Which of the following years is not a leap year under the standard Gregorian calendar rules?

Introduction / Context:
This question tests your understanding of leap year rules in the Gregorian calendar. Leap years are important in calendar calculations, as they affect the number of days in February and shift the day-of-week pattern.

Given Data / Assumptions:

• We have to identify the year that is not a leap year.
• Candidate years: 2000, 2008, 2009, 2012, 2016.
• We use Gregorian leap year rules.

Concept / Approach:
The rules for a year to be a leap year in the Gregorian calendar are:

• If the year is not a century year (not ending in 00), it is a leap year if it is divisible by 4.
• If the year is a century year (ending in 00), it is a leap year only if it is divisible by 400.

Any year that does not satisfy these conditions is a non-leap (ordinary) year with 365 days.

Step-by-Step Solution:
Step 1: Check 2000. It is a century year and is divisible by 400 (2000 / 400 = 5). Therefore, 2000 is a leap year.Step 2: Check 2008. It is not a century year and 2008 / 4 = 502, so it is divisible by 4. Therefore, 2008 is a leap year.Step 3: Check 2009. It is not a century year, but 2009 / 4 is not an integer. Therefore, 2009 is not divisible by 4 and is not a leap year.Step 4: Check 2012. It is divisible by 4 and not a century year, so it is a leap year.Step 5: Check 2016. It is also divisible by 4 and not a century year, so it is a leap year.

Verification / Alternative check:
We can confirm by noting the typical leap year sequence around these dates: 2000, 2004, 2008, 2012, 2016 are all known leap years. 2009 lies between 2008 and 2012 and does not appear in this 4-year pattern, so it must be a non-leap year with only 365 days.

Why Other Options Are Wrong:
2000 is a leap year because it is divisible by 400. 2008, 2012, and 2016 are all divisible by 4 and are not century years, so they are standard leap years. Only 2009 fails the divisibility test and is therefore the correct non-leap year option.

Common Pitfalls:

• Incorrectly thinking that all century years are not leap years, instead of applying the “divisible by 400” rule.
• Forgetting that non-century years simply need to be divisible by 4.
• Making a calculation error when dividing by 4 or 400.

Final Answer:
The only year in the list that is not a leap year is 2009.