Question

Number of students who have opted for subjects A, B and C are 60, 84 and 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions?

• A. 28
• B. 60
• C. 12
• D. 21

Hint:

To minimize the number of rooms, find the greatest common divisor (GCD) of the number of students in each subject to determine the largest group size that can fit evenly in each room.

Answer 1

The Correct Option is D

We need to find the minimum number of rooms such that each room has the same number of students and students from each subject are placed in separate rooms. This implies the number of students in each room must divide evenly into the total number of students for each subject. The total number of students for each subject is: - A: 60 students, - B: 84 students, - C: 108 students. The greatest common divisor (GCD) of 60, 84, and 108 gives us the maximum number of students that can be assigned to each room: \[ \text{GCD}(60, 84, 108) = 12. \] Therefore, the number of rooms required for each subject is: - For A: \( \frac{60}{12} = 5 \), - For B: \( \frac{84}{12} = 7 \), - For C: \( \frac{108}{12} = 9 \). Thus, the total number of rooms required is: \[ 5 + 7 + 9 = 21. \]