Question from Sets Theory

Question

A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25

Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology and

Chemistry while 8 study both Physics and Biology. 3 study all three subjects. How

many studies?

a. Only Physics

b. Only Chemistry

c. Only Biology

d. None of the 3 Subjects

e. all the three subjects

f. only one of the three subjects

g. only two of the three subjects

Answer 1

The best way to tackle this problem is by drawing three intersecting circles. But given this media, I will try to solve it another way. Let's break it apart piece by piece:

A school has 63 students studying Physics, Chemistry and Biology. Total Students = 63

33 study Physics, P = 33 - 10 - 8 - 3 = 12

25 study Chemistry C = 25 - 10 - 9 - 3 = 3

26 study Biology Biology. B = 26 - 9 - 8 - 3 = 6

10 study Physics and Chemistry,

9 study Biology and Chemistry

8 study Physics and Biology.

3 study all three subjects

12 only study Physics

3 only study Chemistry

6 only study Biology

Now we can answer the questions:

a. Only Physics - 12

b. Only Chemistry - 3

c. Only Biology - 6

d. None of the 3 Subjects: All together there are 51 students studying the three subjects. Therefore, 12 are not studying these subjects.

e. all the three subjects - 3

f. only one of the three subjects - 21

g. only two of the three subjects - 27