find the range of values of values of r which satisfies the following inequality, where a, b and c are positive \(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1
A
r > \(\frac{abc}{bc + ac + ab}\)
B
r < abc
C
r > \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\)
D
. \(\frac{1}{abc}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1 = \(\frac{bcr + acr + abr}{abc}\) > 1
r(bc + ac + ba > abc) = r > \(\frac{abc}{bc + ac + ab}\)
Source: Myschool Past Questions Archive (Record #31551)