21/09/2021 Answers

1. In a class, 30 students pass in English and 20 students in Math, while some students among these pass in both. How many more students do only English as compared to those doing only Maths?

Answer: 10

Solution: Assume x students pass in both.

Number of students who pass only in English = 30-x, only in Math = 20-x.

Num of students more = 30-x - (20-x) = 10

2. In an examination, 70% of the students passed in English, 65% in Mathematics, 27% failed in both the subjects and 248 passed in both the subjects. Find the total number of students who wrote the exam.

Answer: 400

Solution: Students who passed atleast in 1 subject = 100-27 = 73%

Let the total number of students who wrote the test be x.

0.73x = 0.7x + 0.65x - 248,

x = 248/0.62 = 400

3. A dance instructor conducts an annual workshop in which he holds sessions for basic learners and trainers. In a particular year, 2000 people attended the workshop. 1500 participated as learners and 800 as trainers. How many participated as only trainers?

Answer: 500

Solution: Participation as both trainers and learners = 1500 + 800 - 2000 = 300.

Hence num of participation only as trainers = 800 - 300 = 500

4. In conference was attended by 550 delegates. The number of delegates who drink tea is 400 and the number of delegates who drink tea only is 200. Find how many drink only coffee (if all the 550 had a drink) ?

Answer: 150

Solution: n(Coffee U Tea) = n(Tea) + n(Coffee) - n(Tea n Coffee)

n(Coffee U Tea) = 550

n(Tea) = 400

n(Tea n Coffee) = 400-200 = 200

n(Coffee) = 550 + 200 - 400 = 350

n(Coffee Only) = 350 - n(Tea n Coffee) = 350-200 = 150

5. In a certain company, 20% of the men and 40% of the women attended the annual company picnic. If 35% of all the employees are men, what percent of all the employees went to the picnic?

Answer: 33%

Solution: Let x be the total number of employees.

65% are women.

So 0.2 * 0.35x + 0.4 * 0.65x = 0.33x

Hence 33% attended.

6. Participation in sports is compulsory in a school. A class has 80 students out of which 60 students play football and 40 students play basketball. Find how many students play both football and basketball ?

Answer: 20

Solution: Students who play both = 60 + 40 -80 = 20

7. 70% of the students in a school play football and 80% play cricket. What is the minimum percentage that could play both?

Answer: 50%

Solution: Minimum percentage = 80+70-100 = 50%

8. In a class of 150 students, 55 speak English, 85 speak Telugu and 30 speak neither English or Telugu. How many speak only Telugu.

Answer: 65

Solution: 150-30 = 120 speak English or Telugu or both.

120 = 55+85-(speak both English and Telugu)

People who speak both = 20.

Thus people who speak only Telugu = 85-20 = 65

9. Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home, 65 percent said that they use them in hotels, and 52 percent said that they use them both at home and in hotels. How many of the business people surveyed said that they do not use their laptop computers either at home or in hotels?

Answer: 45

Solution: Percentage of people who use it at home or hotel or both = 78+65-52 = 91%

Hence 9% do not use it at all.

Reqd number of people = 9% of 500 = 45

10. In a class, 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what percent of the students of the class did not enroll for either of the two subjects?

Answer: 5%

Solution: Students who enrolled atleast for one subject = 40+70-15 = 95%.

Hence 5% did not enroll for either of the two subjects.

11. Participation in sports is compulsory in a school. A class has 80 students out of which 60 students play football and 40 students play basketball. Find how many students play only basketball ?

Answer: 20

Solution: Students who play both = 60 + 40 -80 = 20

Students who play basket ball only = 40 - Students who play both = 40-20 = 20

12. An organization has three committees. Only two persons are members of all three committees, but every pair of committees has three members in common. What is the LEAST possible number of the members on any one committee?

Answer: 4

Solution: Let the committees/groups be a,b,c

a n b n c = 2

a n b = b n c = c n a = 3

So total members in committee a = Number of members who are not common with any of the committee + number of members common with committee b and c + number of members common with committee b ALONE + number of members common with committee c ALONE

For the least possible number, Number of members who are not common with any of the committee = 0.

Hence least possible number = 0 + 2 + (3-2) + (3-2) = 4

Note: We have 3-2 because though there are 3 members common for a group, 2 are common across all groups.

13. In a housing society, out of 120 children, 60 play chess, 50 play Cricket and 50 play Carrom, 14 play Chess and Cricket, 16 play cricket and Carrom, 19 play Chess and Carrom. Only 9 children play all the 3 games. If all the children play at least one of the 3 games then how many children play only one game?

Answer: 89

Solution: From the venn diagram, children who play only one game = 36+24+29 = 89

http://cdn.skillrack.com/exhibit/questionv2/1393585794237/v1.png

14. In a class of 150 students, 55 speak English, 85 speak Telugu and 30 speak neither English or Telugu. How many speak both English and Telugu

Answer: 20

Solution: 150-30 = 120 speak English or Telugu or both.

120 = 55+85-(speak both English and Telugu)

Thus reqd number = 140-120 = 20

15. A conference was attended by 550 delegates. The number of delegates who drink tea is 400 and the number of delegates who drink tea only is 200. Find how many drink coffee (if all the 550 had a drink) ?

Answer: 350

Solution: n(Coffee U Tea) = n(Tea) + n(Coffee) - n(Tea n Coffee)

n(Coffee U Tea) = 550

n(Tea) = 400

n(Tea n Coffee) = 400-200 = 200

n(Coffee) = 550 + 200 - 400 = 350

16. In a society, out of 151 children, 64 play chess, 71 play Cricket and 47 play Carrom, 18 play Chess and Cricket, 9 play cricket and Carrom, 10 play Chess and Carrom. Only 6 children play all the 3 games. If all the children play at least one of the 3 games then how many children play only one game?

Answer: 126

Solution: From the venn diagram, children who play only one game = 42+50+34 = 126

http://cdn.skillrack.com/exhibit/questionv2/1393586152861/v2.png

17. In a group of 400 readers who read science fiction or literacy works or both, 250 read science fiction and 230 read literacy works. How many read both science fiction and literacy works?

Answer: 80

Solution: Num of people who read both = 250+230-400 = 80.

18. In a certain office, every employee drinks tea or coffee. 80% of the employees drink only tea and 40% drink only coffee. 80 employees like tea and coffee and hence can drink both. Find the total number of employees in the office.

Answer: 400

Solution: Let total num of employees be N.

N = 0.8N + 0.4N - 80,

N=400

19. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?

Answer: 15%

Solution: Let us assume total num of students

% of students who took either finance or marketing = 60%.

% of students who took both = P(F) + P(M) - P(F U M) =50+25-60 = 15%

20. A group of 50 students were required to clear 2 tasks, one in rock-climbing and the other in bridge crossing during an adventure sports expedition. 30 students cleared both the tasks. 37 cleared bridge crossing, 38 students cleared rock climbing. How many students could not clear any task?

Answer: 5

Solution: Number of students who cleared atleast one task = 37+38-30 = 45

Num of students who did not clear any task = 50-45 = 5