Question

The mein value of the median and mean of the odd divisors of $360$ is

• A. $13$
• B. $7$
• C. $6$
• D. $10$

Answer 1

Answer: (D)

$360=2^3{3}^2{5}^1=2^a{3}^b{5}^c$
Number of odd divisors of $360=(b+1)(c+1)$
$=3\times 2=6$
Sum of all odd divisors $=\frac{\text{Sum of odd divisors}}{\text{Number of odd divisors}}$
$=\frac{78}{6}=13$
Again, odd divisors of $360$ are the factors of $3^2\times 5^1=45$
i.e., odd divisors are $1$, $3$, $5$, $9$, $15$, $45$
Now median value of the divisor is
$\frac{\text{Value of 3rd divisor + Value of 4th divisor}}{2}$
$=\frac{5+9}{2}=7$
$\therefore$ Median $=7$
$\therefore$ Mean of median and mean of odd divisors of $360$
$=\frac{13+7}{2}=10$