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SSAT Middle Level Math : Venn Diagrams

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Example Questions

Example Question #643 : Ssat Middle Level Quantitative (Math)

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 percent of the respondents like both tamales and tacos?

Possible Answers:

$1\%$

$5\%$

$20\%$

$25\%$

Correct answer:

$20\%$

Explanation:

The total number of survey respondents is equal to 100 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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Example Question #644 : Ssat Middle Level Quantitative (Math)

Vt_custome_venn_diagram_series_

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?

Possible Answers:

$23\%$

$33\%$

$26\%$

$21\%$

Correct answer:

$23\%$

Explanation:

In order to find the value of the common area of this Venn diagram, find the sum of percent and percent.

Then find the difference from the sum to 100 percent.

The solution is:

56+21=77

100-77=23

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Example Question #1 : How To Use A Venn Diagram

Venn_diagram

See the above Venn diagram. Which of the following sets is represented by the gray region?

Possible Answers:

$\overline{A} \cup \overline{B}$

$\overline{A} \cap B$

$A \cup \overline{B}$

$A \cap \overline{B}$

$\overline{A} \cup B$

Correct answer:

$\overline{A} \cap B$

Explanation:

The shaded area represents the set of all elements that are both in and not in . This the intersection of and the complement of , or $\overline{A} \cap B$ .

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Example Question #11 : Venn Diagrams

Venn_diagram_2

See the above Venn diagram. Which of the following sets is represented by the gray region?

Possible Answers:

$\overline{A }\cup \overline{B}$

$\overline{A }\cup B$

$\overline{A }\cap B$

$\overline{A }\cap \overline{B}$

$A \cup \overline{B}$

Correct answer:

$A \cup \overline{B}$

Explanation:

The gray region represents all elements that either are in , are not in - that is, are in $\overline{B}$ - or both. This is the union of and $\overline{B}$ , or $A \cup \overline{B}$ .

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Example Question #2 : Venn Diagrams

Given the Venn diagram below, which of the following does not belong to $A \cup B$ ?

Possible Answers:

Correct answer:

Explanation:

The symbol $\cup$ stands for the union between two sets. Therefore, $A\cup B$ means the set of all numbers that are in either A or B. Looking at our choices, the only number that isn't in either A, B, or both is 23.

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Example Question #3 : How To Use A Venn Diagram

Venn_4

Let set $U = \mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 6 }

= { | is a multiple of 9 }

Which of the following numbers would appear in the gray region of the Venn diagram?

Possible Answers:

8,544

4,077

4,572

9,349

3,438

Correct answer:

4,077

Explanation:

The gray area represents the portion of that is not in - in other words, all multiples of 9 that are not also multiples of 6.

$4,572 \div 6 = 762$

$3,438 \div 6 = 573$

$8,544 \div 6 =1,424$

Therefore, 4,572, 3,438, and 8,544 can be eliminated.

$9,349 \div 9 = 1,038 \;R\; 7$ , so 9,349 can be eliminated because it isn't a multiple of 9.

$4,077 \div 6 = 679 \; R \; 3$ and $4,077 \div 9 = 453$ , so, as both a nonmultiple of 6 and a multiple of 9, 4.077 is the correct choice.

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Example Question #2 : How To Use A Venn Diagram

Vt custom venn series ssat middle

The above Venn diagram represents survey respondents from a recent political poll. Based on the respondent's political affiliation, they were classified into group only, only or both groups.

What percentage of the respondents were classified into both groups?

Possible Answers:

$78\%$

$29\%$

$26\%$

$60\%$

$62\%$

Correct answer:

$29\%$

Explanation:

The common portion of this Venn diagram represents the percentage of respondents that were classified into both groups. In order to calculate the percentage that represents the amount of respondents classified into both groups, first find the sum of group and group . Then subtract that quantity from 100 percent.

The solution is:

62+9=71

100-71=29

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Example Question #4 : How To Use A Venn Diagram

Vt custom venn series ssat middle

Mr. Robinson surveyed his class to find out what his students planned on doing during their summer vacation. Every student in his class stated that they planned on swimming with their friends and/or travel with their family.

What percentage of Mr. Robinson’s class planned on both swimming with their friends and traveling with their family?

Possible Answers:

$46\%$

$56\%$

$23\%$

$54\%$

$77\%$

Correct answer:

$23\%$

Explanation:

The common portion of this Venn diagram represents the percentage of Mr. Robinson's students that stated they planned on both swimming and traveling during the summer. In order to calculate the percentage that represents the amount of students classified into both groups, first find the sum of the swimming group and traveling group. Then subtract that sum from $100\%$ .

The solution is:

54+23=77

100-77=23

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Example Question #6 : How To Use A Venn Diagram

Vt custom venn series ssat middle

Kelly and Antonio are in a group together on a popular social media website. They realized that within the group they have mutual friendships as well as friendships exclusive of one another.

What ratio accurately represents the amount of friendships within the group that they have in common to those that they do not have in common?

Possible Answers:

2:5

3:4

6:20

10:60

1:4

Correct answer:

2:5

Explanation:

In order to find the ratio of friends that Kelly and Antonio have in common compared to the group members who are only friends with one or the other first find the percentage value of the common portion of the Venn diagram. To calculate this value, find the sum of the two exclusive groups and then subtract that sum from $100\%$ .

27+33=60

100-60=40

This means that $40\%$ of the group members are common friends of Kelly and Antonio. To convert this percentage to a ratio, first write $40\%$ as a fraction, and then simplify as a ratio.

$40\%$ is equal to: $\frac{40}{100}=40:100=4:10=2:5$

This means that out of every group members are mutual friends of Kelly and Antonio.

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Example Question #5 : How To Use A Venn Diagram

Vt custom venn series ssat middle

Kelly and Antonio are in a group together on a popular social media website. They realized that within the group they have mutual friendships as well as friendships exclusive of one another.

What ratio accurately represents the amount of friendships within the group that they do not have in common to those that they do have in common.

Possible Answers:

1:6

3:5

2:5

2:3

1:5

Correct answer:

3:5

Explanation:

To find the ratio of Kelly and Antonio's exclusive friendships to their mutual friendships--find the sum of the two exclusive groups in the Venn diagram:

27+33=60

This means that $60\%$ of the members in the group are not friends with both Kelly and Antonio. To convert this percent to a ratio, first write $60\%$ as a fraction, and then simplify as a ratio.

$60\%$ is equal to: $\frac{60}{100}=60:100=6:10=3:5$

This means that out of every group members are not mutual friends of Kelly and Antonio.

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SSAT Middle Level Math : Venn Diagrams

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #643 : Ssat Middle Level Quantitative (Math)

Example Question #644 : Ssat Middle Level Quantitative (Math)

Example Question #1 : How To Use A Venn Diagram

Example Question #11 : Venn Diagrams

Example Question #2 : Venn Diagrams

Example Question #3 : How To Use A Venn Diagram

Example Question #2 : How To Use A Venn Diagram

Example Question #4 : How To Use A Venn Diagram

Example Question #6 : How To Use A Venn Diagram

Example Question #5 : How To Use A Venn Diagram

All SSAT Middle Level Math Resources

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