Interval reasoning – Two siblings recall their father’s birthday within overlapping date ranges in December. Sangeeta remembers it was certainly after 8th but before 13th (i.e., 9th–12th). Natasha remembers it was definitely after 9th but before 14th (i.e., 10th–13th). On which date in December did their father’s birthday fall?

Introduction / Context:
Many reasoning problems ask you to intersect two people’s partial memories to find a unique date. If the overlap still leaves multiple possibilities, the information is insufficient.

Given Data / Assumptions:

• Sangeeta: after 8th and before 13th → {9, 10, 11, 12}.
• Natasha: after 9th and before 14th → {10, 11, 12, 13}.
• We assume “after” and “before” are strict.

Concept / Approach:
Compute the intersection of both sets. Only if the intersection has exactly one date can we answer uniquely; otherwise, the data are insufficient.

Step-by-Step Solution:
Intersection = {9,10,11,12} ∩ {10,11,12,13} = {10, 11, 12}.There are three feasible dates; no rule picks just one.

Verification / Alternative check:
If any added constraint (e.g., “even date only”) existed, the set might reduce; here, none exists.

Why Other Options Are Wrong:
10th/11th/12th are each possible but not uniquely determined. “None of these” is invalid because there are feasible dates; the issue is non-uniqueness.

Common Pitfalls:
Misreading “after/before” as inclusive; that would alter the bounds.

Final Answer:
Data inadequate