Difficulty: Medium
Correct Answer: Sunday
Explanation:
Introduction / Context:
Here you must determine the weekday of Reyansh's birthday given the weekday of Chirag's birthday, with both dates occurring in the same year. The dates lie in June and December, so several full months are between them. The task is to count the intervening days accurately and then use modulo 7 arithmetic to convert that difference into a shift in weekdays.
Given Data / Assumptions:
Concept / Approach:
We count the total number of days from 1st June to 3rd December. We then reduce this total modulo 7 to find how many days forward we move from Thursday. The resulting shift tells us the weekday of Reyansh's birthday.
Step-by-Step Solution:
Step 1: Days remaining in June after 1st June: 30 - 1 = 29 days (2nd to 30th).
Step 2: Full months from July to November:
July: 31 days, August: 31 days, September: 30 days, October: 31 days, November: 30 days.
Step 3: Sum of days in July to November = 31 + 31 + 30 + 31 + 30 = 153 days.
Step 4: Days in December up to 3rd December = 3 days.
Step 5: Total days between 1st June and 3rd December = 29 (rest of June) + 153 (July to November) + 3 (December) = 185 days.
Step 6: Compute 185 mod 7. Since 7 * 26 = 182, remainder is 185 - 182 = 3.
Step 7: A remainder of 3 means we move 3 days forward from Thursday.
Step 8: Starting from Thursday: Friday (1), Saturday (2), Sunday (3).
Step 9: Therefore, Reyansh's birthday on 3rd December falls on a Sunday.
Verification / Alternative check:
Interpreting 185 days as 26 full weeks (182 days) plus 3 days highlights the weekday logic clearly. Full weeks do not change the weekday, so we only care about the 3 remaining days. Moving three steps from Thursday indeed lands on Sunday. Because all months involved are after February, this result does not depend on whether the year is leap or non-leap.
Why Other Options Are Wrong:
Wednesday would be one day before Thursday, not three days later. Friday corresponds to only one day of shift, Saturday to two days, and Monday to four days. None of these match the computed 3-day forward shift from Thursday, so they cannot be correct.
Common Pitfalls:
Errors often arise from miscounting the days in the starting or ending month, or forgetting that June has 30 days rather than 31. Another issue is failing to use modulo 7, which can cause confusion when dealing with large day counts. A systematic breakdown by month, followed by modulo arithmetic, avoids these problems.
Final Answer:
Reyansh's birthday in that year falls on Sunday.
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