Karan knows that his sister birthday is not after 18 August, while his mother remembers that the birthday is before 20 August but after 17 August. On which exact date in August is Karan sister birthday?

Introduction / Context:
This is a simple logical reasoning and calendar style question that asks you to combine two partial pieces of information about a birthday date in August. By interpreting the phrases like not after, before, and after, you must determine the unique date that satisfies both Karan memory and his mother memory at the same time.

Given Data / Assumptions:
- Karan says that his sister birthday is not after 18 August. - Mother says that the birthday is before 20 August but after 17 August. - We assume all dates refer to the same year and the month is August. - All dates are integer calendar dates such as 17, 18, 19, and so on.

Concept / Approach:
Each statement describes a range of possible dates. The correct birthday must be in both ranges simultaneously. This is essentially an intersection of intervals on the number line, where each number represents a possible date in August. Carefully translating the verbal constraints into inequalities or clear lists of candidate dates makes the intersection easy to find.

Step-by-Step Solution:
Step 1: Interpret not after 18 August. This means that the birthday is on or before 18 August. So Karan possible dates are 1 August up to 18 August inclusive. Step 2: Interpret before 20 August but after 17 August. After 17 August excludes 17 itself and means 18 or later dates, but before 20 August excludes 20 and any later date. So mother possible dates are 18 August and 19 August only. Step 3: Find common dates between Karan and mother sets. Step 4: Karan dates include 18 while mother dates include 18 and 19. Step 5: The intersection is therefore just one date: 18 August. Step 6: Hence the only possible birthday date that satisfies both memories is 18 August.

Verification / Alternative check:
You can also treat these statements as inequalities. Karan says date less than or equal to 18. Mother says date greater than 17 and less than 20. Combining, we get 17 less than date less than or equal to 18 and also date less than 20. The only integer value that satisfies these inequalities is 18. This algebraic style confirms the same result in a compact way.

Why Other Options Are Wrong:
- 17 fails mother condition because the birthday must be after 17 August. - 19 fails Karan condition since he insists the birthday is not after 18 August. - 20 is not before 20 August and is therefore excluded by mother statement. - 16 does not satisfy the after 17 August condition at all.

Common Pitfalls:
A common mistake is to misread not after 18 as after 18 or to treat after 17 as including 17. Precise understanding of inclusive and exclusive language is crucial. Not after means less than or equal to, while after means strictly greater than. Similarly, before 20 means strictly less than 20. Misinterpreting these will lead to incorrect dates such as 17 or 19 instead of the correct 18.

Final Answer:
Karan sister birthday must be on 18 August.