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Four subjects (Physics, Chemistry, Mathematics, Biology) are taught in four consecutive one-hour periods, starting at 8:00 a.m. When was the Chemistry period scheduled? Statements: (I) The Mathematics period concluded at 10:00 a.m. and was preceded by Biology. (II) Physics was scheduled for the final period. (III) The Chemistry period immediately followed the Mathematics period.
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Solution: Step 1: Define the four consecutive one-hour periods starting at 8:00 a.m.:
Period 1: 8:00 a.m. - 9:00 a.m.
Period 2: 9:00 a.m. - 10:00 a.m.
Period 3: 10:00 a.m. - 11:00 a.m.
Period 4: 11:00 a.m. - 12:00 p.m.
Step 2: Analyze Statement I: "Mathematics period ended at 10:00 a.m., which was preceded by Biology."
This means the Mathematics period was from 9:00 a.m. to 10:00 a.m. (Period 2).
The Biology period immediately preceded Mathematics, so Biology was from 8:00 a.m. to 9:00 a.m. (Period 1).
So far: Biology (8-9), Mathematics (9-10).
Step 3: Combine Statement I and II:
From Statement I: Biology (8-9), Mathematics (9-10).
From Statement II: "Physics was scheduled in the last period." So, Physics is from 11:00 a.m. to 12:00 p.m. (Period 4).
The only remaining slot is Period 3 (10:00 a.m. - 11:00 a.m.), which must be for Chemistry. So, Statements I and II are sufficient.
Step 4: Combine Statement I and III:
From Statement I: Mathematics period ended at 10:00 a.m. (9:00 a.m. - 10:00 a.m.).
From Statement III: "Mathematics period was immediately followed by Chemistry." This means Chemistry started at 10:00 a.m. and ended at 11:00 a.m. So, Statements I and III are sufficient.
Step 5: Conclusion: The Chemistry period can be scheduled by combining Statement I with either Statement II or Statement III.