Five volunteers signed up to work a bake sale. George signed up for the 9:00 a.m.-10:00 a.m. slot, and Juan signed up for the 10:00 a.m.-11:00 a.m. slot. The start of Cora's time slot begins with an even number. Which time slot does Cora work? (1) Cora's time slot is not immediately before George's time slot. (2) Cora's time slot is later in the day than George's time slot.
Cora's time slot can be determined independently from both statements.
Cora's time slot must begin with an even hour and cannot be immediately before George's slot, which runs from 9:00 a.m. to 10:00 a.m. Since the only even-numbered hour after George's is 10:00 a.m., her possible slot can only be the 11:00 a.m.-12:00 p.m. slot, making each statement alone sufficient to conclude Cora's time.
Statement (1) indicates that Cora's time slot is not immediately before George's, but it does not provide information on the even-numbered requirement. Therefore, while it suggests a later time, it cannot assure Cora's time slot, making this statement insufficient on its own.
Statement (2) reveals that Cora's time slot is later than George's, which does imply she works in the 10:00 a.m.-11:00 a.m. or 11:00 a.m.-12:00 p.m. slots. However, it does not confirm the even-numbered requirement for her time slot. Thus, this statement alone is also insufficient.
Combining both statements does help establish Cora's time slot, as neither can independently provide the solution. The first rules out the slot before George, while the second confirms it must be later, making them jointly sufficient but not independently so.
This is correct because both statements independently clarify Cora's time slot. Statement (1) confirms she is not in the 10:00 a.m. slot, while statement (2) confirms she must be in the 11:00 a.m. slot, fulfilling both the even and time slot requirements alone.
Each statement can independently determine Cora's time slot as 11:00 a.m.-12:00 p.m. Statement (1) confirms she cannot be in George's time slot, while statement (2) establishes she works later in the day. Hence, both statements are sufficient on their own.
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