Consider the reaction

$\text{C}{\text{H}}_3\text{C}{\text{H}}_2\text{C}{\text{H}}_2\text{B}\text{r}+\text{N}\text{a}\text{C}\text{N}\to \text{C}{\text{H}}_3\text{C}{\text{H}}_2\text{C}{\text{H}}_2\text{C}\text{N}+\text{N}\text{a}\text{B}\text{r}$

This reaction will be the fastest in

The reaction proceeds via ${\mathrm{SN}}_2$ mechanism. It is a unimolecular nucleophilic substitution reaction. The reaction is hence favoured in the presence of a polar aprotic solvent. DMF is a polar aprotic solvent. So, the reaction is the fastest with DMF solvent.