Introduction / Context:
This problem checks your ability to move forward and backward in the calendar by counting days and using remainders modulo 7. We are given a reference date with a known weekday and asked to find the weekday for another date in the following year. Such questions commonly appear in aptitude tests and help strengthen mental calendar skills.
Given Data / Assumptions:
- 15 August 2012 is a Wednesday.
- We need the day of the week on 11 June 2013.
- Year 2012 is a leap year.
- We must use the fact that weeks repeat every 7 days.
Concept / Approach:
The basic idea is to count the total number of days between the two dates, reduce that count modulo 7, and then shift the weekday accordingly. Every complete block of 7 days brings us back to the same weekday, so only the remainder after division by 7 matters. Because 2012 is a leap year, February has 29 days, and this affects the counting of days when we cross that year boundary.
Step-by-Step Solution:
Start at 15 August 2012 (Wednesday) and move to 11 June 2013.
Count days remaining in August 2012 from 16 to 31: 16 days.
Full months from September 2012 to May 2013 contribute:
September: 30 days, October: 31 days, November: 30 days, December: 31 days.
January: 31 days, February 2013: 28 days, March: 31 days, April: 30 days, May: 31 days.
Finally, add 11 days for June 1 to June 11 inclusive.
Total days difference = 16 + (30 + 31 + 30 + 31) + (31 + 28 + 31 + 30 + 31) + 11.
This sum is 16 + 122 + 151 + 11 = 300 days.
Compute 300 modulo 7: 300 = 7 * 42 + 6, so the remainder is 6.
A shift of 6 days ahead from Wednesday lands on Tuesday.
Verification / Alternative check:
Move 7 days at a time: after 42 weeks (294 days) it is still Wednesday.
Add the remaining 6 days: Thursday, Friday, Saturday, Sunday, Monday, Tuesday.
Therefore, 11 June 2013 is a Tuesday.
Why Other Options Are Wrong:
Option A (Wednesday): Would require the total gap to be a multiple of 7, which 300 is not.
Option B (Saturday): Corresponds to a remainder of 3 days, not 6.
Option C (Monday): Would arise from a 5 day remainder, which does not match the calculation.
Option D (Tuesday): Correct, matching the 6 day forward shift from Wednesday.
Common Pitfalls:
Forgetting to treat 2012 as a leap year can change the count of days and give the wrong weekday.
Many learners make arithmetic slips when adding the days in each month.
Another common mistake is to misinterpret inclusive and exclusive counting when moving between dates.
Final Answer:
11 June 2013 falls on a Tuesday.
Discussion & Comments