How to use a Venn Diagram - ISEE Lower Level Quantitative Reasoning
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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
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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 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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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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Use the Venn Diagram to answer the question.
All of the sixth grade students at Park Middle School play at least one instrument.There are 60 total sixth graders at Park Middle School.
How many students play both the drums and the guitar, but do not play the piano?
Use the Venn Diagram to answer the question.
All of the sixth grade students at Park Middle School play at least one instrument.There are 60 total sixth graders at Park Middle School.
How many students play both the drums and the guitar, but do not play the piano?
The shaded area where the circle that contains the word guitar overlaps with the circle that contains the word drums has the number 5. It is incorrect to add the total number of guitar players to the total number of drum players because we are only looking for students who play both instruments.
The shaded area where the circle that contains the word guitar overlaps with the circle that contains the word drums has the number 5. It is incorrect to add the total number of guitar players to the total number of drum players because we are only looking for students who play both instruments.
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Define universal set 
to be the set of integers from 1 to 20 inclusive.
Define sets 
as follows:
Which of the following would be the set of all elements that would go into the grayed region in the above Venn diagram?
Define universal set
Define sets
Which of the following would be the set of all elements that would go into the grayed region in the above Venn diagram?
The grayed region is the set of all elements that are in 
- that is, in both 
and 
. This set is
The grayed region is the set of all elements that are in
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Define universal set 
to be the set of integers from 1 to 20 inclusive.
Define sets 
as follows:
Which of the following would be the set of all elements that would go into the grayed region in the above Venn diagram?
Define universal set
Define sets
Which of the following would be the set of all elements that would go into the grayed region in the above Venn diagram?
The grayed region is the set of all elements that are in 
- that is, in 
but not 
. This set is
The grayed region is the set of all elements that are in
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Use the Venn Diagram to answer the question.
All of the sixth grade students at Park Middle School play at least one instrument.There are 60 total sixth graders at Park Middle School.
Based on the information in the diagram, how many students play the guitar?
Use the Venn Diagram to answer the question.
All of the sixth grade students at Park Middle School play at least one instrument.There are 60 total sixth graders at Park Middle School.
Based on the information in the diagram, how many students play the guitar?
18 students play the guitar, but you must also add the 5 students who play the guitar and drums and the 3 students who play the guitar and piano.
18 students play the guitar, but you must also add the 5 students who play the guitar and drums and the 3 students who play the guitar and piano.
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Use the Venn Diagram to answer the question.
All of the sixth grade students at Park Middle School play at least one instrument.There are 60 total sixth graders at Park Middle School.
If one student plays all three instruments, how many students play both the drums and the piano, but not the guitar?
Use the Venn Diagram to answer the question.
All of the sixth grade students at Park Middle School play at least one instrument.There are 60 total sixth graders at Park Middle School.
If one student plays all three instruments, how many students play both the drums and the piano, but not the guitar?
There are 60 total students. If 1 person plays all 3 instruments, then add that to all of the other numbers on the Venn Diagram to see that 58 students are represented on the Venn Diagram. Subtract that number from the total number of students to find the number of students in the missing category (those who play both the drums and the piano, but not the guitar).
There are 60 total students. If 1 person plays all 3 instruments, then add that to all of the other numbers on the Venn Diagram to see that 58 students are represented on the Venn Diagram. Subtract that number from the total number of students to find the number of students in the missing category (those who play both the drums and the piano, but not the guitar).
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The intersection point of a venn diagram represents the probability of niether event happening. True or false?
The intersection point of a venn diagram represents the probability of niether event happening. True or false?
The intersection of a venn diagram represents when both events happen at the same time, not when neither happen.
The intersection of a venn diagram represents when both events happen at the same time, not when neither happen.
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Use the following Venn Diagram to answer the question.
What hobbies does Andy enjoy doing?
Use the following Venn Diagram to answer the question.
What hobbies does Andy enjoy doing?
When looking at a Venn Diagram, we can see that it is made up of two circles. In this Venn Diagram
we can see Andy's hobbies on the left and Mary's hobbies on the right. We also see what hobbies they have in common in the center where the two circles intersect.
Now, when looking at Andy's circle containing his hobbies, we see that he enjoys sleeping, reading, and cooking. His circle is also part of the intersection, so we must include those hobbies as well. So, he also enjoys eating and singing.
So, overall, Andy's hobbies include sleeping, reading, cooking, eating, and singing.
When looking at a Venn Diagram, we can see that it is made up of two circles. In this Venn Diagram
we can see Andy's hobbies on the left and Mary's hobbies on the right. We also see what hobbies they have in common in the center where the two circles intersect.
Now, when looking at Andy's circle containing his hobbies, we see that he enjoys sleeping, reading, and cooking. His circle is also part of the intersection, so we must include those hobbies as well. So, he also enjoys eating and singing.
So, overall, Andy's hobbies include sleeping, reading, cooking, eating, and singing.
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The area when two circles on a Venn Diagram cross each other is when 
of the events occurs. True or False?
The area when two circles on a Venn Diagram cross each other is when
The point where two circles on a Venn Diagram intersect is the point where both of the events occur, not when neither occur.
The point where two circles on a Venn Diagram intersect is the point where both of the events occur, not when neither occur.
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