Statement: The school authority will open a Summer School this year on the campus for students aged 7–14 years. Assumptions: I. All students will attend the Summer School. II. All parents will prefer to remain in the city rather than travel, so their children can attend. III. Families who cannot afford travel or out-of-station programmes will send their children to the Summer School.

Introduction / Context:
A school announces a Summer School on campus for ages 7–14. We must determine which assumptions are necessary for this decision to be sensible.

Given Data / Assumptions:

• The offering targets a subset of students (7–14 years).
• No compulsion that everyone must attend.
• Parents’ travel plans vary.

Concept / Approach:
An institution launching such a programme typically assumes there is a viable segment that will enrol, not that every single student will or that all parents will stay in the city.

Step-by-Step Solution:
I: “All students will attend” is unnecessary and unrealistic; not implicit.II: “All parents will prefer to remain in the city” is again too strong; not implicit.III: It is reasonable to assume that a significant subset—especially those who cannot afford out-of-station options—will opt for the in-city Summer School. This supports the viability of the programme and is implicit.

Verification / Alternative check:
Even if many families travel, a programme can succeed if a meaningful local subset exists.

Why Other Options Are Wrong:

• Only II / II and III / All: each requires the very strong and unnecessary claim in II.
• None is implicit: wrong, because III underpins demand.

Common Pitfalls:
Watch for universal quantifiers (“all”, “every”) that are rarely necessary as assumptions.

Final Answer:
Only III is implicit.