Catalyzes the phosphorylation of D-xylulose to D-xylulose 5-phosphate (PubMed:17123542). Also catalyzes the phosphorylation of 1-deoxy-D-xylulose to 1-deoxy-D-xylulose 5-phosphate, with lower efficiency (PubMed:11168365). Can also use D-ribulose, xylitol and D-arabitol, but D-xylulose is preferred over the other substrates (PubMed:17123542). Has a weak substrate-independent Mg-ATP-hydrolyzing activity (PubMed:17123542). ATP + D-xylulose = ADP + D-xylulose 5-phosphate + H(+) 1-deoxy-D-xylulose + ATP = 1-deoxy-D-xylulose 5-phosphate + ADP + H(+) Sugar binding is accompanied by a dramatic hinge-bending movement that enhances interactions with Mg-ATP. kcat is 255 sec(-1) with D-xylulose as substrate. kcat is 235 sec(-1) with D-ribulose as substrate. kcat is 237 sec(-1) with xylitol as substrate. kcat is 105 sec(-1) with D-arabitol as substrate. Homodimer. Belongs to the FGGY kinase family.