The main characteristic of the cognitive reflection test (CRT) is that it requires people to overcome a cognitive conflict. Solving this conflict requires (1) inhibitory control of prepotent but incorrect responses and (2) mental set-shifting in order to reframe the problem and reach a meaningful solution. Based on the well-known involvement of the dorsolateral prefrontal cortex (DLPFC) in inhibitory control we hypothesised that transcranial direct current stimulation (tDCS) of the DLPFC would modulate its contribution to problem-solving performance. Thirty-nine participants undergoing anodal, cathodal, or sham tDCS were asked to solve the CRT and similar mathematical problems that were structured to induce an automatic, impulsive but incorrect response. To provide a multi-dimensional picture of the processes underlying responding we assessed impulsivity traits using self-report measures and recorded physiological indices using biofeedback equipment. The results indicated that participants were more likely to provide incorrect impulsive responses after cathodal stimulation, i.e. when inhibitory control associated to the DLPFC was reduced. Baseline values of blood volume pulses predicted solution recognition, highlighting the potential role of individual physiological differences in problem solving. In conclusion, this study provides evidence supporting the role of the DLPFC in modulation of processes involved in solving CRTs and similar problems, thanks to its association to the inhibitory control mechanisms involved in suppressing impulsive responses.