Constraining an April birthday with two correct memories: Pratap remembers that his mother's birthday is after 19 April but before 23 April (i.e., 20th–22nd). His sister remembers that the birthday is not on or after 22 April (i.e., at most 21st). What is the definite date?

Introduction / Context:Some overlap problems do not resolve to a single date; instead, they leave a short list. Recognizing when data are insufficient for uniqueness is as important as calculating a specific result. This question highlights that skill.

Given Data / Assumptions:

• Pratap: after 19 and before 23 ⇒ {20, 21, 22}.
• Sister: “not on or after 22” ⇒ { …, 21 } i.e., in the candidate range, ≤ 21.
• All dates in April of the same year.

Concept / Approach:We again form sets and intersect them. Because the sister statement is limiting but not pinpointing, the result may be a two-element set.

Step-by-Step Solution:

Verification / Alternative check:If the sister had said “before 22” (strict) rather than “not on or after 22,” the effect is the same here—22 is excluded. A further clue would be required to choose between 20 and 21.

Why Other Options Are Wrong:

• 22nd: Excluded by sister’s statement.
• Single-point answers (only 20th or only 21st) claim certainty that we do not possess.
• “Cannot be determined”: Too weak—although we cannot pick one date, we can narrow to two.

Common Pitfalls:Treating “not on or after 22” as “before or equal to 22” (it is the opposite), or assuming inclusivity of forbidden endpoints.

Final Answer:20th or 21st