External tasks evoke characteristic fMRI BOLD signal deactivations in the default mode network (DMN). However, for the corresponding metabolic glucose demands both decreases and increases have been reported. To resolve this discrepancy, functional PET/MRI data from 50 healthy subjects performing Tetris were combined with previously published data sets of working memory, visual and motor stimulation. We show that the glucose metabolism of the posteromedial DMN is dependent on the metabolic demands of the correspondingly engaged task-positive networks. Specifically, the dorsal attention and frontoparietal network shape the glucose metabolism of the posteromedial DMN in opposing directions. While tasks that mainly require an external focus of attention lead to a consistent downregulation of both metabolism and the BOLD signal in the posteromedial DMN, cognitive control during working memory requires a metabolically expensive BOLD suppression. This indicates that two types of BOLD deactivations with different oxygen-to-glucose index may occur in this region. We further speculate that consistent downregulation of the two signals is mediated by decreased glutamate signaling, while divergence may be subject to active GABAergic inhibition. The results demonstrate that the DMN relates to cognitive processing in a flexible manner and does not always act as a cohesive task-negative network in isolation.