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SSAT Middle Level Math : How to use a Venn Diagram

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Example Questions

Example Question #23 : Venn Diagrams

Vt custom venn series ssat middle

The above Venn diagram represents the total number of respondents from a survey administered in 2014 . Respondents were categorized into only group , only group or both of the groups.

What fraction of the respondents were categorized into both groups?

Possible Answers:

$\frac{3}{50}$

$\frac{12}{10}$

$\frac{12}{50}$

$\frac{3}{25}$

$\frac{6}{100}$

Correct answer:

$\frac{3}{25}$

Explanation:

Since the information provided in the Venn diagram represents percentages, convert the quantity in the common portion of the diagram from a percentage to a fraction. To convert a percentage to a fraction, divide the percentage by a divisor of 100 , then simplify the fraction if possible.

Common portion is equal to $12\%$ . Therefore, the solution is:

$12\div100=\frac{12}{100}=\frac{12\div 2}{100\div 2}=\frac{6}{50}=\frac{6\div 2}{50\div 2}=\frac{3}{25}$

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Example Question #21 : Venn Diagrams

Vt custom venn series ssat middle

Ms. Dunn gave her class a survey to find out which states her student's have visited. Ms. Dunn was surprised to find that all of her student's had visited either New York City or Texas, and some of her student's had visited both locations.

The above Venn diagram represents the percentage of students who have visited only NYC, only Texas, and those who have visited both locations.

What percentage of the students have visited both NYC and Texas?

Possible Answers:

$22\%$

$78\%$

$28\%$

$38\%$

$14\%$

Correct answer:

$22\%$

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 how many students have visted both NYC and Texas, first find the sum of group NYC and group . Then subtract that quantity from $100\%$ .

The solution is:

46+32=78

100-78=22

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Example Question #22 : Venn Diagrams

Vt custom venn series ssat middle

Ms. Dunn gave her class a survey to find out which states her student's have visited. Ms. Dunn was surprised to find that all of her student's had visited either New York City or Texas, and some of her student's had visited both locations.

The above Venn diagram represents the percentage of students who have visited only NYC, only Texas, and those who have visited both locations.

What ratio represents the number of students that have gone only to NYC, in comparison to the rest of the class?

Possible Answers:

42:100

4:6

23:39

46:78

23:50

Correct answer:

23:50

Explanation:

Since $46\%$ of Ms. Dunn's class have visited only NYC, out of every 100 students must have only visited NYC. This can be represented by the ratio 46:100 ; however, this ratio does not appear as an answer choice, so we must reduce this ratio by dividing each part by their greatest common divisor.

The solution is:

$46:100=46\div2:100\div2=23:50$

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Example Question #23 : Venn Diagrams

Vt custom venn series ssat middle

Kayla used a popular social media website to survey her friends' hobbies. All of her friends either play sports or enjoy playing video games, and some of her friends do both.

What fraction of her friends only play sports?

Possible Answers:

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{3}{10}$

$\frac{3}{5}$

$\frac{2}{10}$

Correct answer:

$\frac{1}{2}$

Explanation:

In order to calculate the fraction of Kayla's friends who only play sport, first find the sum of the common portion and video game portion of the Venn diagram. Then subtract that sum from whole.

The solution is:

$\frac{3}{10}+\frac{2}{10}=\frac{5}{10}$

Note: $\frac{10}{10}=1$

Thus, $\frac{10}{10}-\frac{5}{10}=\frac{5}{10}=\frac{5\div 5}{10\div 5}=\frac{1}{2}$

This means that half of Kayla's friends only play sports.

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Example Question #23 : Venn Diagrams

Vt custom venn series ssat middle

Kayla used a popular social media website to survey her friends' hobbies. All of her friends either play sports or enjoy playing video games, and some of her friends do both.

What percentage of Kayla's friends play sports and video games?

Possible Answers:

$30\%$

$25\%$

$50\%$

$20\%$

$15\%$

Correct answer:

$30\%$

Explanation:

In order to solve this problem, identify that the common portion of this Venn diagram represents Kayla's friends who play sports and video games. Since $\frac{3}{10}$ of her friends play sports and video games, convert this fraction to a percent.

The solution is:

$\frac{3}{10}=\frac{3\times 10}{10\times 10}=\frac{30}{100}=30\%$

Note: the most efficient way to convert this fraction to a percent is to find an equivalent fraction to $\frac{3}{10}$ with a denominator of 100 .

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Example Question #22 : Venn Diagrams

Vt custom venn series ssat middle

The above Venn diagram represents the total number of respondents from a survey administered in 2014 . Respondents were categorized into only group , only group or both of the groups.

What percentage of respondents were categorized into only group

Possible Answers:

$29\%$

$63\%$

$39\%$

$49\%$

$27\%$

Correct answer:

$49\%$

Explanation:

To find the missing quantity for category , first calculate the sum from the common portion of the Venn diagram and category . Then, subtract that sum from $100\%$ , because the total percentage of respondents must equal $100\%$ .

The algebraic solution is:

39 +12=51

100-51=49

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SSAT Middle Level Math : How to use a Venn Diagram

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #23 : Venn Diagrams

Example Question #21 : Venn Diagrams

Example Question #22 : Venn Diagrams

Example Question #23 : Venn Diagrams

Example Question #23 : Venn Diagrams

Example Question #22 : Venn Diagrams

All SSAT Middle Level Math Resources

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