If the third day of a particular month falls on a Tuesday, then which day of the week will be the 25th day of that same month?

Introduction / Context:
This type of calendar problem checks your understanding of how weekdays shift by a fixed pattern through a month. If you know the weekday for one date, you can determine the weekday for another date by counting the difference in days modulo 7, since the weekly cycle repeats every 7 days.

Given Data / Assumptions:

The 3rd day of a month is a Tuesday.
We need to find the weekday on the 25th day of that month.
A week has 7 days and weekday patterns repeat every 7 days.
The month is long enough to include at least 25 days (which is always true for standard calendar months).

Concept / Approach:
The key idea is to calculate the number of days between the 3rd and 25th of the month. Then, compute this difference modulo 7 to see how many weekday steps we move forward from Tuesday. Adding that many steps to Tuesday gives the weekday for the 25th.

Step-by-Step Solution:
Step 1: Compute the difference in dates. From the 3rd to the 25th is 25 - 3 = 22 days. Step 2: Reduce this difference modulo 7. 22 divided by 7 gives 3 complete weeks (21 days) and a remainder of 1 day. So, 22 mod 7 = 1. The weekday advances by 1 day. Step 3: Move 1 weekday forward from Tuesday. After Tuesday comes Wednesday. Therefore, the 25th day will be a Wednesday.

Verification / Alternative check:
You can list a few days to reassure yourself. If the 3rd is Tuesday, then the 10th (7 days later) is also Tuesday, the 17th is Tuesday, and the 24th is Tuesday. Therefore, the 25th, which is one day after the 24th, must be Wednesday. This confirms the modular arithmetic result.

Why Other Options Are Wrong:
Tuesday would be correct only for dates that differ by a multiple of 7 from the 3rd (like 10th, 17th, or 24th), not the 25th.
Monday and Sunday are backward shifts from Tuesday, whereas we move one day forward when going from the 3rd to the 25th, so those cannot be right.

Common Pitfalls:
A frequent mistake is to count both the 3rd and 25th when computing the difference, giving 23 instead of 22 days and hence the wrong weekday. Another slip is to forget to use modulo 7 and instead shift too far ahead. Always compute the date difference correctly and then reduce it by multiples of 7.

Final Answer:
The 25th day of the month will fall on Wednesday.