Difficulty: Medium
Correct Answer: Sunday
Explanation:
Introduction / Context:
This problem is another example of a calendar based aptitude question that asks for the day of the week for a specific date, 28 May 2006. Such questions can be solved using a stepwise day counting technique or a formula like Zellers congruence, and they are common in competitive examinations where speed and accuracy matter.
Given Data / Assumptions:
- Calendar system: Gregorian calendar.
- Date of interest: 28 May 2006.
- Required: the day of the week (Sunday, Monday, and so on).
- No additional reference date is supplied in the question, so you must either know a useful nearby anchor date or apply a general method.
Concept / Approach:
A practical approach is to use a nearby date whose weekday is easier to determine or already known, and then count forward or backward. Since 1 January 2006 is known to be a Sunday (this is a widely used reference in many exam problems), we can count the number of days from 1 January 2006 to 28 May 2006, compute the remainder when dividing by 7, and then shift that many days from Sunday to reach the weekday for 28 May 2006.
Step-by-Step Solution:
Step 1: Take 1 January 2006 as Sunday.Step 2: Count days in the months leading up to May: January 31 days, February 28 days, March 31 days, April 30 days.Step 3: Days from 1 January to 30 April = 31 + 28 + 31 + 30 = 120 days.Step 4: From 1 May to 28 May there are 28 more days, so total days from 1 January to 28 May inclusive are 120 + 28 = 148 days, but from 1 January to just before 28 May, you move forward 147 days.Step 5: Compute 147 modulo 7. Since 7 * 21 = 147, the remainder is 0.Step 6: A remainder of 0 means that the weekday on 28 May 2006 is the same as on 1 January 2006, namely Sunday.
Verification / Alternative check:
Another way is to check an intermediate date such as 1 May 2006 and then count up to the 28th. As long as the total number of steps from the known Sunday is a multiple of 7, the weekday will again be Sunday. Both approaches, if calculated carefully, point to Sunday as the correct day.
Why Other Options Are Wrong:
Thursday, Friday, Saturday and Monday are all different weekday positions relative to Sunday. They correspond to remainders of 4, 5, 6 or 1 when dividing the total number of days by 7. Since our computation gave a remainder of 0, none of these alternatives can be correct for 28 May 2006.
Common Pitfalls:
Errors often occur when counting days in each month, especially if February in a leap year is involved. In this case, 2006 is not a leap year, so February has 28 days, but some students mistakenly use 29. Others forget whether to count the starting day or the ending day when converting between inclusive and exclusive counts. Carefully setting up the sum and then reducing modulo 7 avoids these issues.
Final Answer:
The day of the week on 28 May 2006 was Sunday.
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