Question

Median of the odd divisors of $720$ is

• A. the mean of $3^{rd}$ and $4^{th}$ item
• B. the mean of $4^{th}$ and $5^{th}$ item
• C. the mean of $5^{th}$ and $6^{ th}$ item
• D. None of these

Answer 1

Answer: (A)

$720 =2^{4}\times 3^{2} \times 5^{1} =2^{a}\,3^{b}\,5^{c}$
Number of odd divisors $=(b+1) (c+1)$ $=(2+1) (1+1)=6$
These six divisors are the factors of $45$, which are $1, 3, 5, 9, 15 , 45$
$\therefore $ Median is the mean of $3^{rd}$ and $4^{th}$ items