Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Middle Level Math : Venn Diagrams

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

Create An Account

All SSAT Middle Level Math Resources

10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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.

Report an Error

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

Report an Error

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:

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

Report an Error

Example Question #221 : Data Analysis

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:

$28\%$

$22\%$

$38\%$

$78\%$

$14\%$

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

Report an Error

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:

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

Report an Error

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.

Report an Error

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 .

Report an Error

Example Question #21 : 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:

$29\%$

$39\%$

$27\%$

$63\%$

$49\%$

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

Report an Error

View SSAT- Middle Level Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SSAT- Middle Level Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View SSAT- Middle Level Tutors

Diana
Certified Tutor

Durham University, UK, Bachelor, Physics & Chemistry. Bristol University, UK, Master's/Graduate, Education.

All SSAT Middle Level Math Resources

10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Phoenix, SSAT Tutors in Phoenix, Biology Tutors in San Diego, English Tutors in Atlanta, ISEE Tutors in Seattle, Chemistry Tutors in Boston, English Tutors in Washington DC, Algebra Tutors in New York City, LSAT Tutors in San Francisco-Bay Area, GMAT Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in Denver, GMAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Chicago, ACT Courses & Classes in Los Angeles, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Denver, MCAT Courses & Classes in Chicago, Spanish Courses & Classes in Phoenix, GRE Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in Atlanta, SSAT Test Prep in Boston, ISEE Test Prep in Phoenix, SSAT Test Prep in Philadelphia, MCAT Test Prep in Atlanta, GMAT Test Prep in San Diego, GRE Test Prep in San Diego, SSAT Test Prep in Denver, LSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in San Diego

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

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 #3 : How To Use A Venn Diagram

Example Question #22 : Venn Diagrams

Example Question #23 : Venn Diagrams

Example Question #221 : Data Analysis

Example Question #22 : Venn Diagrams

Example Question #23 : Venn Diagrams

Example Question #23 : Venn Diagrams

Example Question #21 : Venn Diagrams

All SSAT Middle Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: