For the reaction $\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{Br}+\mathrm{CN}{}^{-}\to \mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{CN}+\mathrm{Br}{}^{-}$ at the same temperature and concentrations, the rate is highest in

This is an ${\mathrm{S}}_{\mathrm{N}}2$ reaction of an anionic nucleophile. Polar protic solvents (water, alcohols) hydrogen-bond to $\mathrm{CN}{}^{-}$ and lower its reactivity; polar aprotic DMSO solvates only the cation, leaving a very reactive nucleophile.