Question

Let ` x_1 , x_2 , x_3,....., x_k` be the divisors of positive integer n (including 1 and n). If `x_1 + x_2 + x_3 + ...... + x_k = 75` Then ` sum_(i=1)^k (1/x_i)` is equal to (A) `75/k` (B)`75/n` (C) `1/n` (D)`1/75`

Answer 1

`sum_(i=1)^k(1/x_i)`
`1/x_1+1/x_2+1/x_3+1/x_4+...+1/x_k`
`x_k/n+x_(k-1)/n+...+x_2/n+x_1/n`
`x_k+x_(k-1)+...+x_2+x_1`
`=75/n`
Option B is correct.