Word Problems
(Venn Diagram)
Practice Exercise
Very Easy (Difficulty Level-1):
1. Of 30 integers, 15 are in set A, 22 are in set B, and 8 are in both set A and B. How many of the integers are in NEITHER set A nor set B?
(A) 1
(B) 5
(C) 10
(D) 15
(E) 20
2. A school has a total enrollment of 150 students. There are 63 students taking French, 48 taking chemistry, and 21 taking both. How many students are taking neither French nor chemistry?
(A) 60
(B) 65
(C) 71
(D) 75
(E) 97
3. If in a certain school 20 students are taking math and 10 are taking history and 7 are taking both, how many students are taking either math or history?
(A) 20
(B) 22
(C) 23
(D) 25
(E) 29
4. In a group of 50 students, 31 are taking French, 17 are taking Spanish, and 10 are taking neither French nor Spanish. How many students are taking both French and Spanish?
Easy (Difficulty Level-2):
5. 70% of the guests at Company X’s annual holiday party are employees of Company X.10% of the guests are women who are not employees of Company X. If half the guests at the party are men, what percent of the guests are female employees of Company X?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 40%
6. In a group of 40 people, 15 have visited Iceland and 23 have visited Norway. If 11 people have visited both Iceland and Norway, how many people have visited neither country?
Medium (Difficulty Level-3):
7. A school has a total enrollment of 90 students. There are 30 students taking physics, 25 taking English, and 13 taking both. What percentages of the students are taking either physics or English?
(A) 30%
(B) 36%
(C) 47%
(D) 51%
(E) 58%
8. In a small town, 16 people own Fords and 11 people own Toyota. If exactly 15 people own only one of the two types of cars, how many people own both types of cars.
(A) 2
(B) 6
(C) 7
(D) 12
(E) 14
9. Hijab estimates that 10% of the children in the world have been good this year but do not celebrate Freedom, and that 50% of the children who celebrate Freedom have been good this year. If 40% of the children in the world have been good, what percentage of children in the world are not good and do not celebrate Freedom?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 40%
10. X and Yare sets of integers. X/Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 5 of the integers are in both X and Y, then X/ Y consists of how many integers?
(A) 5
(B) 10
(C) 18
(D) 23
(E) 28
Hard (Difficulty Level-4):
11. In a group of 100 students, 40 take Physics, 60 take Sociology and 80 take Music. 7 students take physics and sociology, 46 take sociology and music, and 36 take physics and music. If 6 students take all 3 courses, how many students take none of the courses?
12. Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 20 boys and 40 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?
(A) 8
(B) 10
(C) 18
(D) 23
(E) 28
13. Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the Sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?
A. 62
B. 78
C. 74
D. 66
E. 72
14. Students are in clubs as follows: Science-20, Drama-30, and Band-12. No student is in all three clubs, but 8 are in both Science and Drama, 6 are in both Science and Band, and 4 are in Drama and Band. How many different students are in at least one of the three clubs?
A. 36
B. 38
C. 42
D. 44
E. 48
15. There are three country clubs in town: Abacus, Bradley, and Claymore. Abacus has 300 members, Bradley 400, and Claymore has 450. 30 people belong to both Abacus and Bradley, 40 to both Abacus and Claymore, and 50 to both Bradley and Claymore. 20 people are members of all three clubs. How many people belong to at least 1 country club in town?
(A) 750
(B) 850
(C) 950
(D) 1050
(E) 1150
16. The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there?
Very Hard & Tricky (Difficulty Level-5):
17. Every marble in a jar has either a dot, a stripe, or both. The ratio of striped marbles to non-striped marbles is 3:1, and the ratio of dotted marbles to nondotted marbles is 2:3. If six marbles have both a dot and a stripe, how many marbles are there all together?
(A) 16
(B) 18
(C) 20
(D) 36
(E) 40
18. At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women plus tenured then what percent of the men are tenured?
19.At a certain company, 30 percent of the male employees and 50 percent of the female employees have an MBA. If 40 percent of the employees are female, what percent of the employees do not have an MBA?
20.In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?
21.A parking lot contains 80 vehicles. Each vehicle is either a car or a truck, and each vehicle is either red or green. 35 vehicles are red, and 60 vehicles are cars. If there are 9 green trucks how many red cars are there?
Answer Sheet:
1. A
2. A
3. C
4. 8
5. E
6. 13
7. C
8. B
9. D
10. C
11. 3
12. A
13. E
14. D
15. D
16. 2
17. E
18. 75
19. 62
20. 45
21. 24