There are five people - Sarah, Bill, Eric, Molly, Nick - scheduled for appointments at a doctor's office on a specific morning, plus a walk-in, Katie. There are five appointment slots: 9:30, 10:00, 10:30, 11:00, and 11:30. The following conditions apply. Katie will only get a slot if one of the five people with an appointment does not show up. Sarah is not scheduled for 10:00 or 11:00. Eric is scheduled for 11:30. Molly's appointment is immediately before Nick's. If Bill does not show up for his appointment, which possible appointment slot has opened up for Katie to take?

Explanation: Katie gets an appointment if one person cancels. Bill's appointment is open. Bill's possible slots are 10:00 and 11:00. Looking at the diagrams provided (Diagrams 1, 2, 3), Bill is either at **11:00** (Diagram 1 & 2) or **10:00** (Diagram 3 is impossible: S(9:30), B(10:00), M(10:30), N(11:00), E(11:30), S cannot be at 11:00 and the M-N must be consecutive slots). Re-examining the conditions based on possible slots (S is at 9:30 or 10:30 or 11:30. E is at 11:30. So S is at 9:30 or 10:30. M-N must be (9:30, 10:00), (10:00, 10:30), (10:30, 11:00)). If Bill cancels, the slot is either **10:00 or 11:00**.