Effects of Glimepiride on Recovery From Hypoglycemia in Participants With Type 2 Diabetes Mellitus (MK-0000-253)

Inclusion Criteria: * Has clinically confirmed diagnosis of type 2 diabetes mellitus (T2DM) controlled by diet and exercise alone, or treated by metformin only with same dose for \>= 12 weeks prior to screening visit. * Females of reproductive potential who demonstrate nongravid state, agree to use (and/or have partner use) two acceptable methods of birth control starting at least two weeks prior to study, throughout study, and at least two weeks after last dose of study drug. * Females of non-reproductive potential, post menopausal, status post hysterectomy, oophorectomy or tubal ligation. * Is in good health, other than T2DM. * Has been a nonsmoker and/or non user of nicotine-containing products for the previous 6 months. If discontinued use for previous 3 months, may be enrolled at investigator's discretion. * Will follow American Heart Association weight maintaining diet and exercise program or equivalent beginning 2 weeks prior to study until poststudy visit. * At screening visit has a Body Mass Index (BMI) =\< 40 kg/m\^2. * At screening visit has a Hemoglobin A1c (HbA1c) of \>= 7% and \< 10% (+/- 0.1%). * On the morning of randomization at predose has fasting plasma glucose (FPG) \>= 126 mg/dL, and =\< 250 mg/dL. Exclusion Criteria: * Has a history of stroke, chronic seizures, or major neurological disorder. * Has a history of any illness that might confound the results of the study or pose additional risk to the participant. * Has a history of type 1 diabetes mellitus, ketoacidosis, C-peptide =\< 0.8 ng/mL, secondary forms of diabetes or diabetic complications. * Has a history of neoplastic disease. * Is a nursing mother. * Has been treated =\< one year of screening visit with sulfonylurea agents, meglitinides, dipeptidyl peptidase-4 (DPP-4) inhibitors, glucagon-like peptide-1 (GLP-1) analogs, or insulin. * Has received treatment within =\< 12 weeks of screening visit with a peroxisome proliferator-activated receptor γ (PPARγ) agonist. * Is taking medications for a co-morbid condition or anticipates taking new medications beginning 2 weeks prior to study. * Consumes excessive amounts of alcohol or caffeinated beverages. * Is a regular user of illicit drugs, or has a history of drug abuse within the previous 6 months. * Has had major surgery, lost 500 mL of blood, or participated in another investigational study within 4 weeks prior to screening visit. * Is on a weight loss program, but not in the maintenance phase, or treated with a weight loss medication within 8 weeks of prestudy visit. * Has a history of severe allergies, anaphylactic reaction or intolerability to drugs, food, insulin, glimepiride or sulfonamide derivatives.