LOL, I remember thinking "what the fork" when I first saw this entire passage.

This is exactly the type of reasoning you need to master for the MCAT, so I recommend considering both a conceptual answer and a numbers approach.

Conceptually speaking, because the fluid is not moving, the pressure of the column of solution Z on the left (with a height of a+b) must equal the pressure of water above the same baseline (giving it a height of b.) So picture in your mind Z with height (a+b) equal to water with height b.

The pressure of a column of fluid is based on rho x g x h and we know that g is a constant, so on the Z side there must be a slightly lower density (because it has a slightly higher height) than on the water side (where there is a slightly lower height.) The relative heights are equal to the relative densities, so given that a is a small number compared to b, we can see that (a+b) : b is only slightly greater than 1. The ratio of the densities of water and Z must also be that same small value of (a+b) : b, not b : a (way too big) or (a+b) : a (even bigger.)

I think their math solution is pretty good, but I personally like thinking about it conceptually.