Question

In a class of 30 students, 18 offer mathematics (M), 15 offer science (S) and 13 offer english (€). The number of students who offer all the three subjects is equal to the number of students who do not offer any of these subject. 10 students offer both mathematics and english, 8 offer both mathematics and science and 3 offers only english and science. Determine: (i) the number of students who offer all the three subjects (ii) the number of students who offer only one subject (iii) the number of learners who offer at least two subject

Answer 1

18 (M)
15 (S)
13 (E)

10 (M,E)
8 (M,S)
3 (E,S)

I made a venn diagram with 3 circles for this lol.

Math
10 (M,E) + 8 (M,S) = 18
18 (M) - 18 = 0

Science
8 (M,S) + 3 (E,S) = 11
15 (S) - 11 = 4

Eng
10 (M, E) + 3 (E,S) = 13
13 (E) - 13 = 0

10 (M,E) + 8 (M,S) + 3 (E,S) + 0 (M) + 4 (S) + 0 (E) = 25

30 - 25 = 5

I. 5

II. 4 (only 4 were left for Sci; 0 for Math and Eng)

III. 21 (add all the students who offer 2 subjects; given)

Answer 2

I don't understand on the first answer

Answer 3

A class at a college has 30 students and of these, 18 study business mathematics and 20 students
study Micro-economics. Find the percentage of students who study business mathematics only