The complete calendar (days and dates) for the year 2005 will be repeated exactly in which of the following later years?

Introduction:
This problem asks in which later year the calendar for 2005 will repeat exactly. An identical calendar means that both the year type (leap or non-leap) and the weekday on which 1 January falls are the same, so every date in the year has the same weekday as in the base year.

Given Data / Assumptions:
Base year: 2005. Year type: 2005 is a non-leap year (not divisible by 4). We seek the next future year with: (a) Non-leap year status. (b) 1 January on the same weekday as in 2005.

Concept / Approach:
In calendar arithmetic, each non-leap year pushes the starting weekday of the following year forward by 1 day, and each leap year pushes it forward by 2 days. To get a repeating calendar, the total shift in weekdays from the base year to the candidate year must be a multiple of 7 days, and the candidate year must have the same leap or non-leap status as the base year.

Step-by-Step Solution:
Step 1: Note that 2005 is non-leap. Number of days in 2005 = 365 ≡ 1 (mod 7), so the next year starts 1 weekday ahead. Step 2: Consider subsequent years and the total weekday shift. From 2005 up to 2011, count how many leap years and non-leap years occur. The years 2006, 2007, 2009, 2010 are non-leap; 2008 is a leap year. Shift contributions: each non-leap year contributes +1 day, the leap year 2008 contributes +2 days. Total shift from 2005 to 2011 = (number of non-leap years) * 1 + (number of leap years) * 2. When calculated, this total shift turns out to be a multiple of 7, meaning the weekday realigns. Additionally, 2011 is a non-leap year, just like 2005. Therefore, 2011 has the same calendar as 2005.

Verification / Alternative check:
You can verify quickly by checking that both 2005 and 2011 have the same starting weekday for 1 January and that neither year is a leap year. A calendar comparison or an online check (in exam practice, usually remembered facts or prior knowledge) confirms that dates and days match throughout the year.

Why Other Options Are Wrong:
2016, 2020: These are leap years, so they cannot match the non-leap pattern of 2005. 2022: Although non-leap, the accumulated weekday shift from 2005 is not a multiple of 7, so the calendars do not align perfectly. None: This suggests no such year exists, which is incorrect because 2011 works.

Common Pitfalls:
Learners sometimes apply the idea that calendars repeat every 11 years mechanically and may pick 2016 or 2022 without checking leap-year status. It is critical to ensure both the day-of-week shift and the leap-year pattern match.

Final Answer:
The calendar for 2005 is repeated in the year 2011.