2005 AMC 10B Problem 16

The quadratic equation x^2 + mx + n = 0 has roots that are twice those of x^2 + px + m = 0, and none of m, n, and p is zero. What is the value of n/p?

\mathrm{(A)} 1 \qquad \mathrm{(B)} 2 \qquad \mathrm{(C)} 4 \qquad \mathrm{(D)} 8 \qquad \mathrm{(E)} 16

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.