Introduction / Context:
This is a backward calendar question. We are given the weekday on 8 February 2005 and asked to determine the weekday on the same date one year earlier, 8 February 2004. Because 2004 is a leap year, the shift in weekdays over that one year period is not the usual 1 day that comes from a normal year, but 2 days. Understanding this difference is essential in many date and calendar problems.
Given Data / Assumptions:
- 8 February 2005 was a Tuesday.
- We need the day of the week on 8 February 2004.
- 2004 is a leap year (divisible by 4 and not by 100).
- We are using the Gregorian calendar.
Concept / Approach:
A normal year of 365 days contributes 1 odd day, so the same date moves forward by one weekday. A leap year of 366 days contributes 2 odd days, so the same date next year is 2 weekdays ahead. When we go backwards across a normal year, we move 1 day backwards; across a leap year, we move 2 days backwards. Here, we are moving from 8 February 2005 to 8 February 2004, crossing the leap year 2004, so we must shift by 2 days backward.
Step-by-Step Solution:
Given: 8 February 2005 is Tuesday.
The period from 8 February 2004 to 8 February 2005 includes the leap day 29 February 2004.
Total days in that year span = 366 days (leap year length).
366 days = 52 weeks + 2 days, so there are 2 odd days.
This means the weekday moves 2 days forward from 8 February 2004 to reach 8 February 2005.
Going in reverse direction, from 8 February 2005 back to 8 February 2004, we move 2 days backward.
Starting at Tuesday and going 2 days back gives: Monday (1 day back), Sunday (2 days back).
Therefore, 8 February 2004 was a Sunday.
Verification / Alternative check:
You can check using a known calendar or by stepping month by month, but this would be longer.
The key cross check is that the presence of 29 February in 2004 creates exactly 2 odd days.
Hence the weekday must shift by 2 positions between the same dates in the two years.
Why Other Options Are Wrong:
Option A (Tuesday): Would require 0 odd days over a full year, which is impossible.
Option B (Saturday): Is only 3 days backward from Tuesday, not 2.
Option C (Friday): Represents a 4 day backward movement, again incorrect.
Option D (Sunday): Correct, corresponding to a 2 day backward shift from Tuesday.
Common Pitfalls:
Forgetting that 2004 is a leap year and assuming 365 days will give only a 1 day shift.
Some candidates accidentally move forward instead of backward when going to a previous year.
Miscounting the number of days from February to February and losing track of the leap day is also common.
Final Answer:
8 February 2004 was a Sunday.
Discussion & Comments