Question

Let $x_1,x_2,...,x_k$ be the divisors of positive integer $n$ (including $1$ and $n$). If $x_1+x_2+....+x_k=75$, then $\sum _{i=1}\frac{1}{x_i}$ is equal to

• A. $\frac{75}{n^2}$
• B. $\frac{75}{n}$
• C. $\frac{75}{k}$
• D. none of these

Answer 1

Answer: (B)

$\frac{75}{n}$

$\sum _{i=1}^k\frac{1}{x_i}=\frac{1}{x_1}+\frac{1}{x_2}+....+\frac{1}{x_k}=\frac{\sum x_1}{n}=\frac{75}{n}$
(as L.C.M. of $x_1,x_2,...,x_n$ is n)