You don't need to know why for the MCAT, but if you're curious...
The equation K = [A]/[C][D] actually has each species (A, B, C, and D) as a ratio of the concentration of that species divided by its respective standard state. That may sound complicated, but it explains why the terms are unitless and why the equilibrium constant itself is unitless. For aqueous species, the standard state is 1 M, and for gases, 1 bar. Solid and liquids are already in their standard state, so they are always going to be 1/1 = 1 (a term called unity). Since they always reduce to 1 (or unity), solids and liquids can and should be omitted from the equation entirely.
So, for example, using the equation above, let's say A and B are both liquids, C is an aqueous solute (somehow) and D is a gas. The equation reduces to K = 1/ ([C]/1M x Pd/1 bar), where Pd is the pressure of D in bars. It actually gets a little more complicated than this and involves activity coefficients for each term (as well as stoichiometric coefficients as exponents), but I think I've probably been confusing enough as it is.