One characteristic of a person having a critical thinking disposition is engaging in the activity with reflective skepticism. Skeptical attitudes can encourage a person to reflect so as to produce a correct conclusion and make the right decision. This article aims to determine: (1) the cause of students skeptic in dealing with illlogical mathematics problem and (2) the phase involved in skeptic and decision making on ill-logical mathematics problem. This research is a qualitative research with explorative descriptive research type. The subject of this study consisted of two students who were skeptical of ill-logical mathematics problem. The data were collected through a test, direct observation, and interview. The results of data collection were analyzed through data reduction stage, data presentation and conclusion of findings. The results of this study indicate that: (1) there are two causes of skepticism: (a) the presence of cognitive conflict and (b) the presence of two conflicting outcomes; (2) the phases involved in skepticism and decision making on the Ill-logical Mathematics problem from stimulus, skeptic, reflective, and decision making.