Introduction / Context:
This is a calendar based reasoning question. Instead of giving an actual year, the question gives the day of the week for one date and asks for the day of the week for another date in the same year. Such questions test the ability to count the number of days between two dates correctly and then convert that gap into a shift in the weekday using the concept of odd days.
Given Data / Assumptions:
- Dhruv has his birthday on Sunday 28 May in a particular year.
- Sahil has his birthday on 19 October in the same year.
- We must find the day of the week for 19 October of that year.
- The year type, leap or non leap, does not affect the answer because February falls before both dates.
Concept / Approach:The idea is to compute the total number of days between 28 May and 19 October. Once that number is found, we divide it by 7 to determine the remainder, called the number of odd days. Every multiple of seven days completes full weeks and does not affect the day of the week. Only the remainder shifts the weekday forward. We then move that many steps from Sunday to reach the required day.
Step-by-Step Solution:Step 1: Count remaining days in May after 28 May. Since May has 31 days, the remaining days are 31 - 28 = 3 days.Step 2: Add full months between June and September. June has 30 days, July has 31 days, August has 31 days and September has 30 days. So total days in these months equal 30 + 31 + 31 + 30 = 122 days.Step 3: Add days in October up to 19 October, which contribute 19 days.Step 4: Total days between the two birthdays equal 3 + 122 + 19 = 144 days.Step 5: Now compute 144 modulo 7. Since 7 * 20 = 140, the remainder is 4. So there are 4 odd days between the two dates. Starting from Sunday and moving 4 days forward gives Monday (1), Tuesday (2), Wednesday (3) and Thursday (4). Therefore Sahil's birthday falls on Thursday.Verification / Alternative check:We can cross check by noting that any shift by 7 days or 14 days would bring us back to the same weekday. If 140 days correspond to 20 full weeks, they do not change the weekday. The remaining 4 days alone cause the shift, and counting forward from Sunday reinforces that the target day is Thursday. This consistency confirms the calculation.
Why Other Options Are Wrong:Saturday would require a shift of 6 days from Sunday, which does not match the remainder of 4.Wednesday corresponds to a shift of 3 days from Sunday, but we found that there are 4 odd days between the birthdays.Sunday would correspond to zero or seven odd days, which would only be possible if the total gap were a multiple of 7, not 144.Common Pitfalls:Candidates sometimes include the starting date in the count or exclude the last date incorrectly, leading to an error of one day. Others may misremember the number of days in a month such as June or September. Confusing the direction of counting, that is moving backwards instead of forwards, can also lead to a wrong weekday. A neat month wise breakdown avoids these mistakes.
Final Answer:Sahil's birthday on 19 October falls on Thursday.
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