This is a study comparing the incidence of hypoglycemia while using sitagliptin treatment versus sulfonylurea (SU) treatment in participants with type 2 diabetes mellitus (T2DM) who regularly take an SU drug, and choose to fast during the month of Ramadan. The primary hypothesis is that during the 30 days of Ramadan fasting, treatment with sitagliptin (with or without metformin) compared to SU treatment (with or without metformin) results in a lower incidence of hypoglycemia in participants with T2DM.