A Study Comparing the Pharmacokinetic and Pharmacodynamic Profiles for Sitagliptin, Saxagliptin and Vildagliptin in Participants With Type 2 Diabetes Mellitus (T2DM) (MK-0431-142)

Inclusion Criteria: * female participants of reproductive potential must not be pregnant and agree to use (and/or have their partner use) two acceptable methods of birth control beginning at least 2 weeks prior to administration of the first dose of study drug until at least 2 weeks after the last administration of study drug * has a body mass index between 18 and 43 kg/m\^2 inclusive * has a clinically confirmed diagnosis of T2DM * is not currently receiving any oral antihyperglycemic medications and has a screening visit hemoglobin A1c (HbA1c) between 6.5% and 10% inclusive * must not have been previously treated with a DPP-4 inhibitor or glucagon-like peptide-1 analogs within 12 weeks of prestudy visit * has fasting plasma or serum glucose (FPG) ≤200 mg/dL (11.1 mmol/L) at screening and randomization * is a non-smoker or has not used nicotine or nicotine-containing products for at least approximately the last 6 months * is willing to follow the American Heart Association weight maintaining diet and exercise program or equivalent beginning 2 weeks prior to administration of first dose of study drug and throughout the study until the poststudy visit * agrees to refrain from the consumption of grapefruit and grapefruit juice for at least 2 weeks prior to the start of the study and throughout the study * agrees to refrain from the consumption of all fruit juices periodically throughout the study Exclusion Criteria: * is mentally or legally incapacitated, has significant emotional problems at the time of prestudy visit or expected during the conduct of the study or has a history of a clinically significant psychiatric disorder over the last 5 years * has an estimated creatinine clearance of ≤60 mL/min * has a history of stroke, chronic seizures, or major neurological disorder * has a history of clinically significant endocrine, gastrointestinal, cardiovascular, hematological, hepatic, immunological, renal, respiratory, or genitourinary abnormalities or diseases (with the exception of stable thyroid disease, T2DM and typical associated diseases such as hypertension and hyperlipidemia) * must not have been previously treated with any regimen that includes insulin (injected or inhaled) for at least 3 months * has a history of type 1 diabetes mellitus and/or history of ketoacidosis, or C peptide ≤0.8 ng/mL (≤0.26 nmol/L); or secondary forms of diabetes, acute metabolic diabetic complications or evidence of significant diabetic complications (i.e. retinopathy, neuropathy, nephropathy) * has a history of neoplastic disease (including leukemia, lymphoma, malignant melanoma), or myeloproliferative disease * is on a weight loss program and is not in the maintenance phase, or participant has been treated with a weight loss medication within 8 weeks of screening * anticipates the use of any new medication(s), including prescription and non-prescription drugs or herbal remedies beginning approximately 2 weeks prior to administration of the initial dose of study drug and throughout the study until the poststudy visit * anticipates any change in dose of current stable medications * has donated or lost 1 unit of blood within 4 weeks of the prestudy visit * has had major surgery within 30 days prior to screening or has planned major surgery * has a history of uncontrolled hypertension * is taking a medication which is not permitted in the study to treat a co-morbid condition, including but not limited to cytochrome P450 3A4/5 inhibitors and inducers, P-glycoprotein 1 inhibitors, and human organic anion transporter 3 inhibitors * consumes excessive amounts of alcohol, coffee, tea, cola, or other caffeinated beverage daily * has a history of significant multiple and/or severe allergies, or has had an anaphylactic reaction or significant intolerability to prescription or non-prescription drugs or food * is currently a regular user (including "recreational use") of any illicit drugs or has a history of drug (including alcohol) abuse within approximately the past 6 months * is a nursing mother