SSAT Middle Level Quantitative - How to find the common part with a Venn Diagram

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

$\frac{1}{11}$

$\frac{1}{4}$

$\frac{4}{10}$

$\frac{4}{5}$

Explanation

The common portion of this Venn diagram is equal to , 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: \

Thus,

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

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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 percent of the respondents like both tamales and tacos?

Explanation

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

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

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

Thus, the solution is:

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

Now we need to convert the fraction into a percent.

$\frac{1}{5}=\frac{1}{5}\times \frac{20}{20}=\frac{20}{100}=20%$

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

Explanation

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

Thus, the solution is:

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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?

Explanation

The total number of survey respondents is equal to percent.

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

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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).

$\frac{9}{38}$

$\frac{1}{3}$

$\frac{9}{29}$

$\frac{9}{22}$

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 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:

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

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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?

$\sqrt{23}$

Explanation

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

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

What percent of respondents use both Social Media sites?

Explanation

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

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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?

$\frac{1}{5}$

$\frac{1}{10}$

$\frac{2}{5}$

$\frac{4}{10}$

Explanation

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

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

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

Thus, the solution is:

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

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

$\frac{6}{25}$

$\frac{12}{25}$

$\frac{2}{5}$

$\frac{1}{6}$

Explanation

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

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

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The above Venn diagram shows the results from a recent survey. Respondents had the choice of being only a fan of TEAM , only a fan of TEAM , or a fan of both of the teams. What percentage of the respondents are fans of both the teams?