How to find the intersection of a Venn Diagram - GRE Quantitative Reasoning
Card 1 of 40
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
Tap to reveal answer
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
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In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
Tap to reveal answer
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
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In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
Tap to reveal answer
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
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At an overpriced department store there are 
customers. If 
have purchased shirts, 
have purchased pants, and 
have purchased neither, how many purchased both shirts and pants?
At an overpriced department store there are
Tap to reveal answer
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are 
customers; within them there are those that purchased something (pants, shirts, or possibly a combination), and those that purchased nothing.
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since 
bought nothing,
The amount that bought both then is:
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since
The amount that bought both then is:
← Didn't Know|Knew It →
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
Tap to reveal answer
When you add both class rosters you get a total of 55 students
.
You must subtract the 7 that are in both because they are counted twice in the 55
.
The total in neither class will be the total students minus the adjusted enrollment in both classes
.
When you add both class rosters you get a total of 55 students
You must subtract the 7 that are in both because they are counted twice in the 55
The total in neither class will be the total students minus the adjusted enrollment in both classes
← Didn't Know|Knew It →
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
Tap to reveal answer
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
← Didn't Know|Knew It →
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
Tap to reveal answer
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
← Didn't Know|Knew It →
In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
Tap to reveal answer
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
← Didn't Know|Knew It →
At an overpriced department store there are customers. If have purchased shirts, have purchased pants, and have purchased neither, how many purchased both shirts and pants?
At an overpriced department store there are
Tap to reveal answer
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are customers; within them there are those that purchased something (pants, shirts, or possibly a combination), and those that purchased nothing.
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since bought nothing,
The amount that bought both then is:
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since
The amount that bought both then is:
← Didn't Know|Knew It →
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
Tap to reveal answer
When you add both class rosters you get a total of 55 students
.
You must subtract the 7 that are in both because they are counted twice in the 55
.
The total in neither class will be the total students minus the adjusted enrollment in both classes
.
When you add both class rosters you get a total of 55 students
You must subtract the 7 that are in both because they are counted twice in the 55
The total in neither class will be the total students minus the adjusted enrollment in both classes
← Didn't Know|Knew It →
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
Tap to reveal answer
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
← Didn't Know|Knew It →
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
Tap to reveal answer
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
← Didn't Know|Knew It →
In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
Tap to reveal answer
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
← Didn't Know|Knew It →
At an overpriced department store there are customers. If have purchased shirts, have purchased pants, and have purchased neither, how many purchased both shirts and pants?
At an overpriced department store there are
Tap to reveal answer
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are customers; within them there are those that purchased something (pants, shirts, or possibly a combination), and those that purchased nothing.
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since bought nothing,
The amount that bought both then is:
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since
The amount that bought both then is:
← Didn't Know|Knew It →
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
Tap to reveal answer
When you add both class rosters you get a total of 55 students
.
You must subtract the 7 that are in both because they are counted twice in the 55
.
The total in neither class will be the total students minus the adjusted enrollment in both classes
.
When you add both class rosters you get a total of 55 students
You must subtract the 7 that are in both because they are counted twice in the 55
The total in neither class will be the total students minus the adjusted enrollment in both classes
← Didn't Know|Knew It →
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?
Tap to reveal answer
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
Refer to the following Venn Diagram:
If 25% of the 800 CS students are also mathematics students, the number of students sharing these majors is 800 * 0.25 or 200 students. Furthermore, if this represents one third of the total of math students, we then know:
Math students * 1/3 = 200 or (1/3)M = 200
Solving for M we get 600. This means that the number of students that are ONLY math students is 400.
Looking at our diagram above, we must be careful not to "double add" the intersection. The easiest way to do this is to take the intersection and add to it the number of CS-only and math-only students: 600 + 200 + 400 = 1200. This number represents the total number of students that have either a math or CS major (that is, the number of students in the union of the two sets). This leaves 1500 – 1200 or 300 students.
← Didn't Know|Knew It →
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?
Tap to reveal answer
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
In order to find the intersection of chocolate and vanilla, it is easiest to make a Venn Diagram. The outside of the Venn Diagram is 10, and the total of the entire diagram must equal 35. Therefore the two circles of the Venn Diagram including just chocolate, just vanilla and the intersection must equal 25, with the just chocolate plus intersection side equalling 15 and the just vanilla plus intersection side equalling 13.
We know:
(A U B) = A + B – (A ∩ B)
We have found that (A U B) = 25 and we are trying to find (A ∩ B). Plug in A and B
25 = 15 + 13 – (A ∩ B) = 28 – (A ∩ B)
or – (A ∩ B) = –3
(A ∩ B) = 3
← Didn't Know|Knew It →
In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
In a population of cats, 10% are tabby colored, 5% are pregnant, and 3% are both tabby and pregnant. What is the probability that a cat is tabby but not pregnant?
Tap to reveal answer
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
Probability (tabby but not pregnant)
= Prob (tabby) – Prob (tabby and pregnant)
= 10% - 3%
= 7%
← Didn't Know|Knew It →
At an overpriced department store there are customers. If have purchased shirts, have purchased pants, and have purchased neither, how many purchased both shirts and pants?
At an overpriced department store there are
Tap to reveal answer
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are customers; within them there are those that purchased something (pants, shirts, or possibly a combination), and those that purchased nothing.
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since bought nothing,
The amount that bought both then is:
A way of solving this problem is by drawing a Venn diagram based on what is known:
There are
The amount of individuals that purchased something is given as:
The reason that the number of shoppers that bought both is subtracted is so that it is not counted twice when the customers that bought pants and the customers that bought shirts are added together.
Since
The amount that bought both then is:
← Didn't Know|Knew It →
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?
Tap to reveal answer
When you add both class rosters you get a total of 55 students
.
You must subtract the 7 that are in both because they are counted twice in the 55
.
The total in neither class will be the total students minus the adjusted enrollment in both classes
.
When you add both class rosters you get a total of 55 students
You must subtract the 7 that are in both because they are counted twice in the 55
The total in neither class will be the total students minus the adjusted enrollment in both classes
← Didn't Know|Knew It →