This is a study of MK-8242 alone and in combination with cytarabine in adult participants with refractory or recurrent acute myelogenous leukemia (AML). The study will have 2 Arms. Arm A is for participants with refractory or recurrent AML who are considered ineligible for standard chemotherapy. In Part 1 of Arm A, participants will receive MK-8242 monotherapy in escalating doses to determine the recommended phase 2 dose [RP2D]. In Part 2, participants will receive monotherapy with MK-8242 to confirm the RP2D and assess preliminary efficacy. Arm B is for participants with recurrent AML following an initial complete remission (CR) or CR with incomplete marrow recovery (CRi) of 6 to 12 months duration. In Part 1 of Arm B, participants will receive MK-8242 in escalating doses + cytarabine to determine the RP2D in combination with cytarabine. In Part 2, participants will receive MK-8242 + cytarabine to confirm the RP2D and assess preliminary efficacy. The pharmacokinetics of MK-8242 will be studied in both arms. With Amendment 4 (22 August 2013) a 21-day dosing cycle is added, with MK-8242 being given on Days 1-7 of each 21-day cycle in both the monotherapy and combination therapy arms; data from Arm A will be used to determine whether a participant receives 21-day or 28-day therapy in Arm B.