If the third day of a month is a Tuesday, which of the following will be the fourth day before the 27th day of that same month?

Introduction / Context:
This question is another calendar based reasoning problem. A specific day of the week is given for the third day of the month, and we are asked to find the day of the week that is four days before the 27th of the same month. It tests understanding of how days of the week repeat every seven days and how to move forward or backward through the calendar using modular arithmetic.

Given Data / Assumptions:

• The 3rd day of the month is a Tuesday.
• We must determine the day four days before the 27th day of the month.
• The month is continuous without interruptions and follows the standard 7 day weekly cycle.

Concept / Approach:
First determine the day of the week for the 27th. To do that, calculate how many days separate the 3rd and the 27th, and then find the remainder when this difference is divided by 7. That remainder tells us how many net steps forward to move from Tuesday. Once the day for the 27th is known, move four days backward to find the required day, again using the 7 day cycle.

Step-by-Step Solution:
Step 1: The 3rd is Tuesday. Step 2: The 27th is 27 - 3 = 24 days after the 3rd. Step 3: Compute 24 mod 7. Since 21 is a multiple of 7, the remainder is 3. Step 4: Move 3 days forward from Tuesday: Tuesday (start), Wednesday (1), Thursday (2), Friday (3). Thus, the 27th is a Friday. Step 5: We need the day four days before the 27th. Count backward four days from Friday. Step 6: One day before Friday is Thursday, two days before is Wednesday, three days before is Tuesday, and four days before is Monday. Step 7: Therefore, the fourth day before the 27th is Monday.

Verification / Alternative check:
Instead of first finding the day of the 27th, we can go directly from the 3rd to the 23rd, which is four days before the 27th. The difference between the 3rd and the 23rd is 20 days. Now 20 mod 7 is 6, and moving 6 days forward from Tuesday lands on Monday. This shorter route gives the same answer and confirms that the day four days before the 27th is Monday.

Why Other Options Are Wrong:
Tuesday, Wednesday and Sunday do not match the correct backward counting from Friday. They correspond to other offsets that do not equal four days before the 27th.

Common Pitfalls:
Students often miscount the number of days between dates or forget to use remainders modulo 7, which can lead to going too far forward or backward. Another mistake is confusing counting of days inclusively versus exclusively. Carefully calculating the difference in dates and then using mod 7 arithmetic helps keep the process accurate.

Final Answer:
The fourth day before the 27th of the month is Monday.