Introduction / Context:
This question tests the basic concept of leap years in the Gregorian calendar. Knowing how to identify leap years is useful in many aptitude topics such as calendar problems, interest calculations over long periods, and date based reasoning. Many students remember only a partial rule and therefore pick a wrong option when a non multiple of 4 or a century year appears in the choices.
Given Data / Assumptions:
- We are given four years: 1996, 1863, 1984 and 2004.
- We are asked to identify which one is not a leap year.
- The rule for a leap year follows the standard Gregorian calendar convention used in modern examinations.
- No trick is hidden in the wording; only one option is non leap.
Concept / Approach:In the Gregorian calendar a year is a leap year if:
- It is divisible by 4, and
- If it is a century year (ending with 00), then it must also be divisible by 400.
Therefore, for normal non century years, checking divisibility by 4 is enough. For century years such as 1700, 1800, 1900 and 2000, we must additionally test divisibility by 400. A common mistake is to apply only the first part of the rule and forget about the special case for century years, which leads to wrong answers in exams.
Step-by-Step Solution:Step 1: Check 1996. Since 1996 / 4 gives an integer and the year is not a century year, 1996 is a leap year.Step 2: Check 1984. The number 1984 is also divisible by 4 and is not a century year, so 1984 is a leap year.Step 3: Check 2004. The year 2004 is divisible by 4 and again is not a century year, so 2004 is also a leap year.Step 4: Check 1863. When we divide 1863 by 4, we do not get an integer value. Therefore 1863 is not divisible by 4 and hence is not a leap year.Verification / Alternative check:Another quick way is to remember that leap years around 1980 and 2000 occur at regular 4 year intervals such as 1980, 1984, 1988, 1992, 1996, 2000, 2004 and so on. All of these are clearly divisible by 4. A year like 1863 does not fit into such a sequence because it is 3 more than 1860 and 1 less than 1864, both of which are divisible by 4. This confirms that 1863 is not a leap year.
Why Other Options Are Wrong:1996 is divisible by 4 and is not a century year, so it satisfies the leap year rule.1984 is also divisible by 4 and is therefore a leap year.2004 is divisible by 4 and is not a century year, so it is again a leap year.Common Pitfalls:Candidates sometimes confuse century rules and believe that only century years need to be divisible by 400 to be leap years. In reality, ordinary non century years need only be divisible by 4. Another common error is to assume that any odd looking older year such as 1863 is special, without performing the simple divisibility test by 4.
Final Answer:The year that is not a leap year is 1863.
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