Answer: C. On the HR diagram, P is cool and luminous, so it is a red giant; Q is hot and faint, so it is a white dwarf. Using $d\text{ (pc)}=1/p\text{ (arc-second)}$

$$\frac{d_{\text{red giant}}}{d_{\text{white dwarf}}} =\frac{1/p_P}{1/p_Q} =\frac{p_Q}{p_P}.$$

A: Uses the parallax ratio directly, as though distance were proportional to parallax.
B: Reverses the required ratio and adds an unnecessary square.
D: Squares the correct inverse-parallax ratio.

Remember: distance and parallax are inversely proportional.