If Tuesday falls on the 4th day of a month, then which day of the week will fall three days after the 24th day of that same month?

Introduction / Context:
Calendar problems like this one test the ability to move forward and backward through days of the week using modular arithmetic. Once the day for one date is known, you can calculate the day for any other date in the same month by counting the number of days between them and using the 7 day cycle of the week.

Given Data / Assumptions:

• The 4th day of the month is a Tuesday.
• We want to know the day that falls three days after the 24th of the same month.
• A week has 7 days and the pattern repeats every 7 days.
• The month is assumed to be normal with no missing days or irregularities.

Concept / Approach:
The central idea is that the day of the week advances by one for each calendar day. To find the day for the 24th, count how many days lie between the 4th and the 24th and then move that many steps forward from Tuesday. Once the day for the 24th is known, move three more days ahead to get the required day. Because the week repeats every 7 days, we use remainders after dividing by 7 to simplify the counting.

Step-by-Step Solution:
Step 1: The 4th is Tuesday. Step 2: The 24th is 20 days after the 4th, because 24 - 4 = 20. Step 3: Compute 20 mod 7 to find how many net steps forward in the weekly cycle this represents. 20 divided by 7 leaves a remainder of 6. Step 4: Move 6 days ahead from Tuesday: Tuesday + 6 days = Monday (because Tuesday + 5 days is Sunday, and one more day is Monday). Step 5: So, the 24th is a Monday. Step 6: We now need the day three days after the 24th, that is three days after Monday. Step 7: Counting forward: Monday (start), Tuesday (1), Wednesday (2), Thursday (3). Therefore, three days after the 24th is Thursday.

Verification / Alternative check:
You can also move forward directly from the 4th to the 27th, since three days after the 24th is the 27th. The difference between the 4th and the 27th is 23 days. Compute 23 mod 7, which is 2. Moving 2 days ahead from Tuesday gives Thursday, which confirms the result from the detailed step calculation.

Why Other Options Are Wrong:
Monday corresponds to the 24th itself, not three days after. Tuesday and Friday do not match the calculated shifts of 20 days and then 3 more days from the known Tuesday on the 4th.

Common Pitfalls:
A common mistake is to forget that the first day is already counted or to miscount the difference between the two dates. Another frequent error is to not use the remainder by 7 and instead try to count all days manually, which can introduce off by one errors. Working with mod 7 arithmetic keeps the computation structured and reliable.

Final Answer:
The day that falls three days after the 24th is Thursday.