January birthday via overlapping strict ranges: Mohan remembers his father's birthday is before 20 January but after 16 January (i.e., 17–19). His sister remembers it is after 18 January but before 23 January (i.e., 19–22). What is the definite date?

Introduction / Context:Standard overlapping-window problem that reduces to a single date by intersection of two ranges.

Given Data / Assumptions:

• Mohan: 17–19 (after 16, before 20).
• Sister: 19–22 (after 18, before 23).

Concept / Approach:Intersect the two sets.

Step-by-Step Solution:

Verification / Alternative check:Any misread that included 20 in Mohan’s set would still intersect at {19,20}; the sister’s “after 18” excludes 18 and forces the lower bound high enough that only 19 survives.

Why Other Options Are Wrong:

• 17th/18th: Excluded by the sister’s window.
• 20th: Excluded by Mohan’s “before 20.”
• Data inadequate: Intersection is a single date, so data are adequate.

Common Pitfalls:Accidentally reading “before” as inclusive or mixing months.

Final Answer:19th