Question

A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100, Physics 70, Chemistry 40; Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 18. How many students have offered Mathematics alone?

• A. 35
• B. 48
• C. 60
• D. 29

Hint:

To find the number of students offering only one subject, use the inclusion-exclusion principle.

Answer 1

The Correct Option is C

Step 1: Use the principle of inclusion-exclusion.
We know the total number of students offering Mathematics (100), and the number of students offering Mathematics and other subjects. Using inclusion-exclusion: \[ \text{Mathematics alone} = \text{Mathematics total} - (\text{Mathematics and Physics}) - (\text{Mathematics and Chemistry}) + (\text{Mathematics, Physics and Chemistry}) \] \[ \text{Mathematics alone} = 100 - 30 - 28 + 18 = 60 \] Final Answer: \[ \boxed{60} \]