From: Acetone, Dimethsulfoxide, Dimethylformamide, water, HMPA, Ethanol, Acetic acid, DMA.
The number of polar aprotic solvent in the following solvents is
Clearly, water, ethanol and acetic acid are all both polar and protic - meaning they have a hydrogen atom attached to a highly electronegative atom (like oxygen, nitrogen etc.). A sufficiently basic entity can abstract the proton attached to the electronegative atom. For example, elemental sodium can deprotonate alcohols and give alkoxides.
We need to look for compounds that are polar but do not have a hydrogen attached to a highly electronegative atom.