Question

In a survey of 100 students, it was found that 45 students studied economics, 30 took up public administration, and 52 sociology. 6 students took up all the subjects, 17 studied economics and public administration, 15 took economics and sociology, and 8 public administration and sociology.

a) How many students studied only economics?
b) How many students studied only sociology?
c) How many students studied only public administration?
d) How many students did not study any of the three subjects?

Answer 1

a. The number of students who studied only economics is 22.

b. The number of students who studied only sociology is 35.

c. The number of students who studied only public administration is 8.

d. The number of students who did not study any of the three subjects is 15.

Step-by-step explanation:

a. To find the number of students who studied only economics, we subtract the students who studied economics and other subjects. The total students who studied economics are 45. Subtracting the students who studied both economics and public administration (17) and those who studied both economics and sociology (15) gives us the number of students who studied only economics: 45 - 17 - 15 = 22.

b. Similarly, to find the number of students who studied only sociology, we subtract the students who studied sociology and other subjects. The total students who studied sociology are 52. Subtracting the students who studied both economics and sociology (15) and those who studied both public administration and sociology (8) gives us the number of students who studied only sociology: 52 - 15 - 8 = 35.

c. To find the number of students who studied only public administration, we subtract the students who studied public administration and other subjects. The total students who studied public administration are 30. Subtracting the students who studied both economics and public administration (17) and those who studied both public administration and sociology (8) gives us the number of students who studied only public administration: 30 - 17 - 8 = 5.

d. To find the number of students who did not study any of the three subjects, we subtract the students who studied at least one subject from the total number of students. The total number of students is 100. Subtracting the students who studied at least one subject (100 - (45 + 30 + 52 - 6 - 17 - 15 - 8)) gives us the number of students who did not study any of the three subjects: 15.