In this post, you will come across all the possible Venn diagram questions that are likely to show up on the GRE exam. GRE tests questions on double and triple Venn diagrams.
Questions
Question 1
In a certain company, 45% of the employees are females, and 25% of the employees have an MBA. If 60% of the employees either are females or have an MBA or both, then what percentage of the employees who have an MBA are males?
A) 75%
B) 60%
C) 40%
D) 50%
E) 15%
Question 2
Club X has 37 members and Club Y has 49 members. At least 3 of the members in Club X are not in Club Y. Which of the following could be the number of members in Club Y that are not in Club X? Indicate all such numbers.
A) 3
B) 7
C) 15
D) 21
E) 37
F) 49
G) 50
H) 61
Question 3
In a school, students are enrolled in at least one of the following classes: GRE, TOEFL. 34 students are enrolled in the GRE class. 27 students are enrolled in the TOEFL class. 49 students are enrolled in either the GRE class or the TOEFL class, or both classes.
Quantity A: Number of students who are enrolled in both GRE and TOEFL classes
Quantity B: 15
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Question 4
In country W, 20 percent of the males and 60 percent of the females are literate. If 40 percent of the population are females, what percent of the population is not literate
A) 70%
B) 65%
C) 64%
D) 20%
E) 18%
Question 5
In a group of 100 students, x are taking French, y are taking Spanish, and z are taking both French and Spanish. How many students are taking neither French nor Spanish?
(A) 100 – z
(B) 100 – x -y
(C) 100 – x + z
(D) 100 – x – y – z
(E) 100 – x – y + z
Question 6
In a certain university, there are 80 faculty members. 25% of the faculty members are at least 30 years of age but do not have a master’s degree. 75% of the faculty who are less than 30 years old have a master’s degree. 40% of the faculty are at least 30 years old.
Quantity A: 50%
Quantity B: Percent of the faculty who have a master’s degree
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Question 7
A company sold 120 automobiles last month. Each automobile was either a car or a SUV. Moreover, each automobile was either black or white. 65 automobiles were black, and 80 automobiles were SUVs including 40 black SUVs. How many white cars were sold?
A) 10
B) 15
C) 20
D) 25
E) 55
Question 8
In a company of 200 employees, 80 used neither a laptop nor a desktop. 60 used only laptops, and for every employee that used both the laptop and the desktop, 3 used only a desktop. How many of the employees used both a laptop and a desktop?
A) 15
B) 20
C) 30
D) 40
E) 45
Question 9
Of the students in a class, 25% are studying for the GRE and 40% are studying for the TOEFL. If 30% of the students in the class are studying for the TOEFL but not for the GRE, what percent of the students who are taking the GRE are not taking the TOEFL?
Question 10
Of the 52 people travelling for leisure, 17 are travelling to Malaysia and 21 are travelling to Singapore. If 20 people are traveling to neither Malaysia nor Singapore, how many people are travelling to only one of the two countries.
A) 26
B) 31
C) 32
D) 37
E) 38
Question 11
Of all the laborers in a certain factory, 50% work in the production department and the rest work in the operations department. If 80% of those who work in the production department do not have a diploma and if the number of laborers who work in the operations department and have a diploma is 3 times the number of laborers who work in the production department and have a diploma, what fraction of all the laborers work in the operations department and do not have a diploma?
A) 1/15
B) 1/5
C) 4/15
D) 1/3
E) 2/5
Question 12
In a group of 37 people, 13 have visited USA and 21 have visited Brazil. If 9 people have visited both USA and Brazil, how many people have visited at least one country?
Question 13
75% of the businesses in a certain country pay sales tax. 60% of the businesses who pay sales tax also pay value added tax. 90 percent of the businesses who pay value added tax also pay sales tax.
Quantity A: Percent of the businesses pay value added tax
Quantity B: 50%
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Question 14
Every item in a closet is either a pant or a shirt, and every item is either black or grey. There are six shirts, two black pants, and five grey items in the closet.
Quantity A: The number of items in the closet
Quantity B: 7
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Question 15
In a group of 30 respondents, 21 invested in the stock market and 15 invested in the real estate market. 12 of the 30 respondents did both. How many of the respondents invested in either the stock market or the real estate but not in both?
Question 16
In a group of 30 respondents, 21 invested in the stock market and 15 invested in the real estate market. 24 of the 30 respondents invested in stock market or the real estate, or both. How many of the respondents invested in neither the stock market nor in the real estate?
Question 17
James has a total of X books, 25 of which are hardcover GRE books, 40 of which are GRE books and the rest are TOEFL books. 60 of the books are hardcover and the rest are in soft form.
Quantity A: X
Quantity B: 70
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Question 18
In a group of 50 people, 36 have a diploma and 18 have a degree. What is the maximum number of people who neither have a diploma nor have a degree?
Question 19
In a group of 50 people, 36 have a diploma and 18 have a degree. 12 people who have a degree do not have a diploma. How many diploma holders do not have a degree?
Question 20
This year 26 students worked on Project A, 26 students worked on Project B, and 32 students worked on Project C. No students worked on both Project A and Project B, 6 students worked on Project A and Project C, and 11 students worked on Project B and Project C. How many students worked on at least one of these Projects?
A) 52
B) 67
C) 71
D) 73
E) 79
Question 21
In a group of 144 people, 78 like lima beans and 119 like brussels sprouts. What is the greatest possible number of people that like both lima beans and brussels sprouts?
Question 22
Club X has 67 members and Club Y has 149 members. The number of members in both club X and club Y is 40. What is the total number of members that are in club X or club Y, or both?
Question 23
A vaccine was tested on 1000 patients. x% of the patients tested experienced dizziness from the vaccine and y% experienced vomiting. 15% of the patients tested experienced neither dizziness nor vomiting. Of the patients tested, 30% experienced vomiting without dizziness.
Quantity A: x
Quantity B: y
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Question 24
In a certain university, over the course of the junior and senior years, each student leased one of the two laptop brands, Bell or Mell, in the junior year and again leased one of these brands in the senior year. 80% of the students who leased Bell in the junior year leased Bell again in the senior year. Whereas just 50% of the students who leased Mell in the junior year leased Mell again in the senior year. In the junior year, 40% of the students leased Bell. What percent of the students leased Mell in the senior year?
Question 25
In a certain university 90 instructors have an MBA, 75 have a PhD, and 45 have a master’s degree. If 5 instructors have all three qualifications and 5 have none of them, how many instructors have exactly two of these qualifications given that there are 150 total instructors in the university
A) 10
B) 45
C) 50
D) 55
E) 65
Question 26
Of the 37 people, 6 have at least one car and at least one bicycle. 13 have no cars and no bicycles. How many have at least one car or at least one bicycle, but not both.
Question 27
Of the 80 faculty members in a certain university, 49 volunteered to teach underprivileged students during the summers and 19 volunteered both to teach underprivileged students during the summers and to supervise research students during the winters. If the number of faculty members who volunteered to supervise research students during the winters was 50% more than the number of faculty members who neither volunteered to teach underprivileged students during the summers nor volunteered to supervise research students during the winters, how many of the faculty members volunteered to supervise research students during the winters?
Question 28
In a school, students are enrolled in at least one of the following classes: Physics, Sociology, and Music. 34 students are enrolled in the Physics class. 27 students are enrolled in the Sociology class. 49 students are enrolled in either the Physics class or the Sociology class, or both classes. 4 students are enrolled in all three classes.
Quantity A: Students who are enrolled in the Physics and the Sociology but not the Music class
Quantity B: 8
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Question 29
In a group of 160 students, 48 take GRE, 60 take GMAT and 96 take TOEFL. 8 students take GRE and GMAT, 32 take only GMAT and TOEFL, and 24 take GRE and TOEFL. If 6 students take all 3 courses, how many students take none of the courses?
A) 14
B) 20
C) 32
D) 40
E) 48