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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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Example Questions

Example Question #11 : Venn Diagrams

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:

$62\%$

$29\%$

$26\%$

$60\%$

$78\%$

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 #3 : 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:

$77\%$

$56\%$

$54\%$

$23\%$

$46\%$

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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Example Question #3 : How To Use A Venn Diagram

Vt custom venn series ssat middle

Results from a recent political poll are represented by the Venn diagram above. The results indicate the percentage of voters who have only voted for Democratic presidential candidates, only Republican presidential candidates, and those that have voted for both Democratic and Republican candidates in the past.

What percentage of respondents have voted for both Democratic and Republican presidential candidates?

Possible Answers:

$6\%$

Not enough information is provided.

$4\%$

$12\%$

$8\%$

Correct answer:

$8\%$

Explanation:

To solve this problem first find the sum of the two exclusive groups shown in the Venn diagram:

46+46=92

This means that $92\%$ of respondents have exclusively voted for presidential candidates from only one political party.

To find the value of the common portion of the Venn diagram, calculate the difference between 100 and :

100-92=8

This means that $8\%$ of the respondents have voted for both Democratic and Republican presidential candidates.

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Example Question #22 : Venn Diagrams

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 fraction of respondents were classified into only group ?

Possible Answers:

$\frac{9}{100}$

$\frac{9}{10}$

$\frac{4}{50}$

$\frac{3}{50}$

$\frac{90}{10}$

Correct answer:

$\frac{9}{100}$

Explanation:

Since the information provided in the Venn diagram represents percentages, convert the quantity in category from a percentage to a fraction. To convert a percentage to a fraction, divide the percent by a divisor of 100 , then simplify the fraction if applicable; however, in this case the fraction can't be reduced.

The solution is:

Group $B=9\%$

Thus:
$B=9\div100=\frac{9}{100}$

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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 #241 : Data Analysis And Probability

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:

$28\%$

$22\%$

$78\%$

$38\%$

$14\%$

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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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #11 : Venn Diagrams

Example Question #3 : How To Use A Venn Diagram

Example Question #6 : How To Use A Venn Diagram

Example Question #5 : How To Use A Venn Diagram

Example Question #3 : How To Use A Venn Diagram

Example Question #22 : Venn Diagrams

Example Question #23 : Venn Diagrams

Example Question #241 : Data Analysis And Probability

Example Question #22 : Venn Diagrams

Example Question #23 : Venn Diagrams

All SSAT Middle Level Math Resources

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