The function \(f(n)\) is defined as the product of all integers from \(1\) to \(n,\) inclusive, and the function

The function \(f(n)\) is defined as the product of all integers from \(1\) to \(n,\) inclusive, and the function \(g(n)\) is defined as the product of all odd integers from \(1\) to \(n,\) inclusive, where \(n\) is a positive integer. If \(p\) is a prime factor of \(\dfrac{f(150)}{g(150)}+1,\) then which of the following must be true?

A. \(p < 10\)
B. \(10 < p < 25\)
C. \(25 < p < 50\)
D. \(50 < p < 75\)
E. \(p > 75 \)

Answer: E

Source: e-GMAT