Venn Diagrams - ISEE Lower Level Quantitative Reasoning
Card 0 of 16
Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
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Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group 
represents the respondents that answered "yes" to the survey question. Group 
represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.
What percentage of the respondents answered "maybe" to Aracely's survey question?
Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group
What percentage of the respondents answered "maybe" to Aracely's survey question?
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly 
percent of the respondents answered "yes" or "no" to the question
.
The solution is the total percent population take away the percent that answered "yes" or "no":
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly
The solution is the total percent population take away the percent that answered "yes" or "no":
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The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category 
represents the number of players on the team that are left-handed.
Category 
represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that 
and that there are 
players in the overlapping region of the diagram.
What fraction of the players are left-handed pitchers?
The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category
Category
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that
What fraction of the players are left-handed pitchers?
Since there are 
left-handed pitchers and 
total players that are either left-handed, pitchers or both the solution is:
Since there are
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The Venn diagram above represents the results from a recent survey given to middle school students. Category 
represents the amount of students that only like pizza. Category 
represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
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The Venn diagram above represents the results from a recent survey given to middle school students. Category represents the amount of students that only like pizza. Category represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
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If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
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The following Venn diagram depicts the number of students who like soccer, football, or both. How many students like soccer but not football?
The following Venn diagram depicts the number of students who like soccer, football, or both. How many students like soccer but not football?
A Venn diagram is used to demonstrate the number of people (or things) in particular categories. The regions of the circle that are overlapping indicate the number of individuals that belong to multiple groups. Therefore, based on this diagram, 12 students like soccer only, 16 like football only, and 8 like both.
A Venn diagram is used to demonstrate the number of people (or things) in particular categories. The regions of the circle that are overlapping indicate the number of individuals that belong to multiple groups. Therefore, based on this diagram, 12 students like soccer only, 16 like football only, and 8 like both.
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Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group 
represents the respondents that answered "yes" to the survey question. Group 
represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.
What percentage of the respondents answered "no" to Aracely's survey question?
Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group
What percentage of the respondents answered "no" to Aracely's survey question?
The Venn diagram has three separate categories. Category 
represents the respondents that answered "yes" to the survey question, category 
represents the respondents that answered "no" and the overlapping portion of the diagram represents the respondents that answered "maybe" to the survey question.
Category 
.
Thus, 
of the respondents answered "no" to the survey question.
The Venn diagram has three separate categories. Category
Category
Thus,
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Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group 
represents the respondents that answered "yes" to the survey question. Group 
represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.
What fraction represents the amount of respondents that answered "yes" to the survey question?
Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group
What fraction represents the amount of respondents that answered "yes" to the survey question?
The Venn diagram shows that exactly 
percent of the survey respondents answered "yes" to the survey question.
Thus, to find the fraction equivalent we need to rewrite
From here we simplify the fraction.
The Venn diagram shows that exactly
Thus, to find the fraction equivalent we need to rewrite
From here we simplify the fraction.
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The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category 
represents the number of players on the team that are left-handed.
Category 
represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that 
and that there are 
players in the overlapping region of the diagram.
How many players are right-handed pitchers?
The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category
Category
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that
How many players are right-handed pitchers?
Since the question provides the information that there are 
left-handed pitchers and 
total pitchers, one can infer that the number of right-handed pitchers is equal to the difference between the total number of pitchers and the number of left-handed pitchers.
Thus, the solution is:
Since the question provides the information that there are
Thus, the solution is:
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The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category 
represents the number of players on the team that are left-handed.
Category 
represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that 
and that there are 
players in the overlapping region of the diagram.
What fraction of the players are only left-handed?
The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category
Category
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that
What fraction of the players are only left-handed?
Since, there are 
left-handed players total and 
left-handed pitchers there must be 
players that are left-handed but do not pitch, because 
.
To find what fraction this represents we need to do:
Since, there are
To find what fraction this represents we need to do:
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In the above Venn diagram category 
represents the number of Kevin's friends that play the flute, while category 
represents the number of Kevin's friends that play the bass.
If 
of Kevin's friends only play the flute and 
of his friends only play the bass, then what fraction of Kevin's friends play both instruments?
In the above Venn diagram category
If
To find the fraction of Kevin's friends that play both the bass and the flute, consider that the fraction 
represents all of Kevin's friends in this senario.
Thus, the solution can be found by adding those that only play flute with those that only play bass and subtracting that final answer from the fraqction that represents all of Kevin's friends:
To find the fraction of Kevin's friends that play both the bass and the flute, consider that the fraction
Thus, the solution can be found by adding those that only play flute with those that only play bass and subtracting that final answer from the fraqction that represents all of Kevin's friends:
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In the above Venn diagram category 
represents the number of Kevin's friends that play the flute, while category 
represents the number of Kevin's friends that play the bass.
If 
of Kevin's friends only play the flute and 
of his friends only play the bass, then what percentage of Kevin's friends only only play the bass?
In the above Venn diagram category
If
of Kevin's friends only play the bass.
Thus, to find the fractional equivalent we need to multiply the fraction by 100.
The solution becomes:
Thus, to find the fractional equivalent we need to multiply the fraction by 100.
The solution becomes:
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The Venn diagram above represents the results from a recent survey given to middle school students. Category 
represents the amount of students that only like pizza. Category 
represents the amount of students that only chicken nuggets.
What percentage of students only like pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students only like pizza?
Since Category 
represents the amount of students that only like pizza--and shows an amount of 
percent in the Venn diagram, no calculations need to be performed.
Our answer is 
.
Since Category
Our answer is
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The Venn diagram above represents the results from a recent survey given to middle school students. Category 
represents the amount of students that only like pizza. Category 
represents the amount of students that only chicken nuggets.
What fraction of the students only like chicken nuggets?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What fraction of the students only like chicken nuggets?
Since exactly 
of a total 
percent of the students only like chicken nuggets, the solution is:
Since exactly
Compare your answer with the correct one above
The Venn diagram above represents the results from a recent survey given to middle school students. Category 
represents the amount of students that only like pizza. Category 
represents the amount of students that only chicken nuggets.
What fraction of the students only like pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What fraction of the students only like pizza?
Since category 
represents the total number of students that only like pizza, the correct answer is that 
percent is equivalent to 
.
Since category
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