Number of students who have opted for the 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? (CAT 1998)

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Solution

The correct option is D 21
Ans: (d)

Number of students which should be seated in each room is the HCF of 60, 84 and 108 which is 12.

Number of rooms required for subject A, subject B and subject $C = \frac{60}{12} = 5$ rooms, $\frac{84}{12} = 7$ rooms and $\frac{108}{12} = 9$ rooms respectively. Hence minimum number of rooms required to satisfy our condition $= (5 + 7 + 9) = 21.$

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