Question

Which of the following years had the same calendar as that of the year $1998$ ?

• A. $\text{1987 and 2009}$
• B. $\text{1987 and 2004}$
• C. $\text{2004 and 2009}$
• D. $\text{1993 and 2009}$

Answer 1

The correct option is A $\text{1987 and 2009}$

Firstly we will find the year previous to 1998 which has same calendar as that of 1998.
Count the number of odd days backwards starting from the year 1997 to get the sum equal to 0 odd days. The odd days in the different year are calculated as:
1997 - 1 odd day,
1996 (leap year) - 2 odd day,
1995 - 1 odd day,
1994 - 1 odd day,
1993 - 1 odd day
1992 (leap year) - 2 odd day
1991 - 1 odd day
1990 - 1 odd day
1989 - 1 odd day
1988 - 2 odd day
1987 - 1 odd day
Total days = 1 + 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 = 14 days or 2 weeks or 0 odd day.
Hence, the calendar of the year 1987 will be the same as that of 1998.
Now, we will find the year next to 1998 which has same calendar as of 1998.
Count the number of odd days from the year 1998 onwards to the get sum equal to 0 odd day.
1998 - 1 odd
1999 - 1 odd day
2000 (leap year) - 2 odd day,
2001 - 1 odd day,
2002 - 1 odd day,
2003 - 1 odd day,
2004 (leap year) - 2 odd day,
2005 - 1 odd day,
2006 - 1 odd day,
2007 - 1 odd day,
2008 (leap year) - 2 odd day and
Total number of days = 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 = 14 days or 2 weeks or 0 odd day
From 1998 to 2003 the sum of days is also 7 or 0 odd day but the year 2004 is a leap year and 1998 is a non-leap year so, we neglect the year 2004.
Therefore, the year 2009 will have the same calendar as that of 1998.
Hence, option (A) is the correct answer.