At the beginning of year 1, an investor puts \(p\) dollars into an investment whose value increases at a variable rate

At the beginning of year 1, an investor puts \(p\) dollars into an investment whose value increases at a variable rate of \(x_n\) per year, where \(n\) is an integer ranging from 1 to 3 indicating the year. If \(85<x_n<110\) for all \(n\) between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between

A. \(\$p\) and \(\$2p\)
B. \(\$2p\) and \(\$5p\)
C. \(\$5p\) and \(\$10p\)
D. \(\$10p\) and \(\$25p\)
E. \(\$25p\) and \(\$75p\)

Answer: C

Source: Manhattan GMAT