Difficulty: Medium
Correct Answer: Sunday
Explanation:
Introduction / Context:
This is another date to weekday conversion question, this time for 15 August 2010. Such problems check your ability to apply calendar rules or to recall well known dates. Understanding how to move from one year to another, handling leap years properly, and then counting days within the year are typical skills being tested.
Given Data / Assumptions:
- Calendar: Gregorian calendar.
- Date to analyse: 15 August 2010.
- Required: the weekday on this date.
- You may use known reference dates such as 1 January 2010 or earlier years, and then move forward using day counts.
Concept / Approach:
One possible approach is to start from a nearby known date, such as 1 January 2010, and count the days up to 15 August 2010. Alternatively, if you know that 15 August is often used as an example date in calendars, you might have memorised its weekday for certain years, including 2010. In either case, you rely on the structure of the year and the fact that 2010 is not a leap year (February has 28 days).
Step-by-Step Solution:
Step 1: Recognise that 2010 is not a leap year because it is not divisible by 4.Step 2: Suppose you know the weekday for 1 January 2010 (for example, Friday). You can then count the number of days from 1 January to 15 August and reduce modulo 7.Step 3: Count days from January to July: January 31, February 28, March 31, April 30, May 31, June 30, July 31. The sum is 31 + 28 + 31 + 30 + 31 + 30 + 31 = 212.Step 4: Add the first 14 days of August to reach the day before 15 August, adding 14 days, for a total of 212 + 14 = 226 days.Step 5: Compute 226 modulo 7. Since 7 * 32 = 224, the remainder is 2.Step 6: Moving 2 days forward from Friday gives Sunday, confirming that 15 August 2010 was a Sunday.
Verification / Alternative check:
You can cross check by using another method, such as comparing with a known anchor date in a nearby year and working year by year. Both methods should give the same weekday. Many printed calendars and digital tools also show that 15 August 2010 fell on a Sunday, so the calculation is consistent with external references.
Why Other Options Are Wrong:
Saturday, Wednesday, Monday and Friday represent different shifts from the reference day. Small arithmetic mistakes in counting total days or misidentifying leap years can lead to these wrong weekdays. However, when the day count is done correctly, only Sunday is compatible with 15 August 2010.
Common Pitfalls:
Typical mistakes include miscounting the number of days in a month, incorrectly treating 2010 as a leap year, or counting 15 days of August instead of 14 when stepping from the start of the year. Always write out the months and their day counts clearly, sum them carefully, and then reduce the total modulo 7 to find the correct weekday.
Final Answer:
The day of the week on 15 August 2010 was Sunday.
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