Concentrated alkali (like $\mathrm{NaOH}$ ) is used for the concentration of bauxite ore because it dissolves bauxite forming soluble sodium metal aluminate while impurities remain insoluble and precipitate as red mud.
${\mathrm{Al}}_2{\mathrm{O}}_3\cdot 2{\mathrm{H}}_2\mathrm{O}+2\mathrm{NaOH}\to 2{\mathrm{NaAlO}}_2$ $+3{\mathrm{H}}_2\mathrm{O}$