Consider the reaction:
$${\text{CH}}_3{\text{CH}}_2{\text{CH}}_2\text{Br}+\text{NaCN}\to {\text{CH}}_3{\text{CH}}_2{\text{CH}}_2\text{CN}+\text{NaBr}$$
This reaction will be the fastest in:

The given reaction is a nucleophilic substitution reaction of a primary alkyl halide, which typically follows the ${\text{S}}_{\text{N}}2$ mechanism. ${\text{S}}_{\text{N}}2$ reactions are favored by polar aprotic solvents.Water, ethanol, and methanol are polar protic solvents which solvate the nucleophile through hydrogen bonding, reducing its nucleophilicity.$\text{N,N’-dimethylformamide (DMF)}$ is a polar aprotic solvent. It solvates cations but leaves the nucleophile (${\text{CN}}^{-}$) relatively "naked" and highly reactive, thus increasing the rate of the ${\text{S}}_{\text{N}}2$ reaction.