Karan remembers that the birthday of his sister is not after 18 August. The mother of Karan remembers that the sister's birthday is before 20 August but after 17 August. On which date in August is the birthday of the sister?

Introduction / Context:
This is a logical reasoning problem based on dates within a month. Instead of asking you to find a weekday, it asks you to deduce the exact date by combining partial information from two people. Such questions test your ability to interpret phrases like not after, before, and after carefully and to find the intersection of two sets of possible dates.

Given Data / Assumptions:

• Karan remembers that the birthday is not after 18 August. This means it is on or before 18 August.
• The mother remembers that the birthday is before 20 August but after 17 August.
• Dates in August are considered as ordinary calendar dates.
• We must find a single date that satisfies both pieces of information.

Concept / Approach:
The approach is to translate each statement into a range of possible dates and then find the overlap. Karan gives one range based on not after 18 August. The mother gives another range using before 20 August and after 17 August. The intersection of these ranges gives the only possible date that fits both descriptions.

Step-by-Step Solution:
Step 1: Interpret Karan. Not after 18 August means the birthday is on or before 18 August. So the possible dates from his memory are 1 to 18 August. Step 2: Interpret the mother. Before 20 August but after 17 August means the birthday is either 18 August or 19 August. Step 3: Represent Karan's information as the set {1, 2, 3, ..., 18}. Step 4: Represent the mother's information as the set {18, 19}. Step 5: The intersection of these two sets is the common date that appears in both, which is only 18 August. Step 6: Therefore the birthday of the sister must be on 18 August.

Verification / Alternative check:
Check each candidate date allowed by the mother. If the birthday were 18 August, it satisfies Karan because it is not after 18. If it were 19 August, that would conflict with Karan, because 19 is after 18. Since 18 is the only date that satisfies both conditions simultaneously, the answer is unique and well defined.

Why Other Options Are Wrong:
17: This contradicts the mother's statement that the date is after 17 August.

19: This satisfies the mother but violates Karan's statement, because 19 is after 18.

20: This violates the mother's condition that the date is before 20 August.

Common Pitfalls:
A common error is to misread not after 18 as after 18 or not before 18. Another mistake is to interpret before 20 and after 17 as including 17 and 20, but both words before and after in this context mean strict inequalities. Always pay close attention to whether boundaries are inclusive or exclusive when interpreting these verbal clues.

Final Answer:
Thus, the birthday of the sister must fall on 18 August, so the correct option is 18.