Question

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?

• A. $28$
• B. $60$
• C. $12$
• D. $21$

Answer 1

Answer: (D)

$21$

Student opted subject A, B and C are $60,84$ and $108$.
By taking HCF of $60$, $84$ and $108$.
HCF$=12$
Which means there should $12$ students in each room.
No. of rooms for subject A$=\frac{60}{12}=5$
No. of rooms for subject B$=\frac{84}{12}=7$
No. of rooms for subject C$=\frac{108}{12}=9$
$\therefore$ Total no. of rooms $=7+5+9=21$.