equal to $\frac{24}{100}=\frac{12}{50}=\frac{6}{25}$ $\displaystyle \frac{24}{100}=\frac{12}{50}=\frac{6}{25}$

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Example Question #2 : Venn Diagrams

Vt_custome_venn_diagram_series_

The Venn diagram above, shows the results from a recent survey. The respondents were asked whether they enjoy playing video games, reading, or both. What percentage of the survey respondents enjoy both video games and reading?

Possible Answers:

$76\%$ $\displaystyle 76\%$

$52\%$ $\displaystyle 52\%$

$12\%$ $\displaystyle 12\%$

$24\%$ $\displaystyle 24\%$

Correct answer:

$24\%$ $\displaystyle 24\%$

Explanation:

The total number of survey respondents is equal to 100 $\displaystyle 100$ percent.

Since the common part of the Venn diagram represents the respondents that enjoy both video games and reading, the solution is:

$\displaystyle 100-(64+12)=$

$\displaystyle 100-76=24$

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

Vt_custome_venn_diagram_series_

The above Venn diagram depicts the number of students that: only play at the Rec. Center after school, only play at the park after school, and the students that play at both locations after school.

How many students play at both the park and Rec. Center after school?

Possible Answers:

$\displaystyle 9$

$\displaystyle 7$

$\displaystyle 15$

$\displaystyle 2$

Correct answer:

$\displaystyle 9$

Explanation:

To solve this problem, locate the common part of this Venn diagram. Since each of the two outside portions of the Venn diagram represent students that only play at either the park or Rec. Center.

The $\displaystyle 9$ students in the common area of the Venn diagram, play both at the park and at the Rec. Center.

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Example Question #1 : Venn Diagrams

Vt_custome_venn_diagram_series_

Using the Venn diagram above, what fraction of the respondents play at both the Rec. Center and the park. (Keep in mind that the two outside portions of the Venn diagram represent respondents that only play at one location or the other).

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{9}{22}$ $\displaystyle \frac{9}{22}$

$\frac{9}{38}$ $\displaystyle \frac{9}{38}$

$\frac{9}{29}$ $\displaystyle \frac{9}{29}$

Correct answer:

$\frac{9}{38}$ $\displaystyle \frac{9}{38}$

Explanation:

To solve this problem, locate the common part of this Venn diagram. Since each of the two outside portions of the Venn diagram represent students that only play at either the park or Rec. Center. The $\displaystyle 9$ students in the common area of the Venn diagram belong to the group that plays at both the park and the Rec. Center.

This means that the total number of students (the denominator) must equal:

$\displaystyle 22+9+7=38$

Making $\frac{9}{38}$ $\displaystyle \frac{9}{38}$ the correct answer.

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Example Question #4 : Venn Diagrams

Vt_custome_venn_diagram_series_

The Venn diagram shown above represents the number of students that: only took math during summer school, only took social studies during summer school, and the number of students that took both math and social studies during summer school.

How many students took both math and social studies?

Possible Answers:

$\displaystyle 17$

$\displaystyle 21$

$\displaystyle 4$

$\sqrt{23}$ $\displaystyle \sqrt{23}$

Correct answer:

$\displaystyle 4$

Explanation:

The common portion of this Venn diagram is equal to $\displaystyle 4$, which depicts the number of students that took both math and social studies during summer school.

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

Vt_custome_venn_diagram_series_

What fraction of the above Venn diagram represents the number of students that took both math and social studies during summer school?

Possible Answers:

$\frac{1}{11}$ $\displaystyle \frac{1}{11}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{4}{10}$ $\displaystyle \frac{4}{10}$

Correct answer:

$\frac{1}{11}$ $\displaystyle \frac{1}{11}$

Explanation:

The common portion of this Venn diagram is equal to $\displaystyle 4$, which depicts the number of students that took both math and social studies during summer school.

The denominator of the fraction is equal to the total number of students: \

$\displaystyle 23+4+17=44$

Thus,

$\frac{4}{44}=\frac{1}{11}$ $\displaystyle \frac{4}{44}=\frac{1}{11}$

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

Vt_custome_venn_diagram_series_

Using the Venn diagram above shows whether respondents only like Super Hero $\displaystyle 1$, only like Super Hero $\displaystyle 2$, or if they like both Super Heroes. What percentage of respondents like both Super Heroes?

Possible Answers:

$34\%$ $\displaystyle 34\%$

$17\%$ $\displaystyle 17\%$

$15\%$ $\displaystyle 15\%$

$22\%$ $\displaystyle 22\%$

Correct answer:

$17\%$ $\displaystyle 17\%$

Explanation:

The total number of survey respondents is equal to 100 $\displaystyle 100$ percent. Since the common part of the Venn diagram represents the respondents that like both Super Heroes.

Thus, the solution is:

$\displaystyle 100-(34+49)=$

$\displaystyle 100-83=17$

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

Vt_custome_venn_diagram_series_

The Venn diagram shown above displays whether respondents only use Social Media site $\displaystyle 1$, only use Social Media site $\displaystyle 2$, or use both of the Social Media sites.

What percent of respondents use both Social Media sites?

Possible Answers:

$15\%$ $\displaystyle 15\%$

$6\%$ $\displaystyle 6\%$

$13\%$ $\displaystyle 13\%$

$45\%$ $\displaystyle 45\%$

Correct answer:

$13\%$ $\displaystyle 13\%$

Explanation:

The total number of survey respondents is equal to 100 $\displaystyle 100$ percent. Since the common part of the Venn diagram represents the respondents that use both of the Social Media sites, the solution is:

$\displaystyle 100-(36+51)=$

$\displaystyle 100-87=13$

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Example Question #9 : How To Find The Common Part With A Venn Diagram

Vt_custome_venn_diagram_series_

What fraction represents the amount of respondents that use both Social Media site $\displaystyle 1$ and Social Media site $\displaystyle 2$?

Possible Answers:

$\frac{17}{100}$ $\displaystyle \frac{17}{100}$

$\frac{13}{10}$ $\displaystyle \frac{13}{10}$

$\frac{17}{50}$ $\displaystyle \frac{17}{50}$

$\frac{13}{100}$ $\displaystyle \frac{13}{100}$

Correct answer:

$\frac{13}{100}$ $\displaystyle \frac{13}{100}$

Explanation:

The total number of survey respondents is equal to 100 $\displaystyle 100$ percent. Since the common part of the Venn diagram represents the respondents that use both social media sites, the solution is:

$\displaystyle 100-(36+51)=$

$\displaystyle 100-87=13$

$13\%=\frac{13}{100}$ $\displaystyle 13\%=\frac{13}{100}$

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Example Question #3 : How To Find The Common Part With A Venn Diagram

Vt_custome_venn_diagram_series_

The above Venn diagram shows the amount of survey respondents that only like tacos, only like tamales, and those that like both tacos and tamales.

What fraction of respondents like both tacos and tamales?

Possible Answers:

$\frac{4}{10}$ $\displaystyle \frac{4}{10}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{1}{10}$ $\displaystyle \frac{1}{10}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Correct answer:

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

Explanation:

The total number of survey respondents is equal to 100 $\displaystyle 100$ percent, which equals $\frac{5}{5}$ $\displaystyle \frac{5}{5}$.

The total number of respondents that do not like both tacos and tamales: $\frac{3}{5}+\frac{1}{5}=\frac{4}{5}$ $\displaystyle \frac{3}{5}+\frac{1}{5}=\frac{4}{5}$.

The remaining amount equals the respondents that like both tacos and tamales.

Thus, the solution is:

$\frac{5}{5}-\frac{4}{5}=\frac{1}{5}$ $\displaystyle \frac{5}{5}-\frac{4}{5}=\frac{1}{5}$

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SSAT Middle Level Math : How to find the common part with a Venn Diagram

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Venn Diagrams

Example Question #2 : Venn Diagrams

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

Example Question #1 : Venn Diagrams

Example Question #4 : Venn Diagrams

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

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

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

Example Question #9 : How To Find The Common Part With A Venn Diagram

Example Question #3 : How To Find The Common Part With A Venn Diagram

All SSAT Middle Level Math Resources

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