Data sufficiency – school timetable sequencing Four subjects (Physics, Chemistry, Mathematics, Biology) are taught in four consecutive one-hour periods starting at 8:00 a.m. At what time is the Chemistry period scheduled? Statements: (I) The Mathematics period ended at 10:00 a.m. and was preceded by Biology. (II) Physics was scheduled in the last period. (III) The Mathematics period was immediately followed by Chemistry.

Introduction / Context:We must place four subjects into the 8–9, 9–10, 10–11, and 11–12 slots and determine Chemistry’s time. This is a classic sequence/ordering data-sufficiency problem.

Given Data / Assumptions:

• Slots: 8–9, 9–10, 10–11, 11–12.
• Subjects: Physics (P), Chemistry (C), Mathematics (M), Biology (B).
• Statement I: M ends at 10:00 a.m. and is preceded by B → B at 8–9, M at 9–10.
• Statement II: Physics is last → P at 11–12.
• Statement III: M is immediately followed by C.

Concept / Approach:Check which combinations of statements uniquely fix Chemistry’s slot. The aim is sufficiency, not full timetable reconstruction.

Step-by-Step Solution:

Verification / Alternative check:Both (I+II) and (I+III) yield C at 10–11. No contradiction occurs; hence the answer requires I and either II or III.

Why Other Options Are Wrong:

• Only I / Only II / Only II and III: Do not uniquely fix Chemistry’s time.
• Either I only or II only: Incorrect; neither alone suffices.

Common Pitfalls:Confusing 'immediately followed' with 'somewhere after' and overlooking that sufficiency is about uniqueness of Chemistry’s slot, not the entire schedule.

Final Answer:Only I and either II or III