Recent dual process models proposed that the strength of competing intuitions determines reasoning performance. A key challenge at this point is to search for boundary conditions; identify cases in which the strength of different intuitions will be weaker/stronger. Therefore, we ran two studies with the two-response paradigm in which people are asked to give two answers to a given reasoning problem. We adopted base-rate problems in which base rate and stereotypic information can cue conflicting intuitions. By manipulating the information presentation order, we aimed to manipulate their saliency; and by that, indirectly the activation strength of the intuitions. Contrary to our expectation, we observed that the order manipulation had opposite effects in the initial and final response stages. We explain these results by taking into account that the strength of intuitions is not constant but changes over time; they have a peak, a growth, and a decay rate.