Intersecting memories with parity clue – Sneha: father’s birthday is after 11 June but before 16 June; younger brother: after 13 June but before 18 June; elder brother remembers it is an even date. What is the definite date?

Introduction / Context:
This problem combines overlapping date ranges with one extra parity clue (“even date”). Intersect ranges first; then apply the even/odd filter to isolate a single date.

Given Data / Assumptions:

• Sneha: 12–15 June (after 11th, before 16th).
• Younger brother: 14–17 June (after 13th, before 18th).
• Elder brother: the date is even.

Concept / Approach:
Step 1: Compute intersection of the two ranges. Step 2: From the intersection, keep only even dates because of the final clue.

Step-by-Step Solution:
Intersection of {12,13,14,15} and {14,15,16,17} = {14,15}.Apply “even” → {14}.

Verification / Alternative check:
Check both original bounds: 14 is after 11 and before 16; also after 13 and before 18; and 14 is even. All conditions satisfied.

Why Other Options Are Wrong:
12 is not in the second range; 16 is not in Sneha’s range; “Data inadequate” is incorrect because the even-date clue resolves the tie.

Common Pitfalls:
Treating “before” as inclusive; mixing up the parity condition.

Final Answer:
Fourteenth