Introduction / Context:
This problem asks for a future year that has exactly the same calendar as the leap year 1988. When dealing with leap years, the rules for repeating calendars are slightly more restricted. The target year must also be a leap year and the total number of odd days between the two years must be a multiple of 7 so that dates align on the same weekdays.
Given Data / Assumptions:
- Base year: 1988, which is a leap year.
- Options: 2012, 2014, 2016, 2010.
- We must find a leap year among the options that matches 1988 in full calendar layout.
- Gregorian leap year rules apply.
Concept / Approach:
Two leap years can share the same calendar provided that the total number of odd days in the years between them is divisible by 7. A leap year contributes 2 odd days; a non leap year contributes 1 odd day. We check the candidate years that are leap years, compute the cumulative odd days from 1988 up to that year, and identify which year gives a total that is a multiple of 7. Alternatively, we can rely on known calendar matches confirmed by standard references.
Step-by-Step Solution:
Check leap status of the options: 2012 and 2016 are leap years; 2010 and 2014 are non leap years.
So only 2012 and 2016 are possible candidates.
Count leap and non leap years between 1988 and 2016.
Leap years in this interval include 1992, 1996, 2000, 2004, 2008, 2012, 2016.
Non leap years fill the remaining years, and the total odd days can be checked using standard methods.
Calendar references show that 1988 and 2016 share the same starting weekday and leap status, making their calendars identical.
Verification / Alternative check:
Direct comparison of 1 January 1988 and 1 January 2016 shows that both fall on the same weekday.
Because both years are leap years, February has 29 days in both cases, leaving the remainder of the year aligned.
Monthly calendars for March through December also match date by weekday.
Why Other Options Are Wrong:
Option A (2012): Though it is a leap year, the weekday pattern does not perfectly match 1988 for every month.
Option B (2014) and Option D (2010): Both are non leap years, so they cannot match a leap year's calendar.
Option C (2016): Correct, since it is a leap year and its full calendar pattern matches that of 1988.
Common Pitfalls:
Some students forget that leap and non leap years cannot have identical calendars.
Others rely only on the difference in years (for example 28 years) without verifying the exact distribution of leap and normal years.
Not checking whether February has 28 or 29 days in both years can easily lead to wrong conclusions.
Final Answer:
The calendar for 1988 is the same as the calendar for 2016.
Discussion & Comments