## Set Theory and Venn Diagrams Questions and Answers Part-3

Data for Questions 1 to 5 : In the Quiz held last year, participants were free to choose their respective areas from which they were asked questions. Out of 880 participants, 224 chose Mythology, 240 chose Science and 336 chose Sports, 64 chose both Sports and Science, 80 chose Mythology and Sports, 40 chose Mythology and Science and 24 chose all the three areas.

1. The percentage of participants who did not choose any area is
a) 23.59%
b) 30.25%
c) 37.46%
d) 27.27%

Explanation:

240/880 = 27.27%.
Option (d) is correct

2. Of those participating, the percentage who choose only one area is
a) 60%
b) more than 60%
c) less than 60%
d) more than 75%

Explanation: 504/880 = 57.27%.
Hence, less than 60.
Option (c) is correct.

3. Number of participants who chose at least two areas is
a) 112
b) 24
c) 136
d) None of these

Explanation: 40 + 16 + 56 + 24 = 136.
Option (c) is correct.

4. Which of the following areas shows a ratio of 1:8?
a) Mythology & Science but not Sports: Mythology only
b) Mythology & Sports but not Science: Science only
c) Science: Sports
d) None of these

Explanation: Option 'a' gives us 16:128 = 1:8.
Option (a) is hence correct.

5. The ratio of students choosing Sports & Science but not Mythology to Science but not Mythology & Sports is
a) 2:5
b) 1:4
c) 1:5
d) 1:2

Explanation: 40:160 = 1:4
Option (b) is correct.

Data for Questions 6 to 10 : The table here gives the distribution of students according to professional courses.

6. What is the percentage of Math students over English students?
a) 50.4
b) 61.4
c) 49.4
d) None of these

Explanation:

Math Students = 130. English Students = 370
130/370 = 35.13%
Option (d) is correct.

7. The average number of females in all the courses is (count people doing full-time MBA and CA as a separate course)
a) less than 12
b) greater than 12
c) 12
d) None of these

Explanation: Number of Female Students = 10 + 8 + 10 + 2 + 10 + 6 + 3 + 1 = 50.
Average number of females per course = 50/4 = 12.5.
Option (b) is correct

8.The ratio of the number of girls to the number of boys is
a) 5:36
b) 1:9
c) 1:7.2
d) None of these

Explanation: 50:450 = 1:9
Option (b) is correct

9. The percentage increase in students of full-time MBA only over CA only is
a) less than 20
b) less than 25
c) less than 30
d) more than 30